math senior thesis topics

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Senior Theses

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The Department of Mathematical Sciences encourages math majors to write a senior thesis (M 499) in order to fulfill the Advanced College Writing Requirement (formerly known as the Upper-Division Writing Requirement).

Students who plan to write a senior thesis should select a research topic during their Junior year. The best way to do this is to approach a professor with whom you would like to work and ask for suggestions of possible research topics.

Writing a senior thesis improves students’ writing skills as they produce polished mathematical documents that they can share with pride. Revision and resubmission of drafts following the advisor’s comments are required. All senior theses are assessed using the Assessment Rubric included below.

Senior Thesis Assessment Rubric

Department of mathematics, indiana university southeast.

The Senior Thesis is intended to be a paper that demonstrates a student’s ability to learn mathematics on his or her own, and to be able to write in a manner which both demonstrates his or her understanding of the mathematics and clearly communicates the mathematics to the intended audience.  The Senior Thesis will be evaluated on the mathematical content and on the writing, according to the criteria detailed below.  To be judged to be satisfactory, the Senior Thesis must meet all of the criteria below for satisfactory performance; to be judged excellent, the Senior Thesis must also meet the criteria below for excellence in each category.  (This rubric was adapted from a model produced at Southern Oregon University’s Mathematics Department.)

Mathematical Content:

• Excellent: The thesis has a clear, focused statement of a research problem or topic, and the research problem is interesting and of a level appropriate to a senior mathematics major. The research plan is well-thought-out.
• Satisfactory: The statement of research problem may lack some clarity or focus, or the research problem may be of less interest though at a level appropriate to a senior mathematics major. The research plan is adequate to address the research problem.
• Unsatisfactory: The statement of the research problem is missing or confused, or the research problem is uninteresting or trivial. The research plan is inadequate or missing.
• Excellent: The thesis will demonstrate an accurate understanding of the research problem, and it will demonstrate a convincing thoroughness of research. In particular, the thesis should cite a sufficient number of sound, peer-reviewed sources. (While useful, sources on the world-wide web are not generally peer-reviewed and should not be relied upon to the exclusion of peer-reviewed books or periodicals.)
• Satisfactory: The thesis will demonstrate a largely accurate understanding of the research problem. The research may be less than convincing in its thoroughness, citing an insufficient number of sound, peer-reviewed sources, but it will reach essentially the same conclusions as would be reached by a convincing and thorough research effort.
• Unsatisfactory: The thesis fails to demonstrate an accurate understanding of the research problem, and inadequate research (insufficient sources or sources of poor quality) results in erroneous, misleading or missing conclusions.
• Excellent: It is clear from the thesis that the student has a good, working knowledge and understanding of the mathematics he or she is discussing. For example, if a technique for solving a certain type of equation is being discussed, it must be clear that the student can operate the technique on his or her own. The mathematics must be at a level appropriate to a senior thesis.
• Satisfactory: The mathematical content of the thesis is generally correct but displays some minor confusion or lack of clarity, while the student demonstrates a working knowledge of most of the mathematics. The mathematics is at the level expected of a senior but may be somewhat insubstantial.
• Unsatisfactory: The thesis betrays a lack of understanding of the mathematics under discussion. The mathematics is trivial, incorrect or incomplete; in particular, if proofs of theorems would be appropriate, these are missing or garbled.
• Excellent: The thesis has a clear organization that effectively develops the central idea. There is an introduction including a clear statement of the research problem and outline of the research method. The development of arguments through the paper is clear and logically organized, and the conclusion is apt. The thesis does not ramble nor are there awkward or unexpected transitions.
• Satisfactory: The thesis is organized with an introduction which includes a statement of the research problem and outline of the research method, but the organization lacks some clarity or is not completely logical. There is some rambling or awkward or unexpected transitions. There is a conclusion to the thesis which summarizes what has been accomplished.
• Unsatisfactory: The thesis has no clear organization; the thesis lacks an introduction or the introduction does not indicate the research problem; the introduction does not introduce the research method. The development of the central idea is confused or unclear. There are no transitions – the thesis appears to be disconnected sections that have been juxtaposed. There is no conclusion to the thesis summarizing what has been accomplished.
• Excellent: Choice of voice is appropriate for mathematical writing; word use is precise and accurate; and the writing is lively and reads well. The mathematical content is clear, and it is clear from the writing that the student has a correct and complete understanding of the mathematical content of the thesis. Assertions are clearly stated and well-supported.
• Satisfactory: Word use is sometimes inexact or imprecise or the writing is mechanical or plodding. The writing is generally clear but is sometimes confused or hesitant; the student appears to have an understanding of the mathematical content that is largely correct but not completely so. Most assertions are generally clear and are given support.
• Unsatisfactory: The thesis is hard to read or follow; words (particularly technical terms) are used incorrectly; or sentences are incomplete or broken. The writing is confused or hesitant, or betrays a serious lack of understanding of the mathematical content. Assertions are made without support, or are incorrect. The thesis lacks detail.
• Excellent: References and citations are correct and complete; it is clear what information from other sources is integrated into the thesis, and it is clear where that information came from.
• Satisfactory: References and citations are complete and generally correct but it is not always clear exactly what information from other sources is integrated into the thesis.
• Unsatisfactory: References and citations are not complete or have errors that prevent the reader from knowing the source of cited information. It is unclear what information from outside sources is integrated into the thesis.
• Excellent: There are no faults in spelling, punctuation and sentence construction. The thesis is formatted in an appropriate and professional manner. The care in proofreading and formatting has strengthened the development of the central idea of the thesis.
• Satisfactory: The thesis is formatted in an appropriate manner and there are few faults in spelling, punctuation and sentence construction. A lack of thoroughness in proof reading has not seriously marred the thesis nor confused the development of the central idea.
• Unsatisfactory: The thesis is marred by numerous errors of grammar, spelling, punctuation or sentence construction. Formatting is not appropriate for a senior thesis. A lack of proof reading has confused the development of the central idea of the thesis.

