Writing Your Thesis
The thesis should be the heart of your graduate school career. It will certainly be the most involved and difficult thing you do while in grad school.
Of course, before writing the thesis, one needs to have research to report. To make things easier on yourself, it’s a good idea to record your results as you work. Don’t rely on your memory to save you when you need to write everything down in your thesis! While you needn’t have everything written in final draft, having a detailed account of your research progress is a great idea. When you start your research, you and your advisor should try to establish a goal for your thesis as soon as possible. Performing research without a goal can be very difficult and even more frustrating.
When one does mathematical research, one rarely knows exactly where they are going. Gaining mathematical intuition comes from lots of hard work, not simply being very smart. A tried and true method for doing research is to do lots of examples, and make simplifying assumptions when needed. Before you can prove a theorem, you need a conjecture; these aren’t going to just fall in your lap! The idea is that after seeing enough examples, one can make a general conjecture and then hopefully prove it.
It’s a good idea to find out who else in the community (both in and out of the department) thinks about your field. You may find it useful to contact these people from time to time. This serves multiple purposes: you’ll lessen the chance of duplicating someone else’s research; you’ll find multiple sources of advice. While your advisor will likely be the single biggest source of help in writing your thesis, they needn’t be your only source. Talking to many people about your work will give you several different perspectives on the same thing. Seeing the same thing in different ways can be invaluable in understanding something.
When you have enough results such that you and your advisor are satisfied, you need to organize your work into one coherent document. This can be a highly nontrivial task! Make sure that your problem is stated clearly, along with why it is important, and how you solved it. Your thesis shouldn’t simply be a list of definitions, theorems, and proofs; there should be quite a bit of prose to explain the mathematical ambiance of your work. What is the motivation for even thinking about this problem? The more people that find your research interesting, the better.
Please refer to this manual for guidelines on formatting your thesis: http://grad.ucsd.edu/_files/academics/BlueBook%20201718%20updated%204.13.18.pdf
Defending Your Thesis
Setting a time to defend your dissertation can be frustrating. Contact your committee members well in advance in order to check availability and schedule a date/time.
You would think that finding a time for 6 people to meet would be an easy task. However, it can be exceedingly difficult. You may need to be very flexible and accommodating in order to make things work. You may also need to be persistent about asking if you have a nonresponsive committee member.
Please carefully review these guidelines regarding committee attendance:
Department Policy on Graduate Examination Format:
Effective Fall 2022, the default format of a graduate examination in the Mathematics Department is in person , i.e., all the committee members and the student are physically present in the same room for a scheduled examination . (This is set by the Division of GEPA.) However, when an unexpected situation arises and affects a committee member’s ability to participate in the examination synchronously, and when the student agrees, a remote or hybrid examination is allowed and can be decided by the committee chair or cochairs. The following guidelines should be followed to arrange a remote or hybrid, synchronous examination:
 In forming the committee, the student needs to provide different examination options, in person, remote, or hybrid, to potential faculty committee members, and based on the conversation, the student can decide whether or not they want the faculty member on their committee. If such conversation did not take place, and if an unexpected situation arises, the faculty committee member can request remote examination, and can be released from the committee duty should the student refuse the request.
 In general, the graduate student is not allowed to opt for a remote examination unless there are extenuating circumstances, such as illness, travel difficulties related to visa problems, or a graduation deadline. Under such circumstances, the committee chair can decide to reschedule an inperson examination, or have a remote or hybrid examination.
 According to the Division of GEPA, there must be sufficient expertise among present members to examine the student. If a committee member must be absent for the scheduled exam, it is permissible for one absent committee member to examine the candidate on a separate date. The committee chair, or one cochair, must participate synchronously in the scheduled exam.
Make sure to inform the PhD staff advisor in advance if any of your committee members will not be physically present.
During this scheduling phase, you also want to schedule your “Preliminary Appointment” with Graduate Division: https://gradforms.ucsd.edu/calendar/index.php – this appointment is optional but highly recommended! The purpose of this appointment is for them to check the margins and the formatting of your dissertation. While the above information should get you through this part without any problem, sometimes there are minor issues that arise and must be confronted (for example, published work that shows up in your dissertation has some extra requirements associated to it). The meeting should last about 30 minutes and you’ll receive a couple questionnaires to complete before your final appointment. You will also be required to schedule a Final Appointment with Graduate Division – allow at least a few days between your defense and your final appointment in order to finalize department paperwork.
In addition, the following information is critical to you completing your thesis, defending it, and completing your PhD:
 The university requires that your committee members each have a good readable draft of your dissertation at least FOUR WEEKS before your final defense.
 It is your responsibility to make arrangements with each committee member for the date and time of your defense. Room reservations should be made at the Front Desk (in person or email to [email protected])
 The Final Report form must have the original signatures of all members of the doctoral committee; the Final Report must also be signed by the program chair. (The Final Report form is initiated by the graduate coordinator and signatures are obtained from each faculty member through DocuSign.). Proxy signatures are not accepted.
 After your examination, committee chair emails PhD staff advisor confirming the passing of the defense. PhD staff advisor prepares Final Report through DocuSign.
 The final version of the thesis must conform to procedures outlined in the " Preparation and Submission Manual for Doctoral Dissertations and Master's Theses "
 The student submits the final approved dissertation to the Graduate Division at the final document review (the Final Report form is routed electronically from the program’s graduate coordinator via DocuSign). Final approval and acceptance of the dissertation by the Dean of the Graduate Division (on behalf of the University Archivist and Graduate Council) represents the final step in the completion of all requirements for the doctoral degree.
A few other suggestions:
About a week before you defend, you should send an email to your committee to remind them that your defense is coming, and you might even want to send a daybefore or dayof reminder.
You should discuss the details of your defense with your advisor, but it’s basically a 50minute talk where you highlight the main results of your dissertation. The audience is usually your committee plus a few graduate students.
Once Graduate Division has signed off on your thesis, it is time to submit your thesis online to Proquest/UMI. When you do this, they give you an option to purchase bound copies of your thesis from them. This is not particularly appealing for three reasons:
 They are rather pricey, about $40$60 per copy
 They will print it exactly as you submitted it, according to Graduate Division standards: doublespaced, 8.5×11, etc, which doesn’t make for an attractive book. (How many of the math books on your shelf are 8.5×11 doublespaced?)
Fortunately, another option is available: selfpublishing services. Originally these were intended for authors who had written a book, but couldn’t find a publisher for it, so they’d have it printed at their own expense. Nowadays, there are online sites filling this market, where you submit your manuscript and design the book yourself through their site. They can print on demand, so there is no minimum number of copies to order, and they can be quite inexpensive. A former graduate student, Nate Eldredge, chose to go with Lulu, so this article will describe that service.
You can begin by creating an account on Lulu’s site, which is pretty selfexplanatory. They have several different book types available. I decided to go with a 6×9 “casewrap hardcover”, which is a pretty standard size and style for a book. If you have a yellow Springer book on your shelf, that’s a pretty good facsimile of what we’re talking about here.
The main issue, then, is reformatting the thesis into a 6×9 format. Fortunately, LaTeX makes this pretty easy. Pretty much, you just need to swich from the UCSD thesis class to the standard LaTeX book class and make a few other changes. Here is a modified version of the UCSD thesis template, modified to fit this format. Nate put comments in various places indicating the relevant changes and choices he made. In several places he took advantage of the fact that he no longer had to conform to OGS’s awkward requirements to make the thesis more “booklike” and remove some things that wouldn’t appear in a book. It shouldn’t take you more than an hour or two to convert your thesis file, depending how fastidious you are. (If you don’t want to go to this trouble, Lulu will also print 8.5×11 books. You could use your existing PDF without change. It may not look as pretty, but it will still be cheaper than UMI.)
Note that you should check carefully for overfull \hbox’es when you compile the thesis, because changing the paper size may have caused things to run outside the margins or off the page. You may have to manually break up long equations or reword paragraphs. Also, the book class will insert several apparently blank pages; these relate to the fact that the book will be printed doublesided, and guarantee that certain things always appear on the left or righthand side of a spread. If you want a booklike effect, you should not try to defeat this.
Once you’ve generated an appropriate 6×9 PDF file and uploaded it to Lulu, you can design a cover for it. They have a couple of different interfaces. For his thesis, Nate created a pretty simple cover with a UCSDish blue color scheme, and the abstract and a graduation photo on the back cover.
When you are all finished, Lulu creates a page where you or anyone else can buy copies of the book. (You have the option of keeping this private, so that only people you share it with can find it.) Then you can buy as many copies as you want to keep or give away, and you can also send the link to your parents if they want to buy lots of copies for all the relatives. (In this case, Lulu’s “revenue” option may be useful, where you select an amount to add to the price of the book, which Lulu passes along to you after each sale. The page remains up indefinitely if you want more copies later.
If you want to see what a finished product looks like, Nate Eldredge’s thesis Lulu page is located at http://www.lulu.com/content/7559872.
The book turned out quite nice looking, with quality and appearance comparable to commercially published math books. And they were only $15.46 per copy (plus tax and shipping). Overall that is a vast improvement over UMI.
Also, Nate uploaded the template as a Lulu project. It can be found at http://www.lulu.com/content/7686303.
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Senior Thesis Guidelines
A senior thesis can form a valuable part of a student's experience in the Mathematics Major . It is intended to allow students to cover significant areas of mathematics not covered in course work, or not covered there in sufficient depth. The work should be independent and creative. It can involve the solution of a serious mathematics problem, or it can be an expository work, or variants of these. Both the process of doing independent research and mathematics exposition, as well as the finished written product and optional oral presentation, can have a lasting positive impact on a student's educational and professional future.
Supervision
Supervision by a qualified member of the field of mathematics at Cornell is the normal requirement for a senior thesis. Other arrangements are possible, however, provided they are made with the assistance of the student's major advisor, and with the approval of the Mathematics Major Committee.
Finding a supervisor/Encouraging students.
It should be emphasized that both the writing and the supervising of a senior thesis are optional activities, both for students and faculty. Students interested in doing this will need to find a suitable supervisor — perhaps with the aid of their major advisor or another faculty member whom they know. Advisors and other faculty who encounter students whom they think would benefit from this activity are invited to mention this option to them and assist them in finding a supervisor.
Standard venues for senior theses .
One obvious way in which a senior thesis can be produced is through an independent research course (MATH 4900); another way is through an REU experience, either at Cornell or elsewhere. (If the REU work was accomplished or initiated elsewhere, a "local expert" will still be needed to supervise or "vouch for" the work as a senior thesis.) In yet a third way, a student may present a faculty member with a solution or partial solution to an interesting problem. In such cases, this could form the core of a senior thesis. Faculty are invited to encourage such work from their students.
Public Lecture
A public lecture in which the results of the senior thesis are presented is welcome but optional. This should be arranged by the thesis supervisor in conjunction with the undergraduate coordinator and adequately advertised. Department faculty and graduate students are encouraged to attend these presentations.
Submission Deadlines
The supervisor must approve the student's thesis. The student will submit a completed first draft of the thesis to the thesis supervisor. If the supervisor asks the student to make changes, the student will have two weeks to do so and submit a PDF copy of the thesis in final form. The thesis will be posted on the department's web site.
For students graduating in December 2023 , the deadline for the first draft is Friday, November 17 and the final submission is due to the thesis supervisor and the undergraduate coordinator on Friday, December 1.
For students graduating in May 2024 , the deadline for the first draft is Friday, April 19 and the final submission is due to the thesis supervisor and the undergraduate coordinator on Friday, May 3.
Format of the Thesis
Ideally, the final document should be TeXed or prepared in some equivalent technical document preparation system. The document must have large left margins (one and onehalf inches or slightly larger). The title page should contain:
The student's name and graduating class.
The title of the senior thesis.
The name of the faculty supervisor. (If there is more than one supervisor, list both. If one of the supervisors is not in the Mathematics Department, list the department and institution.)
The date of completion of the thesis.
This information will be used to produce a standard frontispiece page, which will be added to the document in its library copies.
Judgment as to the merit of a senior thesis will be based largely on the recommendation of the faculty member supervising the thesis. The Mathematics Major Committee will use this recommendation both in its determination of honors and in its decision on whether to place the thesis in our permanent library collection.
The senior thesis will automatically be considered by the Mathematics Major Committee as one of the ingredients for deciding on an honors designation for the student. Students may receive honors without a thesis and are not guaranteed honors with one. However, an excellent senior thesis combined with an otherwise excellent record can elevate the level of honors awarded.
Library Collection
Meritorious senior theses will be catalogued, bound, and stored in the Mathematics Library.
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Department of Mathematics
Senior theses.
An undergraduate thesis is a singlyauthored mathematics document, usually between 10 and 80 pages, on some topic in mathematics. The thesis is typically a mixture of exposition of known mathematics and an account of your own research.
