msc maths dissertation topics

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Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2024 2024.

On Cheeger Constants of Knots , Robert Lattimer

Information Based Approach for Detecting Change Points in Inverse Gaussian Model with Applications , Alexis Anne Wallace

Theses/Projects/Dissertations from 2023 2023

DNA SELF-ASSEMBLY OF TRAPEZOHEDRAL GRAPHS , Hytham Abdelkarim

An Exposition of the Curvature of Warped Product Manifolds , Angelina Bisson

Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves , Anton Butenko

MATHEMATICS BEHIND MACHINE LEARNING , Rim Hammoud

Statistical Analysis of Health Habits for Incoming College Students , Wendy Isamara Lizarraga Noriega

Reverse Mathematics of Ramsey's Theorem , Nikolay Maslov

Distance Correlation Based Feature Selection in Random Forest , Jose Munoz-Lopez

Constructing Hyperbolic Polygons in the Poincaré Disk , Akram Zakaria Samweil

KNOT EQUIVALENCE , Jacob Trubey

Theses/Projects/Dissertations from 2022 2022

SYMMETRIC GENERATIONS AND AN ALGORITHM TO PROVE RELATIONS , Diddier Andrade

The Examination of the Arithmetic Surface (3, 5) Over Q , Rachel J. Arguelles

Error Terms for the Trapezoid, Midpoint, and Simpson's Rules , Jessica E. Coen

de Rham Cohomology, Homotopy Invariance and the Mayer-Vietoris Sequence , Stacey Elizabeth Cox

Symmetric Generation , Ana Gonzalez

SYMMETRIC PRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Samar Mikhail Kasouha

Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez

LATTICE REDUCTION ALGORITHMS , Juan Ortega

THE DECOMPOSITION OF THE SPACE OF ALGEBRAIC CURVATURE TENSORS , Katelyn Sage Risinger

Verifying Sudoku Puzzles , Chelsea Schweer

AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY , Travis Severns

Theses/Projects/Dissertations from 2021 2021

Non-Abelian Finite Simple Groups as Homomorphic Images , Sandra Bahena

Matroids Determinable by Two Partial Representations , Aurora Calderon Dojaquez

SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Connie Corona

Symmetric Presentation of Finite Groups, and Related Topics , Marina Michelle Duchesne

MEASURE AND INTEGRATION , JeongHwan Lee

A Study in Applications of Continued Fractions , Karen Lynn Parrish

Partial Representations for Ternary Matroids , Ebony Perez

Theses/Projects/Dissertations from 2020 2020

Sum of Cubes of the First n Integers , Obiamaka L. Agu

Permutation and Monomial Progenitors , Crystal Diaz

Tile Based Self-Assembly of the Rook's Graph , Ernesto Gonzalez

Research In Short Term Actuarial Modeling , Elijah Howells

Hyperbolic Triangle Groups , Sergey Katykhin

Exploring Matroid Minors , Jonathan Lara Tejeda

DNA COMPLEXES OF ONE BOND-EDGE TYPE , Andrew Tyler Lavengood-Ryan

Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder

ASSESSING STUDENT UNDERSTANDING WHILE SOLVING LINEAR EQUATIONS USING FLOWCHARTS AND ALGEBRAIC METHODS , Edima Umanah

Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila

VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS , Brian Matthew Friday

Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle , Lacey Taylor James

Geodesics on Generalized Plane Wave Manifolds , Moises Pena

Algebraic Methods for Proving Geometric Theorems , Lynn Redman

Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle , Antonio Saucedo Jr.

THE EFFECTIVENESS OF DYNAMIC MATHEMATICAL SOFTWARE IN THE INSTRUCTION OF THE UNIT CIRCLE , Edward Simons

CALCULUS REMEDIATION AS AN INDICATOR FOR SUCCESS ON THE CALCULUS AP EXAM , Ty Stockham

Theses/Projects/Dissertations from 2018 2018

PROGENITORS, SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS , Diana Aguirre