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Guidelines for Senior Theses in the Mathematics Department

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.

Recent Senior Theses

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.

Submitting the Completed Thesis

The supervisor must approve the student's thesis. No later than April 15th, the student must submit a completed thesis to the thesis supervisor. If the supervisor asks the student to make changes, the student has until April 30th to do so. By April 30th, the student must give the supervisor two paper copies and an electronic copy of the thesis in final form. The electronic copy will be posted on the department's web site. [Students who expect to graduate in January must submit a completed thesis by November 15th and the final form by November 30th.]

Form 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 one-half 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.

Merit of the Senior Thesis

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.

Honors Consideration

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.

Mathematics Library Collection of Senior Theses

Meritorious senior theses will be catalogued, bound, and stored in the Mathematics Library.

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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 check-ins 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

• One-semester thesis: A one-semester thesis may be either in the fall (MATH 457) or winter (MATH 458). One-semester theses are due by the Friday of the final examination period of the semester in which the student is writing their thesis.
• Two-semester thesis: Two-semester 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 two-semester 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 year-long 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 one-semester 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.
• one-semester thesis students present a poster or a talk;
• two-semester non-honors 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 College-designated 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.

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Department of Mathematics

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Senior Project Marketplace

Senior Project (MATH 401) is designed to be a capstone experience for Math undergraduates, where the students engage in research activities guided by a faculty member. To enroll in MATH 401, you need to choose a project topic and get in touch with a faculty member. You can come up with your own project idea, or choose one from the list below. The list is by no means exhaustive but will give you an idea of what kind of research each researcher is working on.  These are examples of projects supervised by math department faculty.

Senior project ideas

Joe champion - math education, statistical modeling of math education achievement.

Learn about large-scale educational achievement data and techniques for predicting students’ math achievement. Involves data wrangling, intermediate coding in R or Python (mostly adapting existing code), and a focus on data visualization. Background in mathematics education and/or statistics preferred.

High School Mathematics Curriculum Development

For mathematics education students – modify and create Desmos Teacher activities to align with high school mathematics standards. Focus on data, modeling, and technology-assisted representations.

Middle School Mathematics Curriculum Development

Adapt activities from the Algebra through Visual Patterns curriculum for delivery in the Desmos Teacher Activities platform. Involves some testing with students and collaboration with math education researchers.

Other project ideas

Dig into the history of a K-12 math topic and write a paper / make a poster, create an original math video.

Contact info

Joe Champion Faculty Profile

Samuel Coskey - Set theory, logic, and combinatorics

Combinatorics and graph theory.

Learn something new in one of these areas that wasn’t covered in Math 189/287/387. Use a new book, book chapter, online notes, or published article as a resource. Present the motivation, examples, and results with a poster.

Algebra or analysis or geometry

Learn something new in one of these areas that wasn’t covered in Math 305/311/314/405/414. Use a new book, book chapter, online notes, or published article as a resource. Present the motivation, examples, and results with a poster.

Math education

Choose a topic in college-level mathematics to present at the middle or high school level. Create a detailed lesson plan.

I am open to exploring anything in pure mathematics (and applied mathematics if you can take the lead). The important thing is to find resources at the right level for you.

Contact Info

https://scoskey.org

Jens Harlander - Topology and Algebra (Group Theory)

Topics in graph theory, topics concerning the topology of surfaces, topics in linear algebra over rings.

Jens Harlander Faculty Profile Page

Uwe Kaiser - Geometric and Algebraic Topology, Quantum Computing

Quantum computing algorithms.

This project asks you to have some programming experience. You work on a specific quantum algorithm. You study programming in Microsoft’s quantum computing kit, see https://www.microsoft.com/en-us/quantum/development-kit, try out examples, and study properties of the algorithm. Basic linear algebra skills are necessary in order to understand how algorithms are implemented using circuits. The minimal expectation is a poster to be presented in the senior showcase.

Tangles and Electrical Networks

In 1993 Goldman and Kauffman interpreted the continued fraction of a tangle as a conductance of a corresponding network. This projects asks to search for further relations between electrical networks and invariants of links and tangles. The starting point is a paper of mine on band-operations on links leading to a formula similar to the one by Goldman/Kauffman. Basic linear algebra and some familiarity with discrete mathematics like graph theory are helpful, also knowledge of basic notions concerning electrical networks. The minimal expectation is a poster to be presented in the senior showcase.

Robotics and Topology

Topology and robotics are related through notion of configuration space. For example the configuration space of a robot arm in 3-space is a product of 2-spheres. Restrictions on motions lead to more interesting topology of configuration spaces. The goal is to study the complexity of basic examples through well-known theory developed by Farber. Knowledge of basic topology (for example MATH 411) is necessary for an understanding of the theory. The minimal expectation is a poster to be presented in the senior showcase.

Analysis Situs

In the years 1899 to 1904, Poincare published a paper with the title Analysis Situs and five supplements introducing basic ideas of topology. This project aims to study the way he introduced a particular concept, like e.g. the orientation of a manifold, and to research pre-Poincare origins of this concept (what was a building on?) and how the concept developed into modern times. The prerequisite for this project is the maturity of a senior, the willingness to read old mathematics literature (English translations are available). The expectation is a poster to be presented in the senior showcase.

