King's College London
Pure mathematics research, key information.
We have a wide range of research opportunities in the four groups that make up the Pure section of the Department of Mathematics, namely the Analysis, Geometry, Number Theory and Probability groups.
We recommend that you identify a broad research area that you are interested in and explore the webpages of the relevant research group(s) . It might be the case that your interest spans more than one group.
You will find links to the personal pages of each of the academic staff in each group and you should try to identify a potential supervisor, who you can then contact directly to discuss further.
You can explore potential supervisors on our research group pages below. Details on how to make an application .
Head of Department: Professor Steven Gilmour
Our department has a large number of active and internationally renowned researchers and postdoctoral research fellows. The research groups organise regular seminars, where top-ranking scientists from around the world present new results, which our research students can witness first hand. The students also organise their own informal seminars and discussion groups. The lively environment and the exceptionally friendly atmosphere at our department contribute to the high success rate of our students. You can apply for supervision in all fields of interest of our staff members. The department provides funding for PhD students to attend suitable schools and conferences during their studies.
More than 80% of the PhD students at the department are fully funded through a number of funding schemes; the most common is departmental funding which covers tuition as well as a living stipend. In recent years, on average, 10 students per year have been admitted to a PhD programme with funding from the department.
- How to apply
- Fees or Funding
For funding opportunities please explore these pages:
- List of funding opportunities
- External funding opportunities for International students
- King’s-China Scholarship Council PhD Scholarship programme (K-CSC)
UK Tuition 2023/24
Full time tuition fees:
£6,540 per year (MPhil/PhD, Mathematics Research)
Part Time Tuition fees:
£3,270 per year (MPhil/PhD, Mathematics Research)
International Tuition Fees 2023/24
£24,360 per year (MPhil/PhD, Mathematics Research)
£12,180 per year (MPhil/PhD, Mathematics Research)
UK Tuition 2024/25
£6,936 per year (MPhil/PhD, Mathematics Research)
£3,468 per year (MPhil/PhD, Mathematics Research)
International Tuition Fees 2024/25
£26,070 per year (MPhil/PhD, Mathematics Research)
£13,035 per year (MPhil/PhD, Mathematics Research)
Mathematics Research with University of Hong Kong or Humboldt-Universität Zu Berlin
£24,360 per year (MPhil/PhD, Mathematics Research with University of Hong Kong)
£24,360 per year (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)
Part time tuition fees: £12,180 (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)
£26,070 per year (MPhil/PhD, Mathematics Research with University of Hong Kong)
£26,070 per year (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)
Part time tuition fees: £13,035 (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)
All of these fees may be subject to additional increases in subsequent years of study, in line with King's terms and conditions.
Bench fees will be applicable to the non-award research programme for visiting students.
- Study environment
Base campus
Strand Campus
Located on the north bank of the River Thames, the Strand Campus houses King's College London's arts and sciences faculties.
You will be assigned a supervisor with whom you will work closely. You will also attend research seminars and take part in other research related activities in your research group, the department and more widely in the University of London. We do not specify fixed attendance hours, but we expect a good level of attendance, and our research students benefit from informal interaction with each other. You will be provided with access to working and storage space, as well as a laptop. On arrival you will discuss your research programme with your supervisor, and you will attend general induction sessions.
Postgraduate training
Carrying out research is learned in apprenticeship mode as PhD student works with a supervisor. Our PhD students receive various forms of training during their period of research, eg attending courses in the London Taught Courses Centre, attendance at EPSRC summer schools; provision of advanced lecture courses; College training courses for graduates who will give tutorial teaching to undergraduates; weekly seminars in the area of your research; frequent research group meetings; attendance at national and international conferences and research meetings.
Communication skills are developed by preparing and presenting seminars in the department, assisted by your supervisor; apprenticeship in writing papers and, in due course, the PhD thesis.
To build your teaching skills and experience, you are strongly encouraged to apply to become a Graduate Teaching Assistant, giving tutorials to our undergraduates (training is provided)
- Entry requirements
- Research groups
The Analysis Group's research interests focus mainly on PDEs, operator theory and spectral theory.
Members of the Geometry Group carry out research on topics within the following areas: algebraic geometry, cohomology theories, differential geometry, geometric analysis, homogeneous space, Lie groups, mirror symmetry, and symplectic geometry.
Number Theory
King's College London has a strong tradition of research in number theory, and this continues today with a particular emphasis on algebraic and representation-theoretic aspects of the subject.
Probability
The Probability group in the Department of Mathematics at King's College London.
Centre for Doctoral Studies
NMES Graduate School
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Funding & Scholarships for PhD students
The Centre for Doctoral Studies helps secure funding for students...
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Pure mathematics projects
- Research projects
By undertaking a project with us, you’ll have the chance to create change within a range of diverse areas.
See our Pure Mathematics Projects
- Pure mathematics
- Algebra and number theory
- Combinatorics
- Computational geometry and topology
- Geometric and nonlinear analysis
- Summer/Winter/SCIE3250
The distribution of prime numbers
Riemannian geometry with symmetries, geometric flows in hermitian geometry, combinatorial and