To write an undergraduate thesis, you need to find a faculty advisor who will sponsor your project. The advisor will almost surely be a faculty member of the pure math department, though on occasion we have accepted theses written by people with applied math advisors. In these rare cases, the theses have been essentially pure math theses.




2010  Alex Kruckman  The AxKochen Theorem: An Application of Model Theory to Algebra  Dan Abramovich/Michael Rosen 
2010  Thomas Lawler  On the Local Structure of Triangulation Graphs  Richard Schwartz 
2011  Andrew Furnas  Mathematical Modeling of Woven Fabric  Govind Menon 
2011  Eric Sporkin  Modifying the BLS Signature Scheme Using Isogenies  Reinier Broker 
2011  Tyler K. Woodruff  Discrepancy Upper Bounds for Certain Families of Rotated Squares  Jill Pipher 
2012  Nadejda Drenska  Representation of Periodic Data with Fourier Methods and Wavelets  Jill Pipher 
2012  Zev Chonoles  Hermite's Theorem for Function Fields  Michael Rosen 
2013  Kevin Casto 
 Richard Schwartz/Govind Menon 
2013  InJee Jeong 
 Richward Schwartz 
2013  Benjamin LeVeque 
 Jeffrey Hoffstein 
2013  Lucas MasonBrown 
 Michael Rosen 
2013  Yilong Yang 
 Richard Schwartz 
2014  Nicholas Lourie 
 Richard Schwartz 
2014  Michael Thaler  Extending Conway's Tiling Groups to a Triangular Lattice with Three Deformations  Richard Schwartz 
2015  Justin Semonsen  Factorization of Birational Maps  Dan Abramovich 
2015  Kamron Vachiraprasith  On the Average Order of Arithmetic Functions Over Monic SquareFree Polynomials in Finite Fields  Michael Rosen 
2015  Francis White 
 Sergei Treil 
2015  Zijian Yao  Arakelov Theory on Arithmetic Surfaces  Stephen Lichtenbaum 
2016  Claire Frechette 
 Melody Chan 
2018  Collin Cademartori 
 Govind Menon 
2018  Michael Mueller 
 Thomas Goodwillie 
2018  Lewis Silletto 
 Richard Schwartz 
2020  Jongyung Lee 
 Dan Abramovich 
2020  Owen Lynch 
 Yuri Sulyma 
2021  Alexander Bauman 
 Bena Tshishiku 
2021  Matei P. Coiculescu 
 Richard Schwartz 
2021  Henry Talbott 
 Richard Schwartz 
2021  Nathan Zelesko 
 Melody Chan 
2022  Griffin Edwards 
 Yuri Sulyma 
2022  Dichuan David Gao 
 Justin Holmer 
2022  Jasper Liu 
 Jeffrey Hoffstein 
2024  Alex Feiner 
 Joseph Silveman 
2024  Tyler Lane 
 Brendan Hassett 
2024  Smita Rajan 
 Brendan Hassett 
Explore Brown University
Universität Bonn
Preparation of the Final Thesis
The mathematics degree programs conclude with a Bachelor's or Master's thesis, in which independent work on a mathematical topic is to be demonstrated. The Examination Board has compiled the most important requirements for theses and some assessment criteria as guidelines.
 Please read the document carefully before you register your thesis.
 When registering the thesis, you confirm with your signature that you have taken note of the requirements in the document.
The teacher training programs also end with a final thesis. This can be completed in the subject mathematics.
Rules for Theses in the SubjectSpecific Study Programs
Here you will find the regulations for registering and submitting final theses that apply to both mathematics programs. Specific deadlines and rules are listed under the respective degree program.
As a rule, students find a supervisor for their thesis on their own initiative.
 Every professor of mathematics in Bonn can of course assign topics for theses.
 Many other doctoral lecturers at Bonn Mathematics have been appointed by the Examination Board to supervise theses. You can enquire about this with the person concerned.
 One of the two reviewers must always be a professor of mathematics at Bonn University.
 If you have not found a supervisor yourself, you can also have one assigned to you by the Examination Board . In this case, please contact the BachelorMaster Office Mathematics.
The thesis must be registered using the form Registration of the Thesis .The form must be signed by both you and the supervisor of the thesis.
 The form must state the topic of the thesis and your first supervisor.
 You also confirm that you have taken note of the requirements for the final theses of your degree program.
 At the same time, you will be registered for the seminar accompanying your thesis.
 The registration form must be submitted to the BachelorMaster Office Mathematics immediately after the topic has been assigned and within four weeks of the supervisor's signature.
 If the registration form is received in February or August, the thesis can still be assessed in the semester in which it is submitted.
 For the accompanying thesis seminar you earn 6 credit points. It is registered for the semester in which your thesis is due for submission.
 During the time you are working on your thesis, there are usually three presentations in the thesis seminar on the topic of the thesis and the results achieved.
 The examination of the thesis seminar consists of a graded (final) presentation, which should be held shortly before or shortly after the submission of the thesis.
 The day on which you give the graded presentation is an examination date and is therefore relevant for your degree.
 Therefore, please make sure that the presentation takes place before the end of the semester in which you wish to graduate.
 The deadline for submitting your thesis is calculated from the signature date of your supervisor plus the working time.
 You can see the submission date of your thesis in BASIS.
 The deadline for submitting your thesis is strict. If you submit the thesis after this date, it will be failed.
 Please note that you are responsible for meeting the submission deadline. Your supervisors are not necessarily aware of your submission deadline, and in no case could they change the deadline for you, as this is set by the examination regulations.
 In the event of illness , the deadline can be extended by up to six weeks.
The thesis must be submitted on time in the required number of copies together with the form Submission of the Thesis at the BachelorMaster Office Mathematics . On the submission form, you confirm that you have written the paper independently and have not used any sources or aids other than those specified and that you have indicated any quotations.
Requirements:
 DIN A4, printed on both sides, with cover page
 in a bound version (no spiral bindings please!)
 If programming code or similar is available, it must be attached to each copy of the work on a CD or a USB stick that is as flat as possible (do not send it by email). The CD or stick must be glued to the last page of a copy.
 A single copy of the submission form must be submitted separately.
Options for submitting the thesis:
 personal delivery during office hours
 personal delivery after making an appointment outside office hours
 by post to the BachelorMaster Office Mathematics The date of the postmark is decisive for the submission.
The thesis is evaluated by two assessors.
 The first assessor is the person who provided the topic of the thesis.
 The second assessor must be proposed by you when you submit your thesis. You are therefore responsible for finding a suitable second reviewer. On request, the supervisor can of course help you with this.
 Both reviewers must be noted on the title page of the thesis (see templates for the title page).
As a rule, the candidate is notified of the thesis' evaluation six to eight weeks after the submission date.
Bachelor's Thesis (B.Sc. Mathematik)
 The topic of the Bachelor's thesis is usually assigned towards the end of the fifth semester.
 You need to have earned at leat 90 credit points in order to register the Bachelor's thesis.
The working period of a Bachelor's thesis is five months.
 The Bachelor's thesis is estimated to require a workload of 360 hours.
 Therefore it earns 12 credit points.
The text part of the Bachelor's thesis must be between 5 and 50 pages long.
 Deviations from this require the approval of the Examination Board.
 In this case, please obtain the consent of both your advisors.
 Then send an application by email to the BachelorMaster Office Mathematics .
The language of the Bachelor's degree program is German. You can write your Bachelor's thesis in English if
 your supervisor agrees with it and
 the thesis contains a summary in German.
There is a coursework for the Bachelor's thesis seminar, the training in subjectspecific literature research . It will be noted in BASIS when you register your Bachelor's thesis and it is a prerequisite for passing the Bachelor's thesis seminar.
The training courses are offered by the University and State Library in the form of a oneoff twohour course. The course imparts knowledge that is very useful for academic work, especially when writing a Bachelor's thesis, for example the use of the relevant academic online archives.
 The courses are held in the MNL departmental library in the training room on the 1st floor.
 Usually three dates are offered every semester, each on a Monday or Wednesday from 16.15 to 18.00 hrs.
 You can register for a date via an online form.
After you have taken part in a course, we will enter the coursework as passed in BASIS.
 You must complete this training shortly before or during the time you are working on your Bachelor's thesis.
The title page of your Bachelor's thesis must be agreed with your supervisor.
 In particular, make sure that you name the correct institute to which your supervisor belongs.
 Please use our LaTeXtemplate for the title page of your Bachelor's thesis.
The submission deadline for the Bachelor's thesis is 5 months after the date on which the supervisor signed the application.
 Three copies of the Bachelor's thesis must be submitted.
Master's Thesis (M.Sc. Mathematics)
 The topic of the Master's thesis is usually assigned towards the end of the second semester.
 You need to have earned at leat 30 credit points in order to register the Master's thesis.
The working period of a Master's thesis is twelve months.
 The Master's thesis is estimated to require a workload of 900 hours.
 Therefore it earns 30 credit points.
The text part of the Master's thesis must be between 10 and 100 pages long.
The language of the Master's degree program is English. You can write your Master's thesis in German if
 the thesis contains a summary in English.
The title page of your Master's thesis must be agreed with your supervisor.
 Please use our LaTeXtemplate for the title page of your Master's thesis.
The submission deadline for the Master's thesis is 12 months after the date on which the supervisor signed the application.
 Four copies of the Master's thesis must be submitted. One copy will be made available to the Mathematics Library.
If you would like to apply for a PhD position at BIGS Mathematics you should find out about the application process at the beginning of the third Master's semester.
Reimbursement of the Printing Costs for the Thesis
The printing costs for the required copies of your thesis can be reimbursed upon application. This also applies to theses in the teacher training programs that were written in mathematics.
 Please fill out the application form and hand it in at the BachelorMaster Office Mathematics.
 The enclosed original receipt must show the number of copies printed.
 Please attach the receipts to the separately printed page 2 of the form using a glue stick.
Please submit the form promptly, as the original receipts are only valid for 6 months.
Examination Office Mathematics
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Home > Physical and Mathematical Sciences > Mathematics Education > Theses and Dissertations
Mathematics Education Theses and Dissertations
Theses/dissertations from 2024 2024.