[email protected]

Michal Kopera - Computational Math, Ocean Modeling

Broncorank - a new university ranking.

In this project, you will explore the idea of using a PageRank algorithm, which Google is using to rank websites in their search engine, for creating a university ranking which does not depend on some editorial board decision but emerges from each university peer institution lists. You will get a chance to work at an intersection of mathematics, programming, data science, and contribute to creating a more fair tool to rank universities across the U.S.

To be successful in this project, you need some background in programming and ideally have enjoyed your MATH 265 and/or 365 courses. Knowledge of basic linear algebra (matrices) is a plus. The minimum expectation is a poster presentation at Senior Showcase.

Ice/ocean interactions

The modeling of the interface between ice and the ocean is of utmost importance for climate science. You will experiment with models of ice/ocean boundary developed in my group and evaluate whether they produce physical results. No ocean science background is required, but you should be comfortable with writing simple code. The minimum expectation is a poster presentation at Senior Showcase.

Computational modeling using ODEs and PDEs

The bulk of my work is using computational methods to simulate phenomena described by ordinary or partial differential equations. I am open to your ideas on what you would like to model, and we can create a project based on your input.

You will likely need to be able to program in MATLAB, Python, Julia, or other languages.  Knowing something about ODEs and/or PDEs is welcome. I am also open to problems that yield themselves to Machine Learning. The minimum expectation is a poster presentation at Senior Showcase.

Game of Life, Fractals and self-similarity

You will explore some of the concepts outlined above and write code to implement them. The minimum expectation is a poster presentation at Senior Showcase.

Mathematical Art

You will work with genetic (or other nature-inspired) algorithms that try to generate art. You can either focus on optimization algorithms that try to reproduce existing images or aim to generate original art and try to measure its esthetics. The minimum expectation is a poster presentation at Senior Showcase.

Michal Kopera Faculty Profile Page

Zach Teitler - Algebra and Algebraic Geometry

My specialty is algebra. I can work with you on projects in algebra, graph theory, combinatorics, number theory, any other area of pure math, or any subject that you’re interested in within pure math, applied math, statistics, or math education.

I am available to work with students on undergraduate senior thesis projects. You can email me if you’re looking for a senior thesis advisor, but first, read about what you can expect if we work together and what project ideas we can work on together.

https://zteitler.github.io/advising/senior_thesis/

Barbara Zubik-Kowal - Applied mathematics

Difference equations and applications.

Difference equations arise naturally in real-world applications involving discrete sets or populations, or as approximations to continuum models in science and engineering. Mathematically, difference equations can be described as mathematical equalities involving the values of a function of a discrete variable. A recurrence relation such as the logistic map, relevant to population dynamics, or the sequence of Fibonacci numbers, are simple examples. Many difference equations can be solved analogously to how one solves ordinary differential equations. However, it is well-known that most difference equations depicting real-life phenomena cannot be solved in closed form and other methods are necessary to obtain qualitative or quantitative information about the desired solutions, including their stability properties. This senior project can go in a number of directions depending upon the interests of the student. The project may involve theoretical aspects, including theoretical derivations and proof-writing, or computations, including writing new codes or modifying existing ones.

Integro-differential equations and applications

Integro-differential equations are central to modelling numerous natural and industrial phenomena across physics, biology, medicine, engineering, and other fields. As an example in the field of epidemiology, integro-differential equations are frequently used in the mathematical modelling of epidemics, such as when the age-structure of the population is important in determining the dynamics of an epidemic. Integro-differential equations involve both integrals and derivatives of a function. As very few systems of integro-differential equations have a closed-form solution, a range of mathematical methods are often used to obtain qualitative information about the solutions of classes of problems involving integro-differential equations, and approximation techniques are often used to obtain quantitative information about the corresponding solutions given some initial data. In contrast to ordinary and partial differential equations, initial data for integro-differential equations is frequently provided on a whole interval, rather than a single initial point in time. This means more initial data is used to supplement systems of integro-differential equations. This senior project can go in a number of directions depending upon the interests of the student. The project may involve theoretical aspects, including theoretical derivations and proof-writing, or computations, including writing new codes or modifying existing ones.

Differential inequalities and applications

Mathematical models for a range of biological, physical or industrial phenomena may be grouped into general classes of systems of differential equations. Even if the underlying mathematical models may involve complexities that make it hard or impossible to solve by hand, it is frequently possible to extract useful qualitative information about its solutions. Such qualitative information frequently suffices to answer key questions about a solution’s behaviour. Examples are its long-term behavior, existence and uniqueness, convergence properties, and its upper and lower bounds, such as maximal and minimal solutions. These properties, in turn, help us derive information about not only one, but a whole family of mathematical models constituting a given class of differential equations. This senior project can go in a number of directions depending upon the interests of the student. The project may involve theoretical aspects, including theoretical derivations and proof-writing, or computations, including writing new codes or modifying existing ones.

Principles of approximation and applications

Smooth functions arise frequently in the mathematical modeling of numerous real-world phenomena in the sciences and engineering, including both natural and industrial processes. An example is the solution to a SIR model of susceptible, infectious, or recovered individuals in epidemiology, or solutions to mathematical models of tumor growth. It is well known, however, that solutions to most mathematical models depicting real-world phenomena cannot, in general, be expressed in closed form. It is, however, possible to make progress by making appropriate approximations to obtain an estimate of the desired solution. Such approximations involve discretizing the domain from a continuous interval to a finite subset of grid points, solving the discrete systems of equations, computing continuous extensions, or interpolations, and performing error analysis. There are many ways of doing this, but it is important to understand how to do it in a way that preserves certain desired properties, in order to ensure that the resulting approximate solutions that we are getting are indeed approximate solutions to the problem we started out with, rather than spurious output. This senior project can go in a number of directions depending upon the interests of the student. The project may involve theoretical aspects, including theoretical derivations and proof-writing, or computations, including writing new codes or modifying existing ones.