Monomial Progenitors and Related Topics , Madai Obaid Alnominy

Progenitors Involving Simple Groups , Nicholas R. Andujo

Simple Groups, Progenitors, and Related Topics , Angelica Baccari

Exploring Flag Matroids and Duality , Zachary Garcia

Images of Permutation and Monomial Progenitors , Shirley Marina Juan

MODERN CRYPTOGRAPHY , Samuel Lopez

Progenitors, Symmetric Presentations, and Related Topics , Joana Viridiana Luna

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN

THE STRUGGLE WITH INVERSE FUNCTIONS DOING AND UNDOING PROCESS , Jesus Nolasco

Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager

MANUAL SYMMETRIC GENERATION , Joel Webster

Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari

CONSTRUCTION OF HOMOMORPHIC IMAGES , Erica Fernandez

Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS , Ulyses Velasco

CONSTRUCTION OF FINITE GROUP , Michelle SoYeong Yeo

Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova

GEODESICS IN LORENTZIAN MANIFOLDS , Amir A. Botros

REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING , Gina Marie Cheney

Solving Absolute Value Equations and Inequalities on a Number Line , Melinda A. Curtis

BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS , Lucille J. Durfee

ANALYSIS AND SYNTHESIS OF THE LITERATURE REGARDING ACTIVE AND DIRECT INSTRUCTION AND THEIR PROMOTION OF FLEXIBLE THINKING IN MATHEMATICS , Genelle Elizabeth Gonzalez

LIFE EXPECTANCY , Ali R. Hassanzadah

PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS , Sean M. Hearon

A Dual Fano, and Dual Non-Fano Matroidal Network , Stephen Lee Johnson

Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity , Nitish Mittal

The Kauffman Bracket and Genus of Alternating Links , Bryan M. Nguyen

Probabilistic Methods In Information Theory , Erik W. Pachas

THINKING POKER THROUGH GAME THEORY , Damian Palafox

Indicators of Future Mathematics Proficiency: Literature Review & Synthesis , Claudia Preciado

Ádám's Conjecture and Arc Reversal Problems , Claudio D. Salas

AN INTRODUCTION TO BOOLEAN ALGEBRAS , Amy Schardijn

The Evolution of Cryptology , Gwendolyn Rae Souza

Theses/Projects/Dissertations from 2015 2015

SYMMETRIC PRESENTATIONS AND RELATED TOPICS , Mashael U. Alharbi

Homomorphic Images And Related Topics , Kevin J. Baccari

Geometric Constructions from an Algebraic Perspective , Betzabe Bojorquez

Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity , Tamara V. Bonn

Symmetric Presentations and Generation , Dustin J. Grindstaff

HILBERT SPACES AND FOURIER SERIES , Terri Joan Harris Mrs.

SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS , Leonard B. Lamp

Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz

CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES , Jessica Luna Ramirez

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Dissertation in mathematics

This module enables you to carry out a sustained, guided, independent study of a topic in mathematics. There’s a choice of topics, for example: algebraic graph theory; aperiodic tilings and symbolic dynamics; advances in approximation theory; history of modern geometry; interfacial flows and microfluidics; variational methods, and Riemann surfaces. Provided study notes, books, research articles, and original sources guide you. You must master the appropriate mathematics and present your work as a final dissertation.

Qualifications

M840 is a compulsory module in our:

• MSc in Mathematics (F04)
• Credits measure the student workload required for the successful completion of a module or qualification.
• One credit represents about 10 hours of study over the duration of the course.
• You are awarded credits after you have successfully completed a module.
• For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.

OU	Postgraduate
SCQF	11
FHEQ	7

Find out more about entry requirements .

What you will study

The list of topics available varies each year. We’ll let MSc in Mathematics students know the available topics that October in the spring, before the module starts.

Recently available topics have included:

• Advances in approximation theory
• Algebraic graph theory
• Aperiodic tilings and symbolic dynamics
• History of modern geometry
• Interfacial flows and microfluidics
• Riemann surfaces
• Variational methods.

Please note:

• Since the available topics vary from year to year, check that we are offering the topic you wish to study before registering.
• For staffing reasons, you might not be able to study your preferred topic. Therefore, we’ll ask you for your first and second choice. We can usually offer you one of your choices, although this cannot be guaranteed.

You will learn

Successful study of this module should enhance your skills in understanding complex mathematical texts, working on open-ended problems and communicating mathematical ideas clearly.

Teaching and assessment

Support from your tutor.

Throughout your module studies, you’ll get help and support from your assigned module tutor. They’ll help you by:

• Marking your assignments (TMAs) and providing detailed feedback for you to improve.
• Guiding you to additional learning resources.
• Providing individual guidance, whether that’s for general study skills or specific module content.

The module has a dedicated and moderated forum where you can join in online discussions with your fellow students. There are also online module-wide tutorials. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part. If you want to participate, you’ll likely need a headset with a microphone.

The assessment details can be found in the facts box.

Course work includes

Tutor-marked assignments (TMAs)

Future availability

Dissertation in mathematics (M840) starts once a year – in October.