New Mathematics Teachers' Goals, Orientations, and Resources that Influence Implementation of Principles Learned in Brigham Young University's Teacher Preparation Program , Caroline S. Gneiting
Theses/Dissertations from 2023 2023
Impact of Applying Visual Design Principles to Boardwork in a Mathematics Classroom , Jennifer Rose Canizales
Practicing Mathematics Teachers' Perspectives of Public Records in Their Classrooms , Sini Nicole White Graff
Parents' Perceptions of the Importance of Teaching Mathematics: A QStudy , Ashlynn M. Holley
Engagement in Secondary Mathematics Group Work: A Student Perspective , Rachel H. Jorgenson
Theses/Dissertations from 2022 2022
Understanding College Students' Use of Written Feedback in Mathematics , Erin Loraine Carroll
Identity Work to Teach Mathematics for Social Justice , Navy B. Dixon
Developing a Quantitative Understanding of USubstitution in FirstSemester Calculus , Leilani Camille Heaton Fonbuena
The Perception of AtRisk Students on Caring StudentTeacher Relationships and Its Impact on Their Productive Disposition , Brittany Hopper
Variational and Covariational Reasoning of Students with Disabilities , Lauren Rigby
Structural Reasoning with Rational Expressions , Dana Steinhorst
StudentCreated Learning Objects for Mathematics Renewable Assignments: The Potential Value They Bring to the Broader Community , Webster Wong
Theses/Dissertations from 2021 2021
Emotional Geographies of Beginning and Veteran Reformed Teachers in Mentor/Mentee Relationships , Emily Joan Adams
You Do Math Like a Girl: How Women Reason Mathematically Outside of Formal and School Mathematics Contexts , Katelyn C. Pyfer
Developing the Definite Integral and Accumulation Function Through Adding Up Pieces: A Hypothetical Learning Trajectory , Brinley Nichole Stevens
Theses/Dissertations from 2020 2020
Mathematical Identities of Students with Mathematics Learning Dis/abilities , Emma Lynn Holdaway
Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures , Porter Peterson Nielsen
Student Use of Mathematical Content Knowledge During Proof Production , Chelsey Lynn Van de Merwe
Theses/Dissertations from 2019 2019
Making Sense of the Equal Sign in Middle School Mathematics , Chelsea Lynn Dickson
Developing Understanding of the Chain Rule, Implicit Differentiation, and Related Rates: Towards a Hypothetical Learning Trajectory Rooted in Nested Multivariation , Haley Paige Jeppson
Secondary Preservice Mathematics Teachers' Curricular Reasoning , Kimber Anne Mathis
“Don’t Say Gay. We Say Dumb or Stupid”: Queering ProspectiveMathematics Teachers’ Discussions , Amy Saunders Ross
Aspects of Engaging Problem Contexts From Students' Perspectives , Tamara Kay Stark
Theses/Dissertations from 2018 2018
Addressing PreService Teachers' Misconceptions About Confidence Intervals , Kiya Lynn Eliason
How Teacher Questions Affect the Development of a Potential Hybrid Space in a Classroom with Latina/o Students , Casandra Helen Job
Teacher Graphing Practices for Linear Functions in a CovariationBased College Algebra Classroom , Konda Jo Luckau
Principles of Productivity Revealed from Secondary Mathematics Teachers' Discussions Around the Productiveness of Teacher Moves in Response to Teachable Moments , Kylie Victoria Palsky
Theses/Dissertations from 2017 2017
Curriculum Decisions and Reasoning of Middle School Teachers , Anand Mikel Bernard
Teacher Response to Instances of Student Thinking During Whole Class Discussion , Rachel Marie Bernard
Kyozaikenkyu: An InDepth Look into Japanese Educators' Daily Planning Practices , Matthew David Melville
Analysis of Differential Equations Applications from the Coordination Class Perspective , Omar Antonio Naranjo Mayorga
Theses/Dissertations from 2016 2016
The Principles of Effective Teaching Student Teachershave the Opportunity to Learn in an AlternativeStudent Teaching Structure , Danielle Rose Divis
Insight into Student Conceptions of Proof , Steven Daniel Lauzon
Theses/Dissertations from 2015 2015
Teacher Participation and Motivation inProfessional Development , Krystal A. Hill
Student Evaluation of Mathematical Explanations in anInquiryBased Mathematics Classroom , Ashley Burgess Hulet
English Learners' Participation in Mathematical Discourse , Lindsay Marie Merrill
Mathematical Interactions between Teachers and Students in the Finnish Mathematics Classroom , Paula Jeffery Prestwich
Parents and the Common Core State Standards for Mathematics , Rebecca Anne Roberts
Examining the Effects of College Algebra on Students' Mathematical Dispositions , Kevin Lee Watson
Problems Faced by Reform Oriented Novice Mathematics Teachers Utilizing a Traditional Curriculum , Tyler Joseph Winiecke
Academic and Peer Status in the Mathematical Life Stories of Students , Carol Ann Wise
Theses/Dissertations from 2014 2014
The Effect of Students' Mathematical Beliefs on Knowledge Transfer , Kristen Adams
Language Use in Mathematics Textbooks Written in English and Spanish , Kailie Ann Bertoch
Teachers' Curricular Reasoning and MKT in the Context of Algebra and Statistics , Kolby J. Gadd
Mathematical Telling in the Context of Teacher Interventions with Collaborative Groups , Brandon Kyle Singleton
An Investigation of How Preservice Teachers Design Mathematical Tasks , Elizabeth Karen Zwahlen
Theses/Dissertations from 2013 2013
Student Understanding of Limit and Continuity at a Point: A Look into Four Potentially Problematic Conceptions , Miriam Lynne Amatangelo
Exploring the Mathematical Knowledge for Teaching of Japanese Teachers , Ratu Jared R. T. Bukarau
Comparing Two Different Student Teaching Structures by Analyzing Conversations Between Student Teachers and Their Cooperating Teachers , Niccole Suzette Franc
Professional Development as a Community of Practice and Its Associated Influence on the Induction of a Beginning Mathematics Teacher , Savannah O. Steele
Types of Questions that Comprise a Teacher's Questioning Discourse in a ConceptuallyOriented Classroom , Keilani Stolk
Theses/Dissertations from 2012 2012
Student Teachers' Interactive Decisions with Respect to Student Mathematics Thinking , Jonathan J. Call
Manipulatives and the Growth of Mathematical Understanding , Stacie Joyce Gibbons
Learning Within a ComputerAssisted Instructional Environment: Effects on Multiplication Math Fact Mastery and SelfEfficacy in ElementaryAge Students , Loraine Jones Hanson
Mathematics Teacher Time Allocation , Ashley Martin Jones
Theses/Dissertations from 2011 2011
How Student Positioning Can Lead to Failure in Inquirybased Classrooms , Kelly Beatrice Campbell
Teachers' Decisions to Use Student Input During Class Discussion , Heather Taylor Toponce
A Conceptual Framework for Student Understanding of Logarithms , Heather Rebecca Ambler Williams
Theses/Dissertations from 2010 2010
Growth in Students' Conceptions of Mathematical Induction , John David Gruver
Contextualized Motivation Theory (CMT): Intellectual Passion, Mathematical Need, Social Responsibility, and Personal Agency in Learning Mathematics , Janelle Marie Hart
Thinking on the Brink: Facilitating Student Teachers' Learning Through IntheMoment Interjections , Travis L. Lemon
Understanding Teachers' Change Towards a ReformOriented Mathematics Classroom , Linnae Denise Williams
Theses/Dissertations from 2009 2009
A Comparison of Mathematical Discourse in Online and FacetoFace Environments , Shawn D. Broderick
The Influence of Risk Taking on Student Creation of Mathematical Meaning: Contextual Risk Theory , Erin Nicole Houghtaling
Uncovering Transformative Experiences: A Case Study of the Transformations Made by one Teacher in a Mathematics Professional Development Program , Rachelle Myler Orsak
Theses/Dissertations from 2008 2008
Student Teacher Knowledge and Its Impact on Task Design , Tenille Cannon
How EighthGrade Students Estimate with Fractions , Audrey Linford Hanks
Similar but Different: The Complexities of Students' Mathematical Identities , Diane Skillicorn Hill
Choose Your Words: Refining What Counts as Mathematical Discourse in Students' Negotiation of Meaning for Rate of Change of Volume , Christine Johnson
Mathematics Student Teaching in Japan: A MultiCase Study , Allison Turley Shwalb
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What Are Some of the Common Traits in the Thought Processes of Undergraduate Students Capable of Creating Proof? , Karen Malina Duff
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Discovering the Derivative Can Be "Invigorating:" Mark's Journey to Understanding Instantaneous Velocity , Charity Ann Gardner Hyer
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How a Master Teacher Uses Questioning Within a Mathematical Discourse Community , Omel Angel Contreras
Determining High School Geometry Students' Geometric Understanding Using van Hiele Levels: Is There a Difference Between Standardsbased Curriculum Students and NonStandardsbased Curriculum Students? , Rebekah Loraine Genz
The Nature and Frequency of Mathematical Discussion During Lesson Study That Implemented the CMI Framework , Andrew Ray Glaze
Second Graders' Solution Strategies and Understanding of a Combination Problem , Tiffany Marie Hessing
What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses? , Matthew M. Webb
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Reasoning About Motion: A Case Study , Tiffini Lynn Glaze
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Mathematics
Senior thesis information.
Both senior thesis and senior seminar satisfy the Bates W3 writing requirement and highlight mathematical research, writing, presentation, and group collaboration. Senior thesis is a good choice for students wanting to improve all these, with special emphasis on mathematical research on a topic chosen by the student. Senior theses also involve significant amounts of writing, presentations, and checkins with other math thesis writers.
To ensure that each senior thesis writer has an enriching experience, the math department limits how many theses each faculty member advises, typically to no more than two theses per semester per advisor. To help the department determine senior thesis advisors, each junior math major who would like to write a senior thesis completes a request form by NOON on the last day of Winter Semester classes of the junior year, that is, by 12:00pm (noon) on Friday, April 12, 2024 . Some details:
 The request form seeks background information on the student, the student’s preferences regarding senior thesis, the student’s reasoning behind their preferences, and a description of the proposed senior thesis project. The project description should include enough information to show that the student has given their topic serious thought and that the project is feasible, given the student’s background and given the amount of time the student has to do the research.
 The math department strongly advises juniors to discuss senior thesis topics and ideas with faculty members before writing a request. The request form asks whether you have had such discussions.
 Students should plan to work at least 12 hours per week on thesis, and at least 15 hours per week if pursuing an Honors thesis.
 The math department meets to consider all senior thesis and senior seminar proposals. The department chair typically notifies students of the results of the meeting during Short Term.
 The mathematics department keeps copies of past senior theses in our lounge in Hathorn 209. We encourage prospective senior thesis writers to look through these past theses as part of deciding whether to write a thesis: past theses provide topic ideas, writing structures, and a sense of the scope of a senior thesis.
Types of thesis
 Onesemester thesis: A onesemester thesis may be either in the fall (MATH 457) or winter (MATH 458). Onesemester theses are due by the Friday of the final examination period of the semester in which the student is writing their thesis.
 Twosemester thesis: Twosemester theses (MATH 457 and MATH 458) not in the Honors Program are due by the last day of classes of the winter semester.
 Honors thesis: Honors theses (MATH 457 and MATH 458) are always twosemester theses and follow the procedures and deadlines of the Honors Program . While all capstone experiences expect students to demonstrate mathematical reading skills and ability to communicate mathematics, a thesis earning Honors in Mathematics is distinguished by an exceptional level of achievement in these areas. Students preferring to write an Honors thesis state this preference at the time of their senior thesis proposal. The Department then decides which students to nominate for the Honors Program, based on the thesis work presented at the end of the first semester.
 Double thesis with another major: A double thesis is a single yearlong project that satisfies the thesis requirements of both mathematics and another department, and as such, requires a significant amount of mathematics. A student writing a double thesis signs up for their math thesis in one semester (either MATH 457 or MATH 458) and the other department thesis in the other semester. The math department requires the student to present a talk or poster in the “math semester.” A student who applies thesis course credit to another major may not apply that same credit to the Mathematics Major. The Department will not approve a proposal for a onesemester double thesis.
Completing the thesis
 Students turn in their thesis to their advisor, in a format determined by the advisor, and students give the department chair a final printed copy of the thesis to be placed on permanent display in the mathematics lounge.
 onesemester thesis students present a poster or a talk;
 twosemester nonhonors thesis students present a talk in Fall Semester and a poster or a talk in Winter Semester;
 Honors thesis students present a talk in Fall Semester and give their Honors defense during a Collegedesignated Honors defense time period;
 when there is a choice of a poster or a talk, this decision is to be made with the thesis advisor.
Future Students
Majors and minors, course schedules, request info, application requirements, faculty directory, student profile.
Guidelines for writing a thesis
These guidelines are intended for students writing a thesis or project report for a Third Year Project Course , Honours year or Postgraduate Coursework Project . Postgraduate research students should see Information about Research Theses for postgraduate research students.
Before you start your Honours or Project year, you should speak to members of staff about possible thesis topics. Find out who works in the areas that you are interested in and who you find it easy to talk mathematics with. If at all possible, settle on a topic and supervisor before the start of the first semester of your Honours or Project year.
Most students see their supervisor about once a week, although this is usually open to negotiation between the student and the supervisor. Even if you haven't done much between visits it is a good idea to have a regular chat so that your supervisor can keep track of how you are going. You can expect your supervisor to:
 Help you select  and modify  your topic.
 Direct you to useful references on your topic.
 Help explain difficult points.
 Provide feedback on the direction of your research.
 Read and comment on drafts of your thesis.
 Help prepare you for your talk.
 Give general course advice.
Your thesis or project report is an overview of what you have been studying in your Honours or Project year. Write it as if you were trying to explain the area of mathematics or statistics that you have been looking at to a fellow student.
 Include an introduction that explains what the project is all about, and what its contents are. (It is sometimes better to leave writing this part to the end!) For many reports, a conclusion or summary is appropriate.
 Your thesis should be a coherent, selfcontained piece of work.
 Your writing should conform to the highest standards of English. Aim at clarity, precision and correct grammar. Start sentences with capital letters and end them with fullstops. Don't start sentences with a symbol.
 Take great care with bibliographic referencing. Wherever some material has an external source, this should be clear to the reader. Don't just write in the introduction: 'This report contains material from [1],[2] and [3]'  give the references for the material wherever it is used. Don't gratuitously pad your reference list with references that are not referred to in the text. Check current journals for acceptable referencing styles.
 Be careful not to plagiarise. What constitutes plagiarism is perhaps a little different in mathematics and statistics compared to some other subjects since there is a limit to how different you may be able to make a proof (at least in its basic structure). We do, however, expect the report to be written in your own words. A basic rule is: if you put a fact or an idea in your report which is not your own, the reader should be able to tell where you got this fact or idea.
 The University has policies on academic honesty and plagiarism which all students should familiarise themselves with.
Generally, mathematics reports and theses are almost always typed in LaTeX. If you are going to type it yourself, you should allow a certain amount of time to become familiar with this software. Indeed, starting to learn LaTeX well before you actually want to write is a very good idea.
You should not underestimate the time it takes to produce a polished document. You will almost certainly need several drafts. It is very difficult to concentrate on getting the mathematics, spelling, grammar, layout, etc., all correct at once. Try getting another student to proofread what you have written  from their different viewpoint they may pick up on lots of things that you can't see.
P R Halmos (1970) in How to write mathematics, Enseignement Math. ((2) 16, 123152) has the following advice: "The basic problem in writing mathematics is the same as in writing biology, writing a novel, or writing directions for assembling a harpsichord: the problem is to communicate an idea. To do so, and to do it clearly:
 you must have something to say (i.e., some ideas), and you must have someone to say it to (i.e., an audience)
 you must organize what you want to say, and you must arrange it in the order you want it said in
 you must write it, rewrite it, and rerewrite it several times
 and you must be willing to think hard about and work hard on mechanical details such as diction, notation, and punctuation.