Barbara Zubik-Kowal Faculty Profile Page

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181 Mathematics Research Topics From PhD Experts

If you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is). The good news is that you have arrived at just the right place – at the right time. We have just finished updating our list of topics, so you will find plenty of original ideas right on this page. All our topics are 100 percent free to use as you see fit. You can reword them and you don’t need to give us any credit.

And remember: if you need assistance from a professional, don’t hesitate to reach out to us. We are not just the best place for math research topics for high school students; we are also the number one choice for students looking for top-notch research paper writing services.

Our Newest Research Topics in Math

We know you probably want the best and most recent research topics in math. You want your paper to stand out from all the rest. After all, this is the best way to get some bonus points from your professor. On top of this, finding some great topics for your next paper makes it easier for you to write the essay. As long as you know at least something about the topic, you’ll find that writing a great paper or buy phd thesis isn’t as difficult as you previously thought.

So, without further ado, here are the 181 brand new topics for your next math research paper:

Cool Math Topics to Research

Are you looking for some cool math topics to research? We have a list of original topics for your right here. Pick the one you like and start writing now:

• Roll two dice and calculate a probability
• Discuss ancient Greek mathematics
• Is math really important in school?
• Discuss the binomial theorem
• The math behind encryption
• Game theory and its real-life applications
• Analyze the Bernoulli scheme
• What are holomorphic functions and how do they work?
• Describe big numbers
• Solving the Tower of Hanoi problem

Undergraduate Math Research Topics

If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics:

• Methods to count discrete objects
• The origins of Greek symbols in mathematics
• Methods to solve simultaneous equations
• Real-world applications of the theorem of Pythagoras
• Discuss the limits of diffusion
• Use math to analyze the abortion data in the UK over the last 100 years
• Discuss the Knot theory
• Analyze predictive models (take meteorology as an example)
• In-depth analysis of the Monte Carlo methods for inverse problems
• Squares vs. rectangles (compare and contrast)

Number Theory Topics to Research

Interested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics:

• Discuss the greatest common divisor
• Explain the extended Euclidean algorithm
• What are RSA numbers?
• Discuss Bézout’s lemma
• In-depth analysis of the square-free polynomial
• Discuss the Stern-Brocot tree
• Analyze Fermat’s little theorem
• What is a discrete logarithm?
• Gauss’s lemma in number theory
• Analyze the Pentagonal number theorem

Math Research Topics for High School

High school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here:

• Discuss Brun’s constant
• An in-depth look at the Brahmagupta–Fibonacci identity
• What is derivative algebra?
• Describe the Symmetric Boolean function
• Discuss orders of approximation in limits
• Solving Regiomontanus’ angle maximization problem
• What is a Quadratic integral?
• Define and describe complementary angles
• Analyze the incircle and excircles of a triangle
• Analyze the Bolyai–Gerwien theorem in geometry
• Math in our everyday life

Complex Math Topics

If you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics:

• Mathematics and its appliance in Artificial Intelligence
• Try to solve an unsolved problem in math
• Discuss Kolmogorov’s zero-one law
• What is a discrete random variable?
• Analyze the Hewitt–Savage zero-one law
• What is a transferable belief model?
• Discuss 3 major mathematical theorems
• Describe and analyze the Dempster-Shafer theory
• An in-depth analysis of a continuous stochastic process
• Identify and analyze Gauss-Markov processes

Easy Math Research Paper Topics

Perhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics:

• Define the hyperbola
• Do we need to use a calculator during math class?
• The binomial theorem and its real-world applications
• What is a parabola in geometry?
• How do you calculate the slope of a curve?
• Define the Jacobian matrix
• Solving matrix problems effectively
• Why do we need differential equations?
• Should math be mandatory in all schools?
• What is a Hessian matrix?

Logic Topics to Research

We have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now:

• Discuss the reductio ad absurdum approach
• Discuss Boolean algebra
• What is consistency proof?
• Analyze Trakhtenbrot’s theorem (the finite model theory)
• Discuss the Gödel completeness theorem
• An in-depth analysis of Morley’s categoricity theorem
• How does the Back-and-forth method work?
• Discuss the Ehrenfeucht–Fraïssé game technique
• Discuss Aleph numbers (Aleph-null and Aleph-one)
• Solving the Suslin problem

Algebra Topics for a Research Paper

Would you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper:

• Discuss the differential equation
• Analyze the Jacobson density theorem
• The 4 properties of a binary operation in algebra
• Analyze the unary operator in depth
• Analyze the Abel–Ruffini theorem
• Epimorphisms vs. monomorphisms: compare and contrast
• Discuss the Morita duality in algebraic structures
• Idempotent vs. nilpotent in Ring theory
• Discuss the Artin-Wedderburn theorem
• What is a commutative ring in algebra?
• Analyze and describe the Noetherian ring

Math Education Research Topics

There is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics:

• What are the goals a mathematics professor should have?
• What is math anxiety in the classroom?
• Teaching math in UK schools: the difficulties
• Computer programming or math in high school?
• Is math education in Europe at a high enough level?
• Common Core Standards and their effects on math education
• Culture and math education in Africa
• What is dyscalculia and how does it manifest itself?
• When was algebra first thought in schools?
• Math education in the United States versus the United Kingdom

Computability Theory Topics to Research

Writing about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research:

• What is a multiplication table?
• Analyze the Scholz conjecture
• Explain exponentiating by squaring
• Analyze the Myhill-Nerode theorem
• What is a tree automaton?
• Compare and contrast the Pushdown automaton and the Büchi automaton
• Discuss the Markov algorithm
• What is a Turing machine?
• Analyze the post correspondence problem
• Discuss the linear speedup theorem
• Discuss the Boolean satisfiability problem

Interesting Math Research Topics

We know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics:

• What is two-element Boolean algebra?
• The life of Gauss
• The life of Isaac Newton
• What is an orthodiagonal quadrilateral?
• Tessellation in Euclidean plane geometry
• Describe a hyperboloid in 3D geometry
• What is a sphericon?
• Discuss the peculiarities of Borel’s paradox
• Analyze the De Finetti theorem in statistics
• What are Martingales?
• The basics of stochastic calculus

Applied Math Research Topics

Interested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you:

• Discuss Newton’s laws of motion
• Analyze the perpendicular axes rule
• How is a Galilean transformation done?
• The conservation of energy and its applications
• Discuss Liouville’s theorem in Hamiltonian mechanics
• Analyze the quantum field theory
• Discuss the main components of the Lorentz symmetry
• An in-depth look at the uncertainty principle

Geometry Topics for a Research Paper

Geometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today:

• Most useful trigonometry functions in math
• The life of Archimedes and his achievements
• Trigonometry in computer graphics
• Using Vincenty’s formulae in geodesy
• Define and describe the Heronian tetrahedron
• The math behind the parabolic microphone
• Discuss the Japanese theorem for concyclic polygons
• Analyze Euler’s theorem in geometry

Math Research Topics for Middle School

Yes, even middle school children can write about mathematics. We have some original math research topics for middle school right here:

• Finding critical points in a graph
• The basics of calculus
• What makes a graph ultrahomogeneous?
• How do you calculate the area of different shapes?
• What contributions did Euclid have to the field of mathematics?
• What is Diophantine geometry?
• What makes a graph regular?
• Analyze a full binary tree

Math Research Topics for College Students

As you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here:

• What are extremal problems and how do you solve them?
• Discuss an unsolvable math problem
• How can supercomputers solve complex mathematical problems?
• An in-depth analysis of fractals
• Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
• Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
• An in-depth look at Einstein’s field equation
• The math behind computer vision and object recognition

Calculus Topics for a Research Paper

Let’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away:

• When do we need to apply the L’Hôpital rule?
• Discuss the Leibniz integral rule
• Calculus in ancient Egypt
• Discuss and analyze linear approximations
• The applications of calculus in real life
• The many uses of Stokes’ theorem
• Discuss the Borel regular measure
• An in-depth analysis of Lebesgue’s monotone convergence theorem

Simple Math Research Paper Topics for High School

This is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school:

• The life and work of the famous Pierre de Fermat
• What are limits and why are they useful in calculus?
• Explain the concept of congruency
• The life and work of the famous Jakob Bernoulli
• Analyze the rhombicosidodecahedron and its applications
• Calculus and the Egyptian pyramids
• The life and work of the famous Jean d’Alembert
• Discuss the hyperplane arrangement in combinatorial computational geometry
• The smallest enclosing sphere method in combinatorics

Business Math Topics

If you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here:

• Is paying a loan with another loan a good approach?
• Discuss the major causes of a stock market crash
• Best debt amortization methods in the US
• How do bank loans work in the UK?
• Calculating interest rates the easy way
• Discuss the pros and cons of annuities
• Basic business math skills everyone should possess
• Business math in United States schools
• Analyze the discount factor

Probability and Statistics Topics for Research

Probability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research:

• What is the autoregressive conditional duration?
• Applying the ANOVA method to ranks
• Discuss the practical applications of the Bates distribution
• Explain the principle of maximum entropy
• Discuss Skorokhod’s representation theorem in random variables
• What is the Factorial moment in the Theory of Probability?
• Compare and contrast Cochran’s C test and his Q test
• Analyze the De Moivre-Laplace theorem
• What is a negative probability?

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Undergraduate Honors & Senior Thesis

Students excelling in their major coursework and interested in pure math should consider Departmental Honors. Departmental Honors means you will graduate “With Distinction” as opposed to College Honors which is “With Honors”.  The most important component of graduating with Departmental Honors is researching and writing a Senior Thesis.

Requirements for Departmental Honors:

• Must complete a B.S. Mathematics Degree.
• Must satisfactorily complete at least one three-quarter sequence 402-3-4, 424-5-6, or 441-2-3; or two two-quarter sequences from this list. Exceptions must be approved by the chair of the Departmental Honors Committee.
• Must earn a GPA of 3.5 or better in Math coursework completed at the UW.
• Must write a senior thesis (earn a numerical grade for MATH 496).
• Must have a 3.3 minimum cumulative GPA at UW.

Please note: If you are not interested in the College Honors or Departmental Honors in Mathematics, you may still write a Senior Thesis. The process is the same as above, but it does not need to be approved by the Honors Committee.

Research credit (Math 498) may be available with faculty permission.

Beginning of your final year at the UW : think about a thesis topic and seek out a faculty supervisor.  Read below for more details about selecting a topic.

First week of classes the quarter before you expect to graduate: submit a thesis proposal form to the Dept. Honors Committee.  The form is online here: Math Dept. Honors Thesis Proposal Form

Last day of your final quarter: Once your advisor approves the thesis, email it to [email protected] and cc your faculty advisor.  You may also wish to upload it to the University Libraries archive .

Nature of the thesis

The senior thesis shall be an expository account of a topic in pure or applied mathematics related to the student’s area of interest. (Original results or proofs are welcome but are definitely not expected.) The thesis must contain some nontrivial mathematical arguments. (E.g., a non-technical essay on “fractals in nature” would not be acceptable.) The thesis should normally be about 20 to 30 pages in length (double spaced, Times New Roman 12pt font, 1” margins). These figures are guidelines, not rigid requirements. The topic should be something that cannot simply be read out of a standard textbook. Writing the thesis should involve:

• obtaining material from the periodical literature, or
• consulting several books and synthesizing material from them, or
• reading an account of a topic in a book that is substantially more advanced than the student’s regular coursework, digesting it, and putting it into readable form.

Choosing a topic

Finding a topic is the students’ responsibility, although consultation with faculty members is encouraged. The topic must be approved by a faculty member of the Mathematics Department who will supervise the work (the “supervisor”) and by the chair of the Departmental Honors Committee. A Senior Thesis Topic Proposal form can be found at the link above, and should be filled out by the student with the supervisor's support (the Dept. will check in with your supervisor). The topic proposal must be submitted to the chair of the Departmental Honors Committee no later than the end of the first week of classes the quarter preceding the quarter in which the student expects to graduate. Exceptions to this deadline may be granted only by the chair of the Departmental Honors Committee. Students contemplating writing a thesis are strongly encouraged to start thinking about a topic in the autumn quarter of their senior year.

Writing the thesis

The student must register for Math 496 (Honors Senior Thesis) during the last quarter of thesis work. The student may receive three credit hours of W-course credit for writing the thesis. Normally, the students will register for a reading course (Math 498) with the supervisor during the preceding quarter (s). The student will receive three hours of credit for each of these courses, but in exceptional cases, with the approval of the supervisor, the number or credit hours may be increased. The supervisor may allow the student to replace Math 498 with a suitable topics course; however, it is still expected that the student will meet periodically with the supervisor.

There is no specific required thesis template for an undergraduate thesis.  Some students may choose to use a modified version of the graduate thesis templates, but this is not required.

Approval of thesis

The student shall submit a draft of the thesis to the supervisor for comments and criticisms, and then shall submit a final version with appropriate revisions. The supervisor shall read the thesis and certify its acceptability with respect to both content and exposition. In order to ensure sufficient time for these things, the student must submit the first draft no later than three weeks before the last day classes of the quarter in which the student expects to graduate, and the final draft no later than the last day of classes. Exceptions to these deadlines may be granted only by the chair of the Departmental Honors Committee.

Once the thesis has been approved by your faculty supervisor, you will need to email the document to [email protected] (required) as well as submit it to the ResearchWorks archive , part of the University Libraries (optional but strongly recommended).  Submission to the archive will allow your thesis to be included in the dissemination and preservation of scholarly work.  Your thesis will be made publicly available.

Interdisciplinary theses

Theses which are concerned with the application of some part of mathematics to some others field are acceptable, as long as they contain some substantial mathematics. In exceptional cases the student may wish to work most closely with a faculty member in another department in preparing the thesis. However, in such cases the thesis topic and the thesis itself must still be approved by a member of the Mathematics Department.

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• Senior Thesis

A thesis is a more ambitious undertaking than a project. Most thesis writers within Applied Mathematics spend two semesters on their thesis work, beginning in the fall of senior year.  Students typically enroll in Applied Mathematics 91r or 99r (or Economics 985, if appropriate) during each semester of their senior year.  AM 99r is graded on a satisfactory/unsatisfactory basis.  Some concentrators will have completed their programs of study before beginning a thesis; in situations where this is necessary, students may take AM 91r for letter-graded credit, for inclusion in Breadth section (v) of the plan of study.  In the spring semester, the thesis itself may serve as the substantial paper on which the letter grade is based.  Econ 985 is also letter-graded, and may be included in the Breadth section of the plan of study in place of AM 91r.

Another, somewhat uncommon option, is that a project that meets the honors modeling requirement (either through Applied Mathematics 115 or 91r) can be extended to a thesis with about one semester of work.  Obviously the more time that is spent on the thesis, the more substantial the outcome, but students are encouraged to write a thesis in whatever time they have. It is an invaluable academic experience.

The thesis should make substantive use of mathematical, statistical or computational modeling,  though the level of sophistication will vary as appropriate to the particular problem context.  It is expected that conscientious attention will be paid to the explanatory power of mathematical modeling of the phenomena under study, going beyond data analysis to work to elucidate questions of mechanism and causation rather than mere correlation. Models should be designed to yield both understanding and testable predictions. A thesis with a suitable modeling component will automatically satisfy the English honors modeling requirement; however a thesis won't satisfy modeling Breadth section (v) unless the student also takes AM 91r or Econ 985.

Economics 985 thesis seminars are reserved for students who are writing on an economics topic. These seminars are full courses for letter-graded credit which involve additional activities beyond preparation of a thesis. They are open to Applied Mathematics concentrators with suitable background and interests.

Students wishing to enroll in AM 99r or 91r should follow the application instructions on my.harvard.

Thesis Timeline

The timeline below is for students graduating in May. The thesis deadline for May 2024 graduates is Monday, April 1 at 2:00PM. For off-cycle students, a similar timeline applies, offset by one semester. The thesis due date for March 2025 graduates is Friday, November 22, 2024. Late theses are not accepted.

Mid to late August:

Students often find a thesis supervisor by this time, and work with their supervisor to identify a thesis problem. Students may enroll in Econ 985 (strongly recommended when relevant), AM 91r, or AM 99r to block out space in their schedule for the thesis.

