example research proposal in mathematics pdf

Research Proposal Example/Sample

Detailed Walkthrough + Free Proposal Template

If you’re getting started crafting your research proposal and are looking for a few examples of research proposals , you’ve come to the right place.

In this video, we walk you through two successful (approved) research proposals , one for a Master’s-level project, and one for a PhD-level dissertation. We also start off by unpacking our free research proposal template and discussing the four core sections of a research proposal, so that you have a clear understanding of the basics before diving into the actual proposals.

• Research proposal example/sample – Master’s-level (PDF/Word)
• Research proposal example/sample – PhD-level (PDF/Word)
• Proposal template (Fully editable) 

If you’re working on a research proposal for a dissertation or thesis, you may also find the following useful:

• Research Proposal Bootcamp : Learn how to write a research proposal as efficiently and effectively as possible
• 1:1 Proposal Coaching : Get hands-on help with your research proposal

FAQ: Research Proposal Example

Research proposal example: frequently asked questions, are the sample proposals real.

Yes. The proposals are real and were approved by the respective universities.

Can I copy one of these proposals for my own research?

As we discuss in the video, every research proposal will be slightly different, depending on the university’s unique requirements, as well as the nature of the research itself. Therefore, you’ll need to tailor your research proposal to suit your specific context.

You can learn more about the basics of writing a research proposal here .

How do I get the research proposal template?

You can access our free proposal template here .

Is the proposal template really free?

Yes. There is no cost for the proposal template and you are free to use it as a foundation for your research proposal.

Where can I learn more about proposal writing?

For self-directed learners, our Research Proposal Bootcamp is a great starting point.

For students that want hands-on guidance, our private coaching service is recommended.

Psst… there’s more!

This post is an extract from our bestselling short course, Research Proposal Bootcamp . If you want to work smart, you don't want to miss this .

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Research plan

The research plan is a document in which the PhD student develops a plan for his/her thesis. It should include an introduction, a brief state of the art to put in context the plan, the motivation and objectives of the work, the work done so far, a plan, detailing tasks and time planning, and a list of conferences and indexed journals were the work can be presented or submitted to.  A typical table of content is

• Cover page including the text “Research plan”, tentative title of the thesis, PhD program, name of the PhD student, name of the advisor(s) and date.
• Brief summary
• Introduction (state of the art, motivation, objectives)
• Work done so far
• Work plan (work to be done, tasks and time planning, tentative list of conferences and indexed journals, stays, etc). This must include a 1--page schedule of the forthcoming work until the end of the Thesis .

A short document of 10-30 pages is recommended, with annexes for details.

The panel is composed by 3 doctors with relevant expertise in the field, as president, secretary (from UPC) and vocal. As a general rule, the panel is composed by 2 researchers associated to the DMA program and an external one. In any case, the panel must include at least 1 researcher associated to the DMA program, and three of them cannot belong to the same research group. Finally any of the members of the panel can be a coauthor of the PhD student. 

[These rules have been approved by the Board of Studies of DMA at a meeting 05/07/2018, and included the condition of coauthor at the CADMAMAMME meeting 08/04/2021]

Presentation

The presentation should last no more than 30 min, followed by comments and questions from the panel.

• the pdf document of the research plan
• the form detailing the panel proposal (president, secretary and vocal), the date and time for the presentation, and the information for each one of the members of the panel.
• A scan of the registration form , previously signed by the advisors and the student.
• An updated version of the Document d'activitats del Doctorand (DAD)

Please, contact the PhD program admin or the coordinator for further information.

Examples of Successful Grant Applications

The links on this page are only available to viewers with an account in the Department of Mathematics at the University of Arizona

AMS-Simons Travel Grants

Below are examples of successful project descriptions. 

Darlayne Addabbo

Houssam Abdul-Rahman

Paul Carter

Yong Suk Moon

Tracy Stepien

Weinan Wang

Amanda Young

AWM Travel Grants

Example of successful proposal.

NSF Mathematical Sciences Postdoctoral Research Fellowships

Below is an example of a successful research proposal. Additionally, Kevin Lin will share examples of funded and unfunded proposals upon request.

Gabriela Jaramillo (Applied Mathematics)

David Glickenstein will share a successful proposal. Joceline Lega will provide feedback on proposal drafts.

NSF Division of Mathematical Sciences

Below are examples of project descriptions of research proposals that were recently funded by DMS. 

Paul Carter (Applied Mathematics, 2018)

Nick Ercolani (Applied Mathematics, 2015)

Nick Ercolani (Applied Mathematics, 2011)

Below is an example of a conference proposal funded by DMS.

Jim Cushing (Mathematical Biology conference, 2016)

Additionally, a number of faculty will provide feedback on draft project descriptions or share examples of funded or unfunded proposals in a variety of areas.

Computational Mathematics: Kevin Lin

Continuous Mechanics and Materials Science: Joceline Lega

Geometric Analysis: David Glickenstein

Mathematical Biology: Joceline Lega

Mathematical Physics: Nick Ercolani

Partial Differential Equations: Nick Ercolani, Joceline Lega

Probability and Applied Probability: Janek Wehr

NSF Robert Noyce Division For Secondary Mathematics Teacher Development

Example of funded proposal shared by Cynthia Anhalt

Home > College of Natural Sciences > Mathematics > Mathematics Theses, Projects, and Dissertations

Mathematics Theses, Projects, and Dissertations

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

Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field , Nolberto Rezola

ALGEBRA 1 STUDENTS’ ABILITY TO RELATE THE DEFINITION OF A FUNCTION TO ITS REPRESENTATIONS , Sarah A. Thomson

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