That's all there is to it."
His other advice includes:
 Say something: "To have something to say is by far the most important ingredient of good expositionso much so that if the idea is important enough, the work has a chance to be immortal even if it is confusingly misorganized and awkwardly expressed..... To get by one the first principle alone is, however, only rarely possible and never desirable."
 Audience: "The second principle of good writing is to write for someone. When you decide to write something, ask yourself who it is that you want to reach." Your broad audience will be fellow Masters and Honours students, who may not be experts in your thesis topic. "The author must anticipate and avoid the reader's difficulties. As he(/she) writes, he(/she) must keep trying to imagine what in the words being written may tend to mislead the reader, and what will set him(/her) right."
 Organise: "The main contribution that an expository writer can make is to organize and arrange the material so as to minimize the resistance and maximize the insight of the reader and keep him(/her) on the track with no unintended distractions".
 Think about the alphabet: "Once you have some kind of plan of organization, an outline, which may not be a fine one but is the best you can do, you are almost ready to start writing. The only other thing I would recommend that you do first is to invest an hour or two of thought in the alphabet; you'll find it saves many headaches later. The letters that are used to denote the concepts you'll discuss are worthy of thought and careful design. A good, consistent notation can be a tremendous help".
 Write in spirals: "The best way to start writing, perhaps the only way, is to write on the spiral plan. According to the spiral plan the chapters get written in the order 1,2,1,2,3,1,2,3,4 etc. You think you know how to write Chapter 1, but after you've done it and gone on to Chapter 2, you'll realize that you could have done a better job on Chapter 2 if you had done Chapter 1 differently. There is no help for it but to go back, do Chapter 1 differently, do a better job on Chapter 2, and then dive into Chapter 3... Chapter 3 will show up the weaknesses of Chapters 1 and 2".
 Write good English: "Good English style implies correct grammar, correct choice of words, correct punctuation, and, perhaps above all, common sense."
More information on how to write mathematics:
 Lee, K. A guide to writing mathematics
 Lee, K. Some notes on writing mathematics
 Jackson, M. Some notes on writing in mathematics
 Reiter, A. Writing a research paper in mathematics
 Honours thesis
 Postgraduate Coursework Project
 Third Year Project Courses
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Tips for writing an undergraduate thesis in mathematics (Matroid Theory)
Hello, I'm writing my undergraduate thesis in mathematics. I study computer science but I love math so I picked Matroid Theory as a subject for my thesis. The goal is to present some equivalent definitions of matroids. Do you have any tips? My main concern is that it may get to be too long. You see I'm currently writing the introduction and I am planning to include basic notions of Relations over finite sets, Graph Theory, Linear algebra and traversal theory. I am trying to write a mathematical thesis to be both rigorous and easily understood by an undergraduate cs student.
tl;Dr Do you have any tips about how to balance writing a rigorous thesis and keeping it simple enough and self sufficient for a CS student to read (without writing a 10!  factorial of 10 pages text)
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What is expected in a masters thesis of a mathematics student?
What is the level of work expected in the masters thesis of a student of maths?
I know some people's works are worthy of publications while some involve only studying some topic in detail from a book and submitting a summary (since this is akin to a couple of courses, a year worth of work, in that topic in terms of content covered, I would consider this,which I believe is called a literature review thesis , as an extreme opposite of independent research work thesis).
But what is the "average" level of a MS thesis of a mathematics student? Is it usually closer to a literature review thesis or a research work thesis?
In particular, I would also like to know:
How much is it valued (if at all) when one applies for PhD? I have heard that its value is more in Europe than America, which if I were to guess I would say, may be due to absence of GRE like criterion there. Is this true?
Edit : After the wonderful existing answer explaining the case in Germany, I would really like to know the situation in US too. I expect a drastic difference due to the presence of GRE system but would like to know how much importance the thesis has, there.
PS: Please excuse me if one can find answers to some of these questions in already existing questions. I have searched, but couldn't find them. Please provide the links in those cases.
Also, anecdotal details will also be greatly appreciated. Thanks!
 graduateadmissions
 mathematics
 @user54981 Of course that would most certainly be there. – Neeraj Kumar Commented Jun 6, 2016 at 6:01
 2 The difference between US/Canada and Europe is mainly due to the fact that in most European institutions, applicants to a PhD program are expected to held a Masters or equivalent degree, and the PhD program is often research only with close to no coursework. Compare to North American institutions where applicants to a PhD program are not expected to hold a Masters, and generally only hold a Bachelors degree, and where the program tends to be longer with a more significant coursework portion. – Willie Wong Commented Jun 8, 2016 at 13:40
 Note also that the European application process for entering a PhD program is often quite different from the typical North American one. (Search on this site if you want to know more; I'm sure it has been asked before.) – Willie Wong Commented Jun 8, 2016 at 13:41
 @NeerajKumar Not necessarily equations. Almost certainly inequalities such as the element relation. – Jacob Murray Wakem Commented Jun 8, 2016 at 15:35
 @JacobWakem I don't understand what the term element relation is but isn't the presence of inequalities dependent on the topic? For example, a thesis in algebraic topology or geometry is most likely to not use any inequalities but one in functional analysis or number theory may have a lot of it.. – Neeraj Kumar Commented Jun 9, 2016 at 4:03
3 Answers 3
I think this varies a lot. But for Germany your first question can be answers succinctly: In a Master's thesis you should show that you have potential for research .
On the other hand, expectations vary a lot between advisors. But certainly you do not have to prove a new theorem or develop a new theory.
How much is it valued (if at all) when one applies for PhD?
I can only answer for the situation where you apply in Germany. The thesis can be a door opener if it is topic closely related to the field where you want to do a PhD. Also a good mark is important. But also in Germany hiring professors will often contact your advisors or request a reference letter and this is much more important.
I have heard that its value is more in Europe than America, which if I were to guess I would say, may be due to no GRE like criterion. Is this true?
Not sure on this point since I can't provide a comparison with the US and also I am not sure if the situation is uniform with the EU.
 Thanks for the answer. As I mentioned, there are the two extremes in the kinds of thesis. In the first I can imagine the potential for research to be clearly visible( since they are doing actual research work) but how about the second case? If the work is only the study of a topic then? I doubt if it would reflect much on the potential to do research. Though one consideration that I can imagine is if the person spends his thesis studying on a certain topic then would it be of any advantage if person applies into that topic for PhD. Are such considerations taken into account? – Neeraj Kumar Commented May 26, 2016 at 15:37
 Sorry if this is not getting more concrete, but, e. g., a literature review thesis can or can not show research potential. If your question is: What do I have to do in a Master's thesis do get a PhD position, the answer is "Nobody can tell you in advance." Go ahead and choose a thesis topic you find thrilling and write a good thesis. – Dirk Commented May 26, 2016 at 16:27
From my knowledge of the US system (I did my graduate work in the US, and am currently a professor in the US), the average level of a masters thesis is relatively low. (That said, it usually does involve at least some original research).
The reason for this is the structure of Ph.D. programs in the US. Usually students are admitted to Ph.D. programs directly as undergraduates, and the first two years of the Ph.D. are similar to an MS program in Europe. Students who complete a Ph.D. don't generally write a masters thesis along the way. Rather, masters theses are usually written by students who decide in their second year not to continue with our Ph.D. program, but would still like to earn some sort of degree for their efforts. These theses are often weak (but sometimes are quite good).
Some students do use an MS as a stepping stone to Ph.D. programs elsewhere; indeed, I personally know students who successfully transferred to much stronger programs. Their MSlevel work was much better than average.
In short: The degree itself won't be highly valued in the US, but doing an MS can lead to strong letters from your professors and research advisors, and these will be highly valued.
 Another complication with master's theses, in the U.S., is a perception that the student "will do a PhD thesis anyway" if they go on to a PhD program, and so there is less need for the master's thesis to include challenging research. The motivation for writing a master's thesis becomes different from the motivation for writing a PhD thesis. – Oswald Veblen Commented Jun 9, 2016 at 21:19
A great resource I have used to understand the quality of final thesis work for my primary focus is the Open Access Theses and Dissertations which has thousands of master's and Ph. D. final publications. Research this website using your topic and you will see what amount of research is involved, differences and similarities between schools, methodologies, etc.
In addition, a great site for further publications is http://Arxiv.org . Many thesis in the U.S. are 'sandwich' publications, involving an assortment of publications published while student is performing research.
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Updated: April 2024
Math/Stats Thesis and Colloquium Topics 2024 2025
The degree with honors in Mathematics or Statistics is awarded to the student who has demonstrated outstanding intellectual achievement in a program of study which extends beyond the requirements of the major. The principal considerations for recommending a student for the degree with honors will be: Mastery of core material and skills, breadth and, particularly, depth of knowledge beyond the core material, ability to pursue independent study of mathematics or statistics, originality in methods of investigation, and, where appropriate, creativity in research.
An honors program normally consists of two semesters (MATH/STAT 493 and 494) and a winter study (WSP 031) of independent research, culminating in a thesis and a presentation. Under certain circumstances, the honors work can consist of coordinated study involving a one semester (MATH/STAT 493 or 494) and a winter study (WSP 030) of independent research, culminating in a “minithesis” and a presentation. At least one semester should be in addition to the major requirements, and thesis courses do not count as 400level senior seminars.
An honors program in actuarial studies requires significant achievement on four appropriate examinations of the Society of Actuaries.
Highest honors will be reserved for the rare student who has displayed exceptional ability, achievement or originality. Such a student usually will have written a thesis, or pursued actuarial honors and written a minithesis. An outstanding student who writes a minithesis, or pursues actuarial honors and writes a paper, might also be considered. In all cases, the award of honors and highest honors is the decision of the Department.
Here is a list of possible colloquium topics that different faculty are willing and eager to advise. You can talk to several faculty about any colloquium topic, the sooner the better, at least a month or two before your talk. For various reasons faculty may or may not be willing or able to advise your colloquium, which is another reason to start early.
RESEARCH INTERESTS OF MATHEMATICS AND STATISTICS FACULTY
Here is a list of faculty interests and possible thesis topics. You may use this list to select a thesis topic or you can use the list below to get a general idea of the mathematical interests of our faculty.
Colin Adams (On Leave 2024 – 2025)
Research interests: Topology and tiling theory. I work in lowdimensional topology. Specifically, I work in the two fields of knot theory and hyperbolic 3manifold theory and develop the connections between the two. Knot theory is the study of knotted circles in 3space, and it has applications to chemistry, biology and physics. I am also interested in tiling theory and have been working with students in this area as well.
Hyperbolic 3manifold theory utilizes hyperbolic geometry to understand 3manifolds, which can be thought of as possible models of the spatial universe.
Possible thesis topics:
 Investigate various aspects of virtual knots, a generalization of knots.
 Consider hyperbolicity of virtual knots, building on previous SMALL work. For which virtual knots can you prove hyperbolicity?
 Investigate why certain virtual knots have the same hyperbolic volume.
 Consider the minimal Turaev volume of virtual knots, building on previous SMALL work.
 Investigate which knots have totally geodesic Seifert surfaces. In particular, figure out how to interpret this question for virtual knots.
 Investigate ncrossing number of knots. An ncrossing is a crossing with n strands of the knot passing through it. Every knot can be drawn in a picture with only ncrossings in it. The least number of ncrossings is called the ncrossing number. Determine the ncrossing number for various n and various families of knots.
 An übercrossing projection of a knot is a projection with just one ncrossing. The übercrossing number of a knot is the least n for which there is such an übercrossing projection. Determine the übercrossing number for various knots, and see how it relates to other traditional knot invariants.
 A petal projection of a knot is a projection with just one ncrossing such that none of the loops coming out of the crossing are nested. In other words, the projection looks like a daisy. The petal number of a knot is the least n for such a projection. Determine petal number for various knots, and see how it relates to other traditional knot invariants.
 In a recent paper, we extended petal number to virtual knots. Show that the virtual petal number of a classical knot is equal to the classical petal number of the knot (This is a GOOD question!)
 Similarly, show that the virtual ncrossing number of a classical knot is equal to the classical ncrossing number. (This is known for n = 2.)
 Find tilings of the branched sphere by regular polygons. This would extend work of previous research students. There are lots of interesting open problems about something as simple as tilings of the sphere.
 Other related topics.
Possible colloquium topics : Particularly interested in topology, knot theory, graph theory, tiling theory and geometry but will consider other topics.