Early December:

All fourth year concentrators are contacted by the Office of Academic Programs. Those planning to submit a senior thesis are requested to supply certain information. This is the first formal interaction with the concentration about the thesis.

Mid-January:

A tentative thesis title approved by the thesis supervisor is required by the concentration.

Early February:

The student should provide the name and contact information for a recommended second reader, together with assurance that this individual has agreed to serve. Thesis readers are expected to be teaching faculty members of the Faculty of Arts and Sciences or SEAS. Exceptions to this requirement must be first approved by the Directors, Associate Director, or Assistant Director of Undergraduate Studies. For AM/Economics students writing a thesis on a mathematical economics topic for the March thesis deadline, the second reader will be chosen by the Economics Department. For AM/Economics students writing for the November deadline, the student should recommend the second reader.

On the thesis due date:

Thesis due at 2pm. Late theses are not accepted. Electronic copies in PDF format should be delivered by the student to the two readers and to [email protected] (which will forward to the Directors of Undergraduate Studies, Associate and Assistant Director of Undergraduate Studies) on or before that date and time. An electronic copy should also be submitted via the SEAS  online submission tool  on or before that date. SEAS will keep this electronic copy as a non-circulating backup and will use it to print a physical copy of the thesis to be deposited in the Harvard University Archives. During this online submission process, the student will also have the option to make the electronic copy publicly available via DASH, Harvard’s open-access repository for scholarly work.

Contemporaneously, the two readers will receive a rating sheet to be returned to the Office of Academic Programs before the beginning of the Reading Period, together with their copy of the thesis and any remarks to be transmitted to the student.

The Office of Academic Programs will send readers' comments to the student in late May, after the degree meeting to decide honors recommendations.

Thesis Readers

The thesis is evaluated by two readers, whose roles are further delineated below.  The first reader is the thesis adviser.  The second and reader is recommended by the student and adviser, who should secure the agreement of the individual concerned to serve in this capacity.  The reader must be approved by the Directors, Associate Director, or Assistant Director of Undergraduate Studies.  The second reader is normally are teaching members of the Faculty of Arts and Sciences, but other faculty members or comparable professionals will usually be approved, after being apprised of the responsibilities they are assuming.   For theses in mathematical economics, the choice of the second reader is made in cooperation with the Economics department.  The student and thesis adviser will be notified of the designated second reader by mid-March.

The roles of the thesis adviser and of the outside reader are somewhat different.  Ideally, the adviser is a collaborator and the outside reader is an informed critics.  It is customary for the adviser's report to comment not only on the document itself but also on the background and context of the entire effort, elucidating the overall accomplishments of the student.  The supervisor may choose to comment on a draft of the thesis before the final document is submitted, time permitting.  The outside reader is being asked to evaluate the thesis actually produced, as a prospective scientific contribution — both as to content and presentation.  The reader may choose to discuss their evaluation with the student, after the fact, should that prove to be mutually convenient.

The thesis should contain an informative abstract separate from the body of the thesis.  At the degree meeting, the Committee on Undergraduate Studies in Applied Mathematics will review the thesis, the reports from the two readers and the student’s academic record. The readers (and student) are told to assume that the Committee consists of technical professionals who are not necessarily conversant with the subject matter of the thesis so their reports should reflect this audience.

The length of the thesis should be as long as it needs to be to make the arguments made, but no longer!

Thesis Examples

The most recent thesis examples across all of SEAS can be found on the Harvard DASH (Digital Access to Scholarship at Harvard) repository . Search the FAS Theses and Dissertations collection for "applied mathematics" to find dozens of examples.

Note: Additional samples of old theses can be found in McKay Library. Theses awarded Hoopes' Prizes can be found in Lamont Library.

Recent thesis titles

Theses submitted in 2021, theses submitted in 2020, theses submitted in 2019, theses submitted in 2018 , senior thesis submission information for a.b. programs.

Senior A.B. theses are submitted to SEAS and made accessible via the Harvard University Archives and optionally via  DASH  (Digital Access to Scholarship at Harvard), Harvard's open-access repository for scholarly work.

In addition to submitting to the department and thesis advisors & readers, each SEAS senior thesis writer will use an online submission system to submit an electronic copy of their senior thesis to SEAS; this electronic copy will be kept at SEAS as a non-circulating backup. Please note that the thesis won't be published until close to or after the degree date. During this submission process, the student will also have the option to make the electronic copy publicly available via DASH.  Basic document information (e.g., author name, thesis title, degree date, abstract) will also be collected via the submission system; this document information will be available in  HOLLIS , the Harvard Library catalog, and DASH (though the thesis itself will be available in DASH only if the student opts to allow this). Students can also make code or data for senior thesis work available. They can do this by posting the data to the Harvard  Dataverse  or including the code as a supplementary file in the DASH repository when submitting their thesis in the SEAS online submission system.

Whether or not a student opts to make the thesis available through DASH, SEAS will provide an electronic record copy of the thesis to the Harvard University Archives. The Archives may make this record copy of the thesis accessible to researchers in the Archives reading room via a secure workstation or by providing a paper copy for use only in the reading room.  Per University policy , for a period of five years after the acceptance of a thesis, the Archives will require an author’s written permission before permitting researchers to create or request a copy of any thesis in whole or in part. Students who wish to place additional restrictions on the record copy in the Archives must contact the Archives  directly, independent of the online submission system. 

Students interested in commercializing ideas in their theses may wish to consult Dr. Fawwaz Habbal , Senior Lecturer on Applied Physics, about patent protection. See Harvard's policy for information about ownership of software written as part of academic work.