This page describes the module that will start in October 2024.

We expect it to start for the last time in October 2029.

Regulations

Entry requirements.

You must have passed four modules from the MSc in Mathematics (F04) .

If you’ve passed only three modules, you may request exceptional permission to take M840 alongside another module.

Additionally:

• To study the ‘Advances in approximation theory’ topic, you should have passed Advanced mathematical methods (M833) or the discontinued module M832.
• To study the ‘Variational methods applied to eigenvalue problems’ topic, you should have passed Calculus of variations and advanced calculus (M820) .
• To study the ‘Riemann surfaces’ topic, you should have a Grade 1 or 2 pass a course in Complex analysis (M337) or an equivalent course.

All teaching is in English and your proficiency in the English language should be adequate for the level of study you wish to take. We strongly recommend that students have achieved an IELTS (International English Language Testing System) score of at least 7. To assess your English language skills in relation to your proposed studies you can visit the IELTS website.

Start	End	England fee	Register
05 Oct 2024	Jun 2025	£1360.00	Registration closes 05/09/24 (places subject to availability)
This module is expected to start for the last time in October 2029.

Additional costs

Study costs.

There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.

Study events

This module may have an optional in-person study event. We’ll let you know if this event will take place and any associated costs as soon as we can.

Ways to pay for this module

We know there’s a lot to think about when choosing to study, not least how much it’s going to cost and how you can pay.

That’s why we keep our fees as low as possible and offer a range of flexible payment and funding options, including a postgraduate loan, if you study this module as part of an eligible qualification. To find out more, see Fees and funding .

Study materials

What's included.

You’ll have access to a module website, which includes:

• a week-by-week study planner
• course-specific module materials
• audio and video content
• assessment details and submission section
• online tutorial access.

You will need

Some topics require specific books. We’ll let you know which once your topic is confirmed.

Computing requirements

You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS Ventura or higher.

Any additional software will be provided or is generally freely available.

To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).

Our module websites comply with web standards, and any modern browser is suitable for most activities.

Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.

It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop, as described above.

If you have a disability

The material contains small print and diagrams, which may cause problems if you find reading text difficult. Adobe Portable Document Format (PDF) versions of printed material are available. Some Adobe PDF components may not be available or fully accessible using a screen reader and mathematical materials may be particularly difficult to read in this way. Alternative formats of the study materials may be available in the future.

To find out more about what kind of support and adjustments might be available, contact us or visit our disability support pages .

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MSc Mathematical & Computational Finance: sample dissertations

Below are some examples of MSc dissertations from previous years, which received high marks:

• Optimal Strategies from forward versus classical utilities
• Robust Pricing of Derivatives on Realised Variance
• Log Mean-Variance Portfolio Theory and Time Inconsistency
• Multilayer network valuation under bail-in
• Topological Persistence in Market Micro Structure
• Volatility is Rough
• Deep learning approach to hedging (2019 prize for best Master’s Thesis in Quantitative Finance by Natixis Foundation for Research & Innovation.)
• Risk Management with Generative Adversarial Networks.pdf  (Won award for best Masters Thesis in Quantitative Finance in Europe in 2020)
• Hawkes Process-Driven Models for Limit Order Book Dynamics.pdf   (Won award for best Masters Thesis in Quantitative Finance in Europe in 2021)
• Evaluating Credit Portfolios under IFRS 9 in the UK Economy

Mathematics Institute

Msc dissertations, mathematics dissertations.

The MSc dissertation counts for 90 CATS - that is, half of the total MSc load.

A dissertation is usually expository, collecting together results from several research papers into a coherent whole. Sometimes dissertations contain original research, and this is encouraged where appropriate. The general framework of a dissertation must be approved by the supervisor. This page may help to find staff members with interesting topics.

The appropriate length for a dissertation will vary with the topic, the formatting, and whether or not it includes figures, etc. As a guide, most MSc dissertations are between 30 and 50 A4 pages, double spaced, with normal font size and margins. Longer dissertations are not necessarily better, and the marks obtained depend much more on the quality of the content (especially the mathematics) than on the number of words. It is essential that the dissertation is well presented.

The dissertation should normally be produced in TEX or LaTEX. The package here is intended for PhD theses, but it can also be used for MSc dissertations. Suitable past dissertations are available for inspection. If you are in any doubt, please consult your supervisor or the Director of the MSc.