Christina Athanasouli
Research Interests: Differential equations, dynamical systems (both smooth and nonsmooth), mathematical modeling with applications in biological and mechanical systems
My research focuses on analyzing mathematical models that describe various phenomena in Mathematical Neuroscience and Engineering. In particular, I work on understanding 1) the underlying mechanisms of human sleep (e.g. how sleep patterns change with development or due to perturbations), and 2) potential design or physical factors that may influence the dynamics in vibroimpact mechanical systems for the purpose of harvesting energy. Mathematically, I use various techniques from dynamical systems and incorporate both numerical and analytical tools in my work.
Possible colloquium topics: Topics in applied mathematics, such as:
 Mathematical modeling of sleepwake regulation
 Mathematical modeling vibroimpact systems
 Bifurcations/dynamics of mathematical models in Mathematical Neuroscience and Engineering
 Bifurcations in piecewisesmooth dynamical systems
Julie Blackwood
Research Interests: Mathematical modeling, theoretical ecology, population biology, differential equations, dynamical systems.
My research uses mathematical models to uncover the complex mechanisms generating ecological dynamics, and when applicable emphasis is placed on evaluating intervention programs. My research is in various ecological areas including ( I ) invasive species management by using mathematical and economic models to evaluate the costs and benefits of control strategies, and ( II ) disease ecology by evaluating competing mathematical models of the transmission dynamics for both human and wildlife diseases.
 Mathematical modeling of invasive species
 Mathematical modeling of vectorborne or directly transmitted diseases
 Developing mathematical models to manage vectorborne diseases through vector control
 Other relevant topics of interest in mathematical biology
Each topic (13) can focus on a case study of a particular invasive species or disease, and/or can investigate the effects of ecological properties (spatial structure, resource availability, contact structure, etc.) of the system.
Possible colloquium topics: Any topics in applied mathematics, such as:
Research Interest : Statistical methodology and applications. One of my research topics is variable selection for highdimensional data. I am interested in traditional and modern approaches for selecting variables from a large candidate set in different settings and studying the corresponding theoretical properties. The settings include linear model, partial linear model, survival analysis, dynamic networks, etc. Another part of my research studies the mediation model, which examines the underlying mechanism of how variables relate to each other. My research also involves applying existing methods and developing new procedures to model the correlated observations and capture the timevarying effect. I am also interested in applications of data mining and statistical learning methods, e.g., their applications in analyzing the rhetorical styles in English text data.
 Variable selection uses modern techniques such as penalization and screening methods for several different parametric and semiparametric models.
 Extension of the classic mediation models to settings with correlated, longitudinal, or highdimensional mediators. We could also explore ways to reduce the dimensionality and simplify the structure of mediators to have a stable model that is also easier to interpret.
 We shall analyze the English text dataset processed by the Docuscope environment with tools for corpusbased rhetorical analysis. The data have a hierarchical structure and contain rich information about the rhetorical styles used. We could apply statistical models and statistical learning algorithms to reduce dimensions and gain a more insightful understanding of the text.
Possible colloquium topics: I am open to any problems in statistical methodology and applications, not limited to my research interests and the possible thesis topics above.
Richard De Veaux
Research interests: Statistics.
My research interests are in both statistical methodology and in statistical applications. For the first, I look at different methods and try to understand why some methods work well in particular settings, or more creatively, to try to come up with new methods. For the second, I work in collaboration with an investigator (e.g. scientist, doctor, marketing analyst) on a particular statistical application. I have been especially interested in problems dealing with large data sets and the associated modeling tools that work for these problems.
 Human Performance and Aging.I have been working on models for assessing the effect of age on performance in running and swimming events. There is still much work to do. So far I’ve looked at masters’ freestyle swimming and running data and a handicapped race in California, but there are world records for each age group and other events in running and swimming that I’ve not incorporated. There are also many other types of events.
 Variable Selection. How do we choose variables when we have dozens, hundreds or even thousands of potential predictors? Various model selection strategies exist, but there is still a lot of work to be done to find out which ones work under what assumptions and conditions.
 Problems at the interface.In this era of Big Data, not all methods of classical statistics can be applied in practice. What methods scale up well, and what advances in computer science give insights into the statistical methods that are best suited to large data sets?
 Applying statistical methods to problems in science or social science.In collaboration with a scientist or social scientist, find a problem for which statistical analysis plays a key role.
Possible colloquium topics:
 Almost any topic in statistics that extends things you’ve learned in courses — specifically topics in Experimental design, regression techniques or machine learning
 Model selection problems
Thomas Garrity (On Leave 2024 – 2025)
Research interest: Number Theory and Dynamics.
My area of research is officially called “multidimensional continued fraction algorithms,” an area that touches many different branches of mathematics (which is one reason it is both interesting and rich). In recent years, students writing theses with me have used serious tools from geometry, dynamics, ergodic theory, functional analysis, linear algebra, differentiability conditions, and combinatorics. (No single person has used all of these tools.) It is an area to see how mathematics is truly interrelated, forming one coherent whole.
While my original interest in this area stemmed from trying to find interesting methods for expressing real numbers as sequences of integers (the Hermite problem), over the years this has led to me interacting with many different mathematicians, and to me learning a whole lot of math. My theses students have had much the same experiences, including the emotional rush of discovery and the occasional despair of frustration. The whole experience of writing a thesis should be intense, and ultimately rewarding. Also, since this area of math has so many facets and has so many entrance points, I have had thesis students from wildly different mathematical backgrounds do wonderful work; hence all welcome.
 Generalizations of continued fractions.
 Using algebraic geometry to study real submanifolds of complex spaces.
Possible colloquium topics: Any interesting topic in mathematics.
Leo Goldmakher
Research interests: Number theory and arithmetic combinatorics.
I’m interested in quantifying structure and randomness within naturally occurring sets or sequences, such as the prime numbers, or the sequence of coefficients of a continued fraction, or a subset of a vector space. Doing so typically involves using ideas from analysis, probability, algebra, and combinatorics.
Possible thesis topics:
Anything in number theory or arithmetic combinatorics.
Possible colloquium topics: I’m happy to advise a colloquium in any area of math.
Susan Loepp
Research interests: Commutative Algebra. I study algebraic structures called commutative rings. Specifically, I have been investigating the relationship between local rings and their completion. One defines the completion of a ring by first defining a metric on the ring and then completing the ring with respect to that metric. I am interested in what kinds of algebraic properties a ring and its completion share. This relationship has proven to be intricate and quite surprising. I am also interested in the theory of tight closure, and Homological Algebra.
Topics in Commutative Algebra including:
 Using completions to construct Noetherian rings with unusual prime ideal structures.
 What prime ideals of C[[ x 1 ,…, x n ]] can be maximal in the generic formal fiber of a ring? More generally, characterize what sets of prime ideals of a complete local ring can occur in the generic formal fiber.
 Characterize what sets of prime ideals of a complete local ring can occur in formal fibers of ideals with height n where n ≥1.
 Characterize which complete local rings are the completion of an excellent unique factorization domain.
 Explore the relationship between the formal fibers of R and S where S is a flat extension of R .
 Determine which complete local rings are the completion of a catenary integral domain.
 Determine which complete local rings are the completion of a catenary unique factorization domain.
Possible colloquium topics: Any topics in mathematics and especially commutative algebra/ring theory.
Steven Miller
For more information and references, see http://www.williams.edu/Mathematics/sjmiller/public_html/index.htm
Research interests : Analytic number theory, random matrix theory, probability and statistics, graph theory.
My main research interest is in the distribution of zeros of Lfunctions. The most studied of these is the Riemann zeta function, Sum_{n=1 to oo} 1/n^s. The importance of this function becomes apparent when we notice that it can also be written as Prod_{p prime} 1 / (1 – 1/p^s); this function relates properties of the primes to those of the integers (and we know where the integers are!). It turns out that the properties of zeros of Lfunctions are extremely useful in attacking questions in number theory. Interestingly, a terrific model for these zeros is given by random matrix theory: choose a large matrix at random and study its eigenvalues. This model also does a terrific job describing behavior ranging from heavy nuclei like Uranium to bus routes in Mexico! I’m studying several problems in random matrix theory, which also have applications to graph theory (building efficient networks). I am also working on several problems in probability and statistics, especially (but not limited to) sabermetrics (applying mathematical statistics to baseball) and Benford’s law of digit bias (which is often connected to fascinating questions about equidistribution). Many data sets have a preponderance of first digits equal to 1 (look at the first million Fibonacci numbers, and you’ll see a leading digit of 1 about 30% of the time). In addition to being of theoretical interest, applications range from the IRS (which uses it to detect tax fraud) to computer science (building more efficient computers). I’m exploring the subject with several colleagues in fields ranging from accounting to engineering to the social sciences.
Possible thesis topics:
 Theoretical models for zeros of elliptic curve Lfunctions (in the number field and function field cases).
 Studying lower order term behavior in zeros of Lfunctions.
 Studying the distribution of eigenvalues of sets of random matrices.
 Exploring Benford’s law of digit bias (both its theory and applications, such as image, voter and tax fraud).
 Propagation of viruses in networks (a graph theory / dynamical systems problem). Sabermetrics.
 Additive number theory (questions on sum and difference sets).
Possible colloquium topics:
Plus anything you find interesting. I’m also interested in applications, and have worked on subjects ranging from accounting to computer science to geology to marketing….
Ralph Morrison
Research interests: I work in algebraic geometry, tropical geometry, graph theory (especially chipfiring games on graphs), and discrete geometry, as well as computer implementations that study these topics. Algebraic geometry is the study of solution sets to polynomial equations. Such a solution set is called a variety. Tropical geometry is a “skeletonized” version of algebraic geometry. We can take a classical variety and “tropicalize” it, giving us a tropical variety, which is a piecewiselinear subset of Euclidean space. Tropical geometry combines combinatorics, discrete geometry, and graph theory with classical algebraic geometry, and allows for developing theory and computations that tell us about the classical varieties. One flavor of this area of math is to study chipfiring games on graphs, which are motivated by (and applied to) questions about algebraic curves.
Possible thesis topics : Anything related to tropical geometry, algebraic geometry, chipfiring games (or other graph theory topics), and discrete geometry. Here are a few specific topics/questions:
 Study the geometry of tropical plane curves, perhaps motivated by results from algebraic geometry. For instance: given 5 (algebraic) conics, there are 3264 conics that are tangent to all 5 of them. What if we look at tropical conics–is there still a fixed number of tropical conics tangent to all of them? If so, what is that number? How does this tropical count relate to the algebraic count?
 What can tropical plane curves “look like”? There are a few ways to make this question precise. One common way is to look at the “skeleton” of a tropical curve, a graph that lives inside of the curve and contains most of the interesting data. Which graphs can appear, and what can the lengths of its edges be? I’ve done lots of work with students on these sorts of questions, but there are many open questions!
 What can tropical surfaces in threedimensional space look like? What is the version of a skeleton here? (For instance, a tropical surface of degree 4 contains a distinguished polyhedron with at most 63 facets. Which polyhedra are possible?)
 Study the geometry of tropical curves obtained by intersecting two tropical surfaces. For instance, if we intersect a tropical plane with a tropical surface of degree 4, we obtain a tropical curve whose skeleton has three loops. How can those loops be arranged? Or we could intersect degree 2 and degree 3 tropical surfaces, to get a tropical curve with 4 loops; which skeletons are possible there?
 One way to study tropical geometry is to replace the usual rules of arithmetic (plus and times) with new rules (min and plus). How do topics like linear algebra work in these fields? (It turns out they’re related to optimization, scheduling, and job assignment problems.)
 Chipfiring games on graphs model questions from algebraic geometry. One of the most important comes in the “gonality” of a graph, which is the smallest number of chips on a graph that could eliminate (via a series of “chipfiring moves”) an added debt of 1 anywhere on the graph. There are lots of open questions for studying the gonality of graphs; this include general questions, like “What are good lower bounds on gonality?” and specific ones, like “What’s the gonality of the ndimensional hypercube graph?”
 We can also study versions of gonality where we place r chips instead of just 1; this gives us the r^th gonality of a graph. Together, the first, second, third, etc. gonalities form the “gonality sequence” of a graph. What sequences of integers can be the gonality sequence of some graph? Is there a graph whose gonality sequence starts 3, 5, 8?
 There are many computational and algorithmic questions to ask about chipfiring games. It’s known that computing the gonality of a general graph is NPhard; what if we restrict to planar graphs? Or graphs that are 3regular? And can we implement relatively efficient ways of computing these numbers, at least for small graphs?
 What if we changed our rules for chipfiring games, for instance by working with chips modulo N? How can we “win” a chipfiring game in that context, since there’s no more notion of debt?
 Study a “graph throttling” version of gonality. For instance, instead of minimizing the number of chips we place on the graph, maybe we can also try to decrease the number of chipfiring moves we need to eliminate debt.
 Chipfiring games lead to interesting questions on other topics in graph theory. For instance, there’s a conjectured upper bound of (EV+4)/2 on the gonality of a graph; and any graph is known to have gonality at least its treewidth. Can we prove the (weaker) result that (EV+4)/2 is an upper bound on treewidth? (Such a result would be of interest to graph theorists, even the idea behind it comes from algebraic geometry!)