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ScholarWorks

Home > A&S > Math > Math Undergraduate Theses

Mathematics Undergraduate Theses

Theses from 2019 2019.

The Name Tag Problem , Christian Carley

The Hyperreals: Do You Prefer Non-Standard 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 El-Bakri

Axioms of Set Theory and Equivalents of Axiom of Choice , Farighon Abdul Rahim

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Senior Theses

• Categories: Strategies for Learning

Doing a senior thesis is an exciting enterprise. It’s often the first time students are engaging in truly original research and trying to develop a significant contribution to a field of inquiry. But as joyful as an independent research process can be, you don’t have to go it alone. It’s important to have support as you navigate such a large endeavor, and the ARC is here to offer one of those layers of support. 

Whether or not to write a senior thesis is just the first in a long line of questions thesis writers need to consider. In addition to questions about the topic and scope of your thesis, there are questions about timing, schedule, and support. For example, if you are collecting data, when should data collection start and when should it be completed? What kind of schedule will you write on? How will you work with your adviser? Do you want to meet with your adviser about your progress once a month? Once a week? What other resources can you turn to for information, feedback, and support? 

Even though there is a lot to think about and a lot to do, doing a thesis really can be an enjoyable experience! Keep reminding yourself why you chose this topic and why you care about it. 

Tips for Tackling Big Projects:  

• When you’re approaching a big project, it can seem overwhelming to look at the whole thing at once, so it’s essential to identify the smaller steps that will move you towards the completed project. 
• Your advisor is best suited to help you break down the thesis process with field-specific advice. 
• If you need to refine the breakdown further so it makes sense for you, schedule an appointment with an Academic Coach . An academic coach can help you think through the steps in a way that works for you. 
• Pre-determine the time, place, and duration. 
• Keep it short (15 to 60 minutes). 
• Have a clear and reasonable goal for each writing session. 
• Make it a regular event (every day, every other day, MWF). 
• time is not wasted deciding to write if it’s already in your calendar; 
• keeping sessions short reduces the competition from other tasks that are not getting done; 
• having an achievable goal for each session provides a sense of accomplishment (a reward for your work); 
• writing regularly can turn into a productive habit. 
• In addition to having a clear goal for each writing session, it’s important to have clear goals for each week and to find someone to communicate these goals to, such as your adviser, a “thesis buddy,” your roommate, etc. Communicating your goals and progress to someone else creates a useful sense of accountability. 
• If your adviser is not the person you are communicating your progress to on a weekly basis, then request to set up a structure with your adviser that requires you to check in at less frequent but regular intervals. 
• Commit to attending Accountability Hours at the ARC on the same day every week. Making that commitment will add both social support and structure to your week. Use the ARC Scheduler to register for Accountability Hours. 
• Set up an accountability group in your department or with thesis writers from different departments. 
• It’s important to have a means for getting consistent feedback on your work and to get that feedback early. Work on large projects often lacks the feeling of completeness, so don’t wait for a whole section (and certainly not the whole thesis) to feel “done” before you get feedback on it! 
• Your thesis adviser is typically the person best positioned to give you feedback on your research and writing, so communicate with your adviser about how and how often you would like to get feedback. 
• If your adviser isn’t able to give you feedback with the frequency you’d like, then fill in the gaps by creating a thesis writing group or exploring if there is already a writing group in your department or lab. 
• The Harvard College Writing Center is a great resource for thesis feedback. Writing Center Senior Thesis Tutors can provide feedback on the structure, argument, and clarity of your writing and help with mapping out your writing plan. Visit the Writing Center website to schedule an appointment with a thesis tutor . 
• Working on a big project can be anxiety provoking because it’s hard to keep all the pieces in your head and you might feel like you are losing track of your argument. 
• To reduce this source of anxiety, try keeping a separate document where you jot down ideas on how your research questions or central argument might be clarifying or changing as you research and write. Doing this will enable you to stay focused on the section you are working on and to stop worrying about forgetting the new ideas that are emerging. 
• You might feel anxious when you realize that you need to update your argument in response to the evidence you have gathered or the new thinking your writing has unleashed. Know that that is OK. Research and writing are iterative processes – new ideas and new ways of thinking are what makes progress possible. 
• It’s also anxiety provoking to feel like you can’t “see” from the beginning to the end of your project in the way that you are used to with smaller projects. 
• Breaking down big projects into manageable chunks and mapping out a schedule for working through each chunk is one way to reduce this source of anxiety. It’s reassuring to know you are working towards the end even if you cannot quite see how it will turn out. 
• It may be that your thesis or dissertation never truly feels “done” to you, but that’s okay. Academic inquiry is an ongoing endeavor. 
• Thesis work is not a time for social comparison; each project is different and, as a result, each thesis writer is going to work differently. 
• Just because your roommate wrote 10 pages in a day doesn’t mean that’s the right pace or strategy for you. 
• If you are having trouble figuring out what works for you, use the ARC Scheduler to make an appointment with an Academic Coach , who can help you come up with daily, weekly, and semester-long plans. 
• If you’re having trouble finding a source, email your question or set up a research consult via Ask a Librarian . 
• If you’re looking for additional feedback or help with any aspect of writing, contact the Harvard College Writing Center . The Writing Center has Senior Thesis Tutors who will read drafts of your thesis (more typically, parts of your thesis) in advance and meet with you individually to talk about structure, argument, clear writing, and mapping out your writing plan. 
• If you need help with breaking down your project or setting up a schedule for the week, the semester, or until the deadline, use the ARC Scheduler to make an appointment with an Academic Coach . 
• If you would like an accountability structure for social support and to keep yourself on track, come to Accountability Hours at the ARC.