Interdisciplinary Mathematics Dissertations

For MSc Interdisciplinary Mathematics candidates the above holds, although these dissertations may be longer if they contain many diagrams, data or programs for example. The level of sophistication of the mathematics used in the dissertation may be lower than that expected in a straight Mathematics MSc provided that the dissertation demonstrates a compensating degree of understanding of the role or appropriate use of the mathematics described. The mathematics in the dissertation should be correct, appropriate for the interdisciplinary topic under discussion, and should say something of scientific value. This page may help to find staff members in the math dept with interesting topics.

Dissertation Marks

The dissertation is read by two internal examiners (including a supervisor) who report to the Examination Board. For MSc Interdisciplinary Mathematics dissertations, reports are generally requested from an internal examiner in each of the relevant departments to ensure sufficient interdisciplinary quality.

Examiners are asked to discuss the dissertation under the headings: Accuracy and depth of understanding (40%); Level of difficulty and degree of originality (40%); Exposition (10%); Context/Literature Bibliography (10%). The marks are passed to the Examination Board. The external examiner reviews the dissertations and marks prior to the Examination Board meeting.

The dissertation pass mark is 50% and students must pass the dissertation in order to pass the MSc.

Submitting your Dissertation or Postgraduate Diploma Project

The submission deadline is 2nd September 2024. Submissions will be made via Moodle. Further details will be provided closer to the deadline.

The name of the candidate's supervisor must be stated on the title page of the dissertation. The introduction to the dissertation should state clearly all sources used, and should pinpoint clearly any original passages claimed. The candidate should briefly describe how the sources were used and their relation to the dissertation. Acknowledgements should also appear, where appropriate, in the body of the dissertation. References with precise bibliographic details should be included. A dissertation will not be accepted if any reader (including one unfamiliar with the contents of the references cited) could gain a mistaken impression that expository material is the candidate's own original work.

Good English style, with correct grammar and spelling, is expected. The books Writing Mathematics Well by L. Gillman, and How to Write Mathematics by N.E. Steenrod et al. (AMS 1973) are recommended. (Both can be found in the Library catalogue .) In addition, supervisors can often help by suggesting which published mathematical papers are good models of exposition, and which are not.

Postgraduate Diploma Project

The expected standard in a Postgraduate Diploma is less than that for an MSc degree. If a candidate is recommended to transfer to the Postgraduate Diploma as a result of their examination results, the candidate will need to write a (Diploma) project rather than a dissertation. Students on the 2 year MSc course will submit a project at the end of their first year

The Diploma project counts for 24 CATS (rather than 90 CATS for an MSc dissertation). It is usually an expository work describing a piece of mathematics (which may be related to material covered in lectures). Sometimes a project may involve numerical work or a guided exploration of some particular problem. The project should normally be about 10-20 pages long and should show that the candidate is capable of writing about mathematics in a coherent fashion. The general framework of the project must be approved by the supervisor. The project is marked against these criteria and not against that for the MSc.

Edinburgh Research Archive

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Mathematics thesis and dissertation collection

By Issue Date Authors Titles Subjects Publication Type Sponsor Supervisors

Search within this Collection:

This collection contains a selection of the latest doctoral theses completed at the School of Mathematics. Please note this is not a comprehensive record.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.

Recent Submissions

Applications and improvements of the adaptive large neighbourhood search , lᵖ boundary value problems for elliptic and parabolic operators , twistor theory and its applications in asymptotically flat spacetimes , theory and simulation of interacting particle systems and mckean-vlasov processes: the super measure class, ergodicity, and weak error , spencer cohomology, supersymmetry and the structure of killing superalgebras , higher triangulated categories and fourier-mukai transforms on abelian surfaces and threefolds , investigating computer aided assessment of mathematical proof by varying the format of students' answers and the structure of assessment design by stack , estimation and application of bayesian hawkes process models , novel statistical learning approaches for open banking-type data , statistical and machine learning approaches to genomic medicine , using markov chain monte carlo in vector generalized linear mixed models: with an application to integral projection models in ecology , symmetries of riemann surfaces and magnetic monopoles , kan extensions in probability theory , regression analysis for extreme value responses and covariates , categorical torelli theorems for fano threefolds , laplacians for structure recovery on directed and higher-order graphs , efficient interior point algorithms for large scale convex optimization problems , solving sampling and optimization problems via tamed langevin mcmc algorithms in the presence of super-linearities , algebraic combinatorial structures for singular stochastic dynamics , stochastic modelling and inference of ocean transport .

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Theses and dissertations

A selection of PhD theses and MSc dissertations are available for you to read: 

• mathematics PhD theses
• statistics PhD theses
• mathematics MSc dissertations .