 Topics coming from discrete geometry. For example: suppose you want to make “string art”, where you have one shape inside of another with string weaving between the inside and the outside shapes. For which pairs of shapes is this possible?
Possible Colloquium topics: I’m happy to advise a talk in any area of math, but would be especially excited about talks related to algebra, geometry, graph theory, or discrete mathematics.
Shaoyang Ning (On Leave 2024 – 2025)
Research Interest : Statistical methodologies and applications. My research focuses on the study and design of statistical methods for integrative data analysis, in particular, to address the challenges of increasing complexity and connectivity arising from “Big Data”. I’m interested in innovating statistical methods that efficiently integrate multisource, multiresolution information to solve reallife problems. Instances include tracking localized influenza with Google search data and predicting cancertargeting drugs with highthroughput genetic profiling data. Other interests include Bayesian methods, copula modeling, and nonparametric methods.
 Digital (disease) tracking: Using Internet search data to track and predict influenza activities at different resolutions (nation, region, state, city); Integrating other sources of digital data (e.g. Twitter, Facebook) and/or extending to track other epidemics and social/economic events, such as dengue, presidential approval rates, employment rates, and etc.
 Predicting cancer drugs with multisource profiling data: Developing new methods to aggregate genetic profiling data of different sources (e.g., mutations, expression levels, CRISPR knockouts, drug experiments) in cancer cell lines to identify potential cancertargeting drugs, their modes of actions and genetic targets.
 Social media text mining: Developing new methods to analyze and extract information from social media data (e.g. Reddit, Twitter). What are the challenges in analyzing the largevolume but shortlength social media data? Can classic methods still apply? How should we innovate to address these difficulties?
 Copula modeling: How do we model and estimate associations between different variables when they are beyond multivariate Normal? What if the data are heavily dependent in the tails of their distributions (commonly observed in stock prices)? What if dependence between data are nonsymmetric and complex? When the size of data is limited but the dimension is large, can we still recover their correlation structures? Copula model enables to “link” the marginals of a multivariate random variable to its joint distribution with great flexibility and can just be the key to the questions above.
 Other crossdisciplinary, datadriven projects: Applying/developing statistical methodology to answer an interesting scientific question in collaboration with a scientist or social scientist.
Possible colloquium topics: Any topics in statistical methodology and application, including but not limited to: topics in applied statistics, Bayesian methods, computational biology, statistical learning, “Big Data” mining, and other crossdisciplinary projects.
Anna Neufeld
Research interests: My research is motivated by the gap between classical statistical tools and practical data analysis. Classic statistical tools are designed for testing a single hypothesis about a single, prespecified model. However, modern data analysis is an adaptive process that involves exploring the data, fitting several models, evaluating these models, and then testing a potentially large number of hypotheses about one or more selected models. With this in mind, I am interested in topics such as (1) methods for model validation and selection, (2) methods for testing datadriven hypotheses (postselection inference), and (3) methods for testing a large number of hypotheses. I am also interested in any applied project where I can help a scientist rigorously answer an important question using data.
 Crossvalidation for unsupervised learning. Crossvalidation is one of the most widelyused tools for model validation, but, in its typical form, it cannot be used for unsupervised learning problems. Numerous adhoc proposals exist for validating unsupervised learning models, but there is a need to compare and contrast these proposals and work towards a unified approach.
 Identifying the number of cell types in singlecell genomics datasets. This is an application of the topic above, since the cell types are typically estimated via unsupervised learning.
 There is growing interest in “postprediction inference”, which is the task of doing valid statistical inference when some inputs to your statistical model are the outputs of other statistical models (i.e. predictions). Frameworks have recently been proposed for postprediction inference in the setting where you have access to a goldstandard dataset where the true inputs, rather than the predicted inputs, have been observed. A thesis could explore the possibility of postprediction inference in the absence of this goldstandard dataset.
 Any other topic of student interest related to selective inference, multiple testing, or postprediction inference.
 Any collaborative project in which we work with a scientist to identify an interesting question in need of nonstandard statistics.
 I am open to advising colloquia in almost any area of statistical methodology or applications, including but not limited to: multiple testing, postselection inference, postprediction inference, model selection, model validation, statistical machine learning, unsupervised learning, or genomics.
Allison Pacelli
Research interests: Math Education, Math & Politics, and Algebraic Number Theory.
Math Education. Math education is the study of the practice of teaching and learning mathematics, at all levels. For example, do high school calculus students learn best from lecture or inquirybased learning? What mathematical content knowledge is critical for elementary school math teachers? Is a flipped classroom more effective than a traditional learning format? Many fascinating questions remain, at all levels of education. We can talk further to narrow down project ideas.
Math & Politics. The mathematics of voting and the mathematics of fair division are two fascinating topics in the field of mathematics and politics. Research questions look at types of voting systems, and the properties that we would want a voting system to satisfy, as well as the idea of fairness when splitting up a single object, like cake, or a collection of objects, such as after a divorce or a death.
Algebraic Number Theory. The Fundamental Theorem of Arithmetic states that the ring of integers is a unique factorization domain, that is, every integer can be uniquely factored into a product of primes. In other rings, there are analogues of prime numbers, but factorization into primes is not necessarily unique!
In order to determine whether factorization into primes is unique in the ring of integers of a number field or function field, it is useful to study the associated class group – the group of equivalence classes of ideals. The class group is trivial if and only if the ring is a unique factorization domain. Although the study of class groups dates back to Gauss and played a key role in the history of Fermat’s Last Theorem, many basic questions remain open.
Possible thesis topics:
 Topics in math education, including projects at the elementary school level all the way through college level.
 Topics in voting and fair division.
 Investigating the divisibility of class numbers or the structure of the class group of quadratic fields and higher degree extensions.
 Exploring polynomial analogues of theorems from number theory concerning sums of powers, primes, divisibility, and arithmetic functions.
Possible colloquium topics: Anything in number theory, algebra, or math & politics.
Anna Plantinga
Research interests: I am interested in both applied and methodological statistics. My research primarily involves problems related to statistical analysis within genetics, genomics, and in particular the human microbiome (the set of bacteria that live in and on a person). Current areas of interest include longitudinal data, distancebased analysis methods such as kernel machine regression, highdimensional data, and structured data.
 Impacts of microbiome volatility. Sometimes the variability of a microbial community is more indicative of an unhealthy community than the actual bacteria present. We have developed an approach to quantifying microbiome variability (“volatility”). This project will use extensive simulations to explore the impact of betweengroup differences in volatility on a variety of standard tests for association between the microbiome and a health outcome.
 Accounting for excess zeros (sparse feature matrices). Often in a data matrix with many zeros, some of the zeros are “true” or “structural” zeros, whereas others are simply there because we have fewer observations for some subjects. How we account for these zeros affects analysis results. Which methods to account for excess zeros perform best for different analyses?
 Longitudinal methods for compositional data. When we have longitudinal data, we assume the same variables are measured at every time point. For highdimensional compositions, this may not be the case. We would generally assume that the missing component was absent at any time points for which it was not measured. This project will explore alternatives to making that assumption.
 Applied statistics research. In collaboration with a scientist or social scientist, use appropriate statistical methodology (or variations on existing methods) to answer an interesting scientific question.
Any topics in statistical application, education, or methodology, including but not restricted to:
 Topics in applied statistics.
 Methods for microbiome data analysis.
 Statistical genetics.
 Electronic health records.
 Variable selection and statistical learning.
 Longitudinal methods.
Cesar Silva
Research interests : Ergodic theory and measurable dynamics; in particular mixing properties and rank one examples, and infinite measurepreserving and nonsingular transformations and group actions. Measurable dynamics of transformations defined on the padic field. Measurable sensitivity. Fractals. Fractal Geometry.
Possible thesis topics: Ergodic Theory. Ergodic theory studies the probabilistic behavior of abstract dynamical systems. Dynamical systems are systems that change with time, such as the motion of the planets or of a pendulum. Abstract dynamical systems represent the state of a dynamical system by a point in a mathematical space (phase space). In many cases this space is assumed to be the unit interval [0,1) with Lebesgue measure. One usually assumes that time is measured at discrete intervals and so the law of motion of the system is represented by a single map (or transformation) of the phase space [0,1). In this case one studies various dynamical behaviors of these maps, such as ergodicity, weak mixing, and mixing. I am also interested in studying the measurable dynamics of systems defined on the padics numbers. The prerequisite is a first course in real analysis. Topological Dynamics. Dynamics on compact or locally compact spaces.
Topics in mathematics and in particular:
 Any topic in measure theory. See for example any of the first few chapters in “Measure and Category” by J. Oxtoby. Possible topics include the BanachTarski paradox, the BanachMazur game, Liouville numbers and sHausdorff measure zero.
 Topics in applied linear algebra and functional analysis.
 Fractal sets, fractal generation, image compression, and fractal dimension.
 Dynamics on the padic numbers.
 BanachTarski paradox, space filling curves.
Mihai Stoiciu
Research interests: Mathematical Physics and Functional Analysis. I am interested in the study of the spectral properties of various operators arising from mathematical physics – especially the Schrodinger operator. In particular, I am investigating the distribution of the eigenvalues for special classes of selfadjoint and unitary random matrices.
Topics in mathematical physics, functional analysis and probability including:
 Investigate the spectrum of the Schrodinger operator. Possible research topics: Find good estimates for the number of bound states; Analyze the asymptotic growth of the number of bound states of the discrete Schrodinger operator at large coupling constants.
 Study particular classes of orthogonal polynomials on the unit circle.
 Investigate numerically the statistical distribution of the eigenvalues for various classes of random CMV matrices.
 Study the general theory of point processes and its applications to problems in mathematical physics.
Possible colloquium topics:
Any topics in mathematics, mathematical physics, functional analysis, or probability, such as:
 The Schrodinger operator.
 Orthogonal polynomials on the unit circle.
 Statistical distribution of the eigenvalues of random matrices.
 The general theory of point processes and its applications to problems in mathematical physics.
Elizabeth Upton
Research Interests: My research interests center around network science, with a focus on regression methods for networkindexed data. Networks are used to capture the relationships between elements within a system. Examples include social networks, transportation networks, and biological networks. I also enjoy tackling problems with pragmatic applications and am therefore interested in applied interdisciplinary research.
 Regression models for network data: how can we incorporate network structure (and dependence) in our regression framework when modeling a vertexindexed response?
 Identify effects shaping network structure. For example, in social networks, the phrase “birds of a feather flock together” is often used to describe homophily. That is, those who have similar interests are more likely to become friends. How can we capture or test this effect, and others, in a regression framework when modeling edgeindexed responses?
 Extending models for multilayer networks. Current methodologies combine edges from multiple networks in some sort of weighted averaging scheme. Could a penalized multivariate approach yield a more informative model?
 Developing algorithms to make inference on large networks more efficient.
 Any topic in linear or generalized linear modeling (including mixedeffects regression models, zeroinflated regressions, etc.).
 Applied statistics research. In collaboration with a scientist or social scientist, use appropriate statistical methodology to answer an interesting scientific question.
 Any applied statistics research project/paper
 Topics in linear or generalized linear modeling
 Network visualizations and statistics
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COLLEGE OF LIBERAL ARTS AND SCIENCES
Department of Mathematics
Thesis formatting, introduction.
If you write a Ph.D. thesis, you have to follow the specifications of the graduate school.
Additional information and answers to frequently asked questions can be found the graduate school’s Doctoral Degree Programs page.
A thesis in mathematics is invariably written in some form of LaTeX. It is usually quite a large LaTeX project, so it should not be your first attempt at typesetting. This implies that you should have typed a couple articles, quizzes, homeworks or exams in LaTeX before embarking on this. Below, two options have been created that conform to the guidelines set forth by the graduate school. The first is a minimal option that builds on the familiar book class that comes standard with any LaTeX distribution, while the second is a class file to be used in place of the book class, but contains extra content not suitable for all users. You may choose the option that works best in your case.
Below are a few of the welldone thesis variants from our department.
 Thesis class by Waseet Kazmi – 2023
 Thesis class by Ben Salisbury – 2012
 Thesis class by Marc Corluy – 2000
After unzipping put files into one directory. Some browsers (e.g. Safari on the Macs in the department) will put the files on your desktop. In this case create a new folder and put them all in there. In any case, make this move before you start compiling, because LaTeX generates a multitude of files when compiling and your desktop will turn into a (more?) disorderly mess.
Also make sure that the extensions are preserved. Some browsers have a tendency to slap on “.txt” at the end.
Open a text editor or a dedicated LaTeX editor, such as TeXShop (installed on department Macs). When you are typing LaTeX code, it is usually clearer to use a fixed width font so that you have a clear view of your indentations and matrices (should there be any). In TeXShop, a good choice is “Courier Bold 14pts”. This font also has different characters for “” and lowercase L. This is particularly important if you are trying to typeset tables where both “” and lowercase L are used in the declaration.
You will now have to open some of the files that you downloaded and edit them. Here are descriptions of the set of files prepared by Ben Salisbury, listed (as best as possible) in order of priority.
 macros.tex This file is the heart of your personalization. If you have been using LaTeX for your other manuscripts and have developed your own set of userdefined commands, then you should put them in this file. If you are importing text into one of the later files from an older LaTeX file with predefined commands, you will want your personal macros to be loaded already before fumbling with LaTeX error messages.
so those who prefer to use, say,
 thesis.tex Lines 8 through 17 of this file require the user to input their personal data; i.e., name, degrees, year of graduation, advisory committee, and title. Further down in the file, you’ll notice the command \input{ch1.tex} . This imports the text from ch1.tex to the current position in this file. By copying the command and changing ch1 to ch2 (and so on), you will be able to link all chapters of your work to this file. Essentially, this file is the glue that holds the whole project together. This is also the file on which the TeX engine is run to obtain the desired output.
 abstract.tex , acknowledgments.tex , and ch1.tex should be selfexplanatory. Of course, you should have more than one chapter to their thesis. The challenge of creating LaTeX files for the subsequent chapters is left to the user. Good luck!
 thesis.bib This is a standard BibTeX file to be used as the source for your bibliography output. This may take some time to learn, so the file comes preloaded with a sample .bib file. Your best bet is find some literature on BibTeX to tackle this beast. Of course, one could simply replace the bibligraphy declarations in the thesis.tex with a manual bibliography, as Marc Corluy does in his setup below. To each his own.
 frontmatter.tex Simply put: don’t touch it. If you need to make changes here, you should probably consider using Marc Corluy’s template (unless you are familiar enough to make the appropriate changes).
Here are comments on the files prepared by Marc Corluy.
 bibliography.tex is not your first concern. The references that are listed in there are there to give you an idea about the exact format in which a book or article should be entered into this file.
 chapter1.tex , chapter2.tex , and introchapter.tex are almost empty; they are merely there to show you how to use titles and sections.
 The file definitions.tex you can completely ignore if you want to. It contains (re)definitions of some symbols and a fairly long list of basic mathematical symbols and functions. It can be handy to get a certain feel for how to use “def” in LaTeX and you can also add whatever you end up using often in your thesis.
 Most of the static data (title of the thesis, your previous degrees, your advisors, acknowledgment etc.) are entered in front_matter.tex . The comments in this file will explain you what to put where.
 If you want to explain some of the notation that you use in your thesis, you should do so in notationpage.tex . It is technically part of the front matter of the thesis, but it is a separate file because this is probably the only part of the front matter data that changes as the thesis evolves.
 You will probably not change much to settings.tex . This file loads a lot of the extensions to LaTeX and defines the elements of the amsthm.sty package, as is explained in the comments in settings.tex .
 As you can guess, thesis.tex is the file where it all comes together. The includeonly command will allow you to compile only parts of your thesis if you prefer to do so. Note that you should compile the thesis twice to make sure that all the labels are set correctly.
 In principle, you should never change anything to uconnthesis.cls .
Write your thesis. Good Luck.
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Mathematics PhD theses
A selection of Mathematics PhD thesis titles is listed below, some of which are available online:
2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991
Reham Alahmadi  Asymptotic Study of Toeplitz Determinants with FisherHartwig Symbols and Their DoubleScaling Limits
Anne Sophie Rojahn – Localised adaptive Particle Filters for large scale operational NWP model
Melanie Kobras – Low order models of storm track variability
Ed Clark – Vectorial Variational Problems in L∞ and Applications to Data Assimilation
Katerina Christou – Modelling PDEs in Population Dynamics using Fixed and Moving Meshes
Chiara Cecilia Maiocchi – Unstable Periodic Orbits: a language to interpret the complexity of chaotic systems
Samuel R Harrison – Stalactite Inspired Thin Film Flow
Elena Saggioro – Causal network approaches for the study of subseasonal to seasonal variability and predictability
Cathie A Wells – Reformulating aircraft routing algorithms to reduce fuel burn and thus CO 2 emissions
Jennifer E. Israelsson – The spatial statistical distribution for multiple rainfall intensities over Ghana
Giulia Carigi – Ergodic properties and response theory for a stochastic twolayer model of geophysical fluid dynamics
André Macedo – Localglobal principles for norms
Tsz Yan Leung – Weather Predictability: Some Theoretical Considerations
Jehan Alswaihli – Iteration of Inverse Problems and Data Assimilation Techniques for Neural Field Equations
Jemima M Tabeart – On the treatment of correlated observation errors in data assimilation
Chris Davies – Computer Simulation Studies of Dynamics and SelfAssembly Behaviour of Charged Polymer Systems
Birzhan Ayanbayev – Some Problems in Vectorial Calculus of Variations in L∞
Penpark Sirimark – Mathematical Modelling of Liquid Transport in Porous Materials at Low Levels of Saturation
Adam Barker – Path Properties of Levy Processes
Hasen Mekki Öztürk – Spectra of Indefinite Linear Operator Pencils
Carlo Cafaro – Information gain that convectivescale models bring to probabilistic weather forecasts
Nicola Thorn – The boundedness and spectral properties of multiplicative Toeplitz operators
James Jackaman – Finite element methods as geometric structure preserving algorithms
Changqiong Wang  Applications of Monte Carlo Methods in Studying Polymer Dynamics
Jack Kirk  The molecular dynamics and rheology of polymer melts near the flat surface
Hussien Ali Hussien Abugirda  Linear and Nonlinear NonDivergence Elliptic Systems of Partial Differential Equations
Andrew Gibbs  Numerical methods for high frequency scattering by multiple obstacles (PDF2.63MB)
Mohammad Al Azah  Fast Evaluation of Special Functions by the Modified Trapezium Rule (PDF913KB)
Katarzyna (Kasia) Kozlowska  RiemannHilbert Problems and their applications in mathematical physics (PDF1.16MB)
Anna Watkins  A Moving Mesh Finite Element Method and its Application to Population Dynamics (PDF2.46MB)
Niall Arthurs  An Investigation of Conservative MovingMesh Methods for Conservation Laws (PDF1.1MB)
Samuel Groth  Numerical and asymptotic methods for scattering by penetrable obstacles (PDF6.29MB)
Katherine E. Howes  Accounting for Model Error in FourDimensional Variational Data Assimilation (PDF2.69MB)
Jian Zhu  Multiscale Computer Simulation Studies of Entangled Branched Polymers (PDF1.69MB)
Tommy Liu  Stochastic Resonance for a Model with Two Pathways (PDF11.4MB)
Matthew Paul Edgington  Mathematical modelling of bacterial chemotaxis signalling pathways (PDF9.04MB)
Anne Reinarz  Sparse spacetime boundary element methods for the heat equation (PDF1.39MB)
Adam ElSaid  Conditioning of the WeakConstraint Variational Data Assimilation Problem for Numerical Weather Prediction (PDF2.64MB)
Nicholas Bird  A MovingMesh Method for High Order Nonlinear Diffusion (PDF1.30MB)
Charlotta Jasmine Howarth  New generation finite element methods for forward seismic modelling (PDF5,52MB)
Aldo Rota  From the classical moment problem to the realizability problem on basic semialgebraic sets of generalized functions (PDF1.0MB)
Sarah Lianne Cole  Truncation Error Estimates for Mesh Refinement in Lagrangian Hydrocodes (PDF2.84MB)
Alexander J. F. Moodey  Instability and Regularization for Data Assimilation (PDF1.32MB)
Dale Partridge  Numerical Modelling of Glaciers: Moving Meshes and Data Assimilation (PDF3.19MB)
Joanne A. Waller  Using Observations at Different Spatial Scales in Data Assimilation for Environmental Prediction (PDF6.75MB)
Faez Ali ALMaamori  Theory and Examples of Generalised Prime Systems (PDF503KB)
Mark Parsons  Mathematical Modelling of Evolving Networks
Natalie L.H. Lowery  Classification methods for an illposed reconstruction with an application to fuel cell monitoring
David Gilbert  Analysis of largescale atmospheric flows
Peter Spence  Free and Moving Boundary Problems in Ion Beam Dynamics (PDF5MB)
Timothy S. Palmer  Modelling a single polymer entanglement (PDF5.02MB)
Mohamad Shukor Talib  Dynamics of Entangled Polymer Chain in a Grid of Obstacles (PDF2.49MB)
Cassandra A.J. Moran  Wave scattering by harbours and offshore structures
Ashley Twigger  Boundary element methods for high frequency scattering
David A. Smith  Spectral theory of ordinary and partial linear differential operators on finite intervals (PDF1.05MB)
Stephen A. Haben  Conditioning and Preconditioning of the Minimisation Problem in Variational Data Assimilation (PDF3.51MB)
Jing Cao  Molecular dynamics study of polymer melts (PDF3.98MB)
Bonhi Bhattacharya  Mathematical Modelling of Low Density Lipoprotein Metabolism. Intracellular Cholesterol Regulation (PDF4.06MB)
Tamsin E. Lee  Modelling timedependent partial differential equations using a moving mesh approach based on conservation (PDF2.17MB)
Polly J. Smith  Joint state and parameter estimation using data assimilation with application to morphodynamic modelling (PDF3Mb)
Corinna Burkard  Threedimensional Scattering Problems with applications to Optical Security Devices (PDF1.85Mb)
Laura M. Stewart  Correlated observation errors in data assimilation (PDF4.07MB)
R.D. Giddings  Mesh Movement via Optimal Transportation (PDF29.1MbB)
G.M. Baxter  4DVar for high resolution, nested models with a range of scales (PDF1.06MB)
C. Spencer  A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table.
P. Jelfs  A Cproperty satisfying RKDG Scheme with Application to the Morphodynamic Equations (PDF11.7MB)
L. Bennetts  Wave scattering by ice sheets of varying thickness
M. Preston  Boundary Integral Equations method for 3D water waves
J. Percival  Displacement Assimilation for Ocean Models (PDF  7.70MB)
D. Katz  The Application of PVbased Control Variable Transformations in Variational Data Assimilation (PDF 1.75MB)
S. Pimentel  Estimation of the Diurnal Variability of sea surface temperatures using numerical modelling and the assimilation of satellite observations (PDF5.9MB)
J.M. Morrell  A cell by cell anisotropic adaptive mesh Arbitrary Lagrangian Eulerian method for the numerical solution of the Euler equations (PDF7.7MB)
L. Watkinson  Four dimensional variational data assimilation for Hamiltonian problems
M. Hunt  Unique extension of atomic functionals of JB*Triples
D. Chilton  An alternative approach to the analysis of twopoint boundary value problems for linear evolutionary PDEs and applications
T.H.A. Frame  Methods of targeting observations for the improvement of weather forecast skill
C. Hughes  On the topographical scattering and neartrapping of water waves
B.V. Wells  A moving mesh finite element method for the numerical solution of partial differential equations and systems
D.A. Bailey  A ghost fluid, finite volume continuous rezone/remap Eulerian method for timedependent compressible Euler flows
M. Henderson  Extending the edgecolouring of graphs
K. Allen  The propagation of large scale sediment structures in closed channels
D. Cariolaro  The 1Factorization problem and same related conjectures
A.C.P. Steptoe  Extreme functionals and StoneWeierstrass theory of inner ideals in JB*Triples
D.E. Brown  Preconditioners for inhomogeneous anisotropic problems with spherical geometry in ocean modelling
S.J. Fletcher  High Order Balance Conditions using Hamiltonian Dynamics for Numerical Weather Prediction
C. Johnson  Information Content of Observations in Variational Data Assimilation
M.A. Wakefield  Bounds on Quantities of Physical Interest
M. Johnson  Some problems on graphs and designs
A.C. Lemos  Numerical Methods for Singular Differential Equations Arising from Steady Flows in Channels and Ducts
R.K. Lashley  Automatic Generation of Accurate Advection Schemes on Structured Grids and their Application to Meteorological Problems
J.V. Morgan  Numerical Methods for Macroscopic Traffic Models
M.A. Wlasak  The Examination of Balanced and Unbalanced Flow using Potential Vorticity in Atmospheric Modelling
M. Martin  Data Assimilation in Ocean circulation models with systematic errors
K.W. Blake  Moving Mesh Methods for NonLinear Parabolic Partial Differential Equations
J. Hudson  Numerical Techniques for Morphodynamic Modelling
A.S. Lawless  Development of linear models for data assimilation in numerical weather prediction .
C.J.Smith  The semi lagrangian method in atmospheric modelling
T.C. Johnson  Implicit Numerical Schemes for Transcritical Shallow Water Flow
M.J. Hoyle  Some Approximations to Water Wave Motion over Topography.
P. Samuels  An Account of Research into an Area of Analytical Fluid Mechnaics. Volume II. Some mathematical Proofs of Property u of the Weak End of Shocks.
M.J. Martin  Data Assimulation in Ocean Circulation with Systematic Errors
P. Sims  Interface Tracking using Lagrangian Eulerian Methods.
P. Macabe  The Mathematical Analysis of a Class of Singular ReactionDiffusion Systems.
B. Sheppard  On Generalisations of the StoneWeisstrass Theorem to Jordan Structures.
S. Leary  Least Squares Methods with Adjustable Nodes for Steady Hyperbolic PDEs.
I. Sciriha  On Some Aspects of Graph Spectra.
P.A. Burton  Convergence of flux limiter schemes for hyperbolic conservation laws with source terms.
J.F. Goodwin  Developing a practical approach to water wave scattering problems.
N.R.T. Biggs  Integral equation embedding methods in wavediffraction methods.
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I. MacDonald  Analysis and computation of steady open channel flow .
A. Morton  Higher order Godunov IMPES compositional modelling of oil reservoirs.
S.M. Allen  Extended edgecolourings of graphs.
M.E. Hubbard  Multidimensional upwinding and grid adaptation for conservation laws.
C.J. Chikunji  On the classification of finite rings.
S.J.G. Bell  Numerical techniques for smooth transformation and regularisation of timevarying linear descriptor systems.
D.J. Staziker  Water wave scattering by undulating bed topography .
K.J. Neylon  Nonsymmetric methods in the modelling of contaminant transport in porous media. .
D.M. Littleboy  Numerical techniques for eigenstructure assignment by output feedback in aircraft applications .
M.P. Dainton  Numerical methods for the solution of systems of uncertain differential equations with application in numerical modelling of oil recovery from underground reservoirs .
M.H. Mawson  The shallowwater semigeostrophic equations on the sphere. .
S.M. Stringer  The use of robust observers in the simulation of gas supply networks .
S.L. Wakelin  Variational principles and the finite element method for channel flows. .
E.M. Dicks  Higher order Godunov blackoil simulations for compressible flow in porous media .
C.P. Reeves  Moving finite elements and overturning solutions .
A.J. Malcolm  Data dependent triangular grid generation. .
Masters and PhD Thesis and Defense Guidelines
The crucial work produced in the course of graduate study for PhD students is a doctoral dissertation. MS students may also choose to culminate their studies by completing a master's thesis. There is no length requirement for these works, and they are read and approved by a committee put together by the student and their advisor. For PhD candidates, this committee consists of four members of which one must be an outside examiner from outside Tufts. For MS candidates, the committee must include at least 3 faculty members. The department provides a LaTeX template designed to help students meet the Tufts formatting requirements with basic instructions for setting up the document, which can be found on the Organization for Graduate Students in Mathematics Resources page .
Thesis submissions deadlines and other important guidelines can be found in the GSAS Handbook and GSAS' Graduation website . It is essential that you read and understand the Graduate School requirements in order to ensure an ontime graduation. Additionally, students must submit the "Thesis/Dissertation – Request for Final Approval" form to the chair of their committee once a final draft of the document, including any revisions recommended by the committee, is approved for publication.
During the electronic submission process, students are given the opportunity to order bound paper copies of their thesis or dissertation from ProQuest. The department requests that PhD students reserve one of these bound copies to be kept in our library, and will cover the costs for that extra copy.
Thesis Defense
In the last term before graduation, the student and advisor will schedule a thesis defense, which is announced to and open to the whole department and to visitors invited by the candidate.
The standard format is a presentation by the student followed by questions from the audience. The general audience is then asked to leave, and questions from the committee follow. In addition to the Graduate School rules, the Math Department has some additional requirements regarding thesis defenses:
 The defense must be scheduled for a date at least 1 week prior to the thesis submission deadline, allowing time for any corrections to the thesis suggested by the committee to be made;
 The defense date must be finalized and confirmed with the thesis committee 2 weeks in advance;
 The defense date must be announced to the Department and advertised at least 2 weeks prior to the defense date, and with subsequent reminders announced by the office;
 Students are expected to send a draft of their thesis to their committee 2 weeks prior to their defense. This does not have to be a finalized version, but should be substantially complete;
 While the defense must occur with the student and all committee members (except one with permission) attending in person, the defense may be streamed virtually with the consent of the student and committee, allowing for a diverse audience. Similarly, if the student and committee agrees, the public portion of the defense may be recorded. It is strongly encouraged that faculty and graduate students in the department attend these defenses to show support for each other.
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Mathematics Undergraduate Theses
Theses from 2019 2019.
The Name Tag Problem , Christian Carley
The Hyperreals: Do You Prefer NonStandard Analysis Over Standard Analysis? , Chloe Munroe
Theses from 2018 2018
A Convolutional Neural Network Model for Species Classification of Camera Trap Images , Annie Casey
Pythagorean Theorem Area Proofs , Rachel Morley
Euclidian Geometry: Proposed Lesson Plans to Teach Throughout a One Semester Course , Joseph Willert
Theses from 2017 2017
An Exploration of the Chromatic Polynomial , Amanda Aydelotte
Complementary Coffee Cups , Brandon Sams
Theses from 2016 2016
Nonlinear Integral Equations and Their Solutions , Caleb Richards
Principles and Analysis of Approximation Techniques , Evan Smith
Theses from 2014 2014
An Introductory Look at Deterministic Chaos , Kenneth Coiteux
A Brief Encounter with Linear Codes , Brent ElBakri
Axioms of Set Theory and Equivalents of Axiom of Choice , Farighon Abdul Rahim
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A.I. Can Write Poetry, but It Struggles With Math
A.I.’s math problem reflects how much the new technology is a break with computing’s past.
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By Steve Lohr
In the school year that ended recently, one class of learners stood out as a seeming puzzle. They are hardworking, improving and remarkably articulate. But curiously, these learners — artificially intelligent chatbots — often struggle with math.
Chatbots like Open AI’s ChatGPT can write poetry, summarize books and answer questions, often with humanlevel fluency. These systems can do math, based on what they have learned, but the results can vary and be wrong. They are finetuned for determining probabilities, not doing rulesbased calculations. Likelihood is not accuracy , and language is more flexible, and forgiving, than math.
“The A.I. chatbots have difficulty with math because they were never designed to do it,” said Kristian Hammond, a computer science professor and artificial intelligence researcher at Northwestern University.
The world’s smartest computer scientists, it seems, have created artificial intelligence that is more liberal arts major than numbers whiz.
That, on the face of it, is a sharp break with computing’s past. Since the early computers appeared in the 1940s, a good summary definition of computing has been “math on steroids.” Computers have been tireless, fast, accurate calculating machines. Crunching numbers has long been what computers are really good at, far exceeding human performance.
Traditionally, computers have been programmed to follow stepbystep rules and retrieve information in structured databases. They were powerful but brittle. So past efforts at A.I. hit a wall.
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COMMENTS
Advice on Writing a Senior Thesis Harvard University Mathematics Department Last update: March 2017 This document contains advice from students who wrote a senior thesis, and from faculty involved in the senior thesis process, from advising to reading theses and examining students on them. Advice from students
Honors in Mathematics Writing a Senior Thesis (20212022) 1. Candidacy for Honors. A senior thesis is required for high or highest honors in Mathematics, whereas for straight honors (neither high nor highest), a senior thesis can be submit or four extra courses in Mathematics or approved related fields can be taken (above the required twelve ...
A senior thesis is required by the Mathematics concentration to be a candidate for graduation with the distinction of High or Highest honors in Mathematics. See the document ' Honors in Mathematics ' for more information about honors recommendations and about finding a topic and advisor for your thesis. With regards to topics and advisors ...
Defending Your Thesis. Setting a time to defend your dissertation can be frustrating. Contact your committee members well in advance in order to check availability and schedule a date/time. You would think that finding a time for 6 people to meet would be an easy task. However, it can be exceedingly difficult.
Overview. A senior thesis can form a valuable part of a student's experience in the Mathematics Major. It is intended to allow students to cover significant areas of mathematics not covered in course work, or not covered there in sufficient depth. The work should be independent and creative.
A Mathematician's Survival Guide: Graduate School and Early Career Development. A Primer of Mathematical Writing. The first one contains subsection 4.6 which deals specifically with writing a thesis, the second one is on mathematical writing in general but it does not really deal with the theses per se. Share.
Senior Theses. An undergraduate thesis is a singlyauthored mathematics document, usually between 10 and 80 pages, on some topic in mathematics. The thesis is typically a mixture of exposition of known mathematics and an account of your own research. To write an undergraduate thesis, you need to find a faculty advisor who will sponsor your project.
The mathematics degree programs conclude with a Bachelor's or Master's thesis, in which independent work on a mathematical topic is to be demonstrated. The Examination Board has compiled the most important requirements for theses and some assessment criteria as guidelines. Please read the document carefully before you register your thesis.
Theses/Dissertations from 2020. Mathematical Identities of Students with Mathematics Learning Dis/abilities, Emma Lynn Holdaway. Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures, Porter Peterson Nielsen. Student Use of Mathematical Content Knowledge During Proof Production, Chelsey Lynn ...
Senior thesis is a good choice for students wanting to improve all these, with special emphasis on mathematical research on a topic chosen by the student. Senior theses also involve significant amounts of writing, presentations, and checkins with other math thesis writers. To ensure that each senior thesis writer has an enriching experience ...
The paper size used should be 8 1⁄2" by 11". The left margin should be 1.25 inches, and the top, bottom, and right margins should each be 1 inch. All pages should be numbered. The text should be doublespaced, except for quotations of five lines or longer, which should be singlespaced and indented. The text in the body of the thesis ...
For many reports, a conclusion or summary is appropriate. Your thesis should be a coherent, selfcontained piece of work. Your writing should conform to the highest standards of English. Aim at clarity, precision and correct grammar. Start sentences with capital letters and end them with fullstops.
In writing a mathematical Ph.D. thesis, it is far more tolerable to be tediouslylengthy than having a gap in the proofs. I think what he means is that whenever in doubt, adding more details to make the argument clearer is always better, even if sometimes doing this may make the proof too wordy. Now if I really follow his advice literally, it ...
I am trying to write a mathematical thesis to be both rigorous and easily understood by an undergraduate cs student. tl;Dr Do you have any tips about how to balance writing a rigorous thesis and keeping it simple enough and self sufficient for a CS student to read (without writing a 10!  factorial of 10 pages text)
9. I think this varies a lot. But for Germany your first question can be answers succinctly: In a Master's thesis you should show that you have potential for research. On the other hand, expectations vary a lot between advisors. But certainly you do not have to prove a new theorem or develop a new theory.
The whole experience of writing a thesis should be intense, and ultimately rewarding. Also, since this area of math has so many facets and has so many entrance points, I have had thesis students from wildly different mathematical backgrounds do wonderful work; hence all welcome. Possible thesis topics: Generalizations of continued fractions.
advice about writing any mathematics paper, not just a thesis, is provided in [3], and also [2, 4, 5].) 1. Basic requirements Your thesis must make a contribution to some eld of mathematics, and also report what was previously known about the topic. A Ph.D. thesis is expected to have a signi cant amount of original mathematical research.
Introduction. If you write a Ph.D. thesis, you have to follow the specifications of the graduate school. Additional information and answers to frequently asked questions can be found the graduate school's Doctoral Degree Programs page.. A thesis in mathematics is invariably written in some form of LaTeX.
original mathematics, but most do not. Why Write a Thesis? The Mathematics Department strongly recommends that its concentrators write a senior thesis. Writing a thesis provides a glimpse of life as a graduate student in mathematics, and as a professionalmathematician. It will also propel you towards the frontiers of current mathematical ...
A selection of Mathematics PhD thesis titles is listed below, some of which are available online: 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991. 2024. Reham Alahmadi  Asymptotic Study of Toeplitz Determinants with FisherHartwig Symbols and Their DoubleScaling Limits
The defense must be scheduled for a date at least 1 week prior to the thesis submission deadline, allowing time for any corrections to the thesis suggested by the committee to be made; The defense date must be finalized and confirmed with the thesis committee 2 weeks in advance; The defense date must be announced to the Department and ...
The Senior Thesis in Mathematical Sciences course allows students to engage in independent mathematical work in an active and modern subject area of the mathematical sciences, guided by an official research faculty member in the department of mathematics and culminating in a written thesis presented in an appropriate public forum.
biomathematics: introduction to the mathematical model of the hepatitis c virus, lucille j. durfee. pdf. analysis and synthesis of the literature regarding active and direct instruction and their promotion of flexible thinking in mathematics, genelle elizabeth gonzalez. pdf. life expectancy, ali r. hassanzadah. pdf
Writing a thesis is unlike any other undergraduate assignment that you've undertaken, and, to do it well, you'll need to commit a substantial amount of time towards its completion. While the time commitment will vary over the course of junior spring to senior spring, you should expect to allocate at least part of your summer towards work 
Can Write Poetry, but It Struggles With Math A.I.'s math problem reflects how much the new technology is a break with computing's past. Listen to this article · 7:22 min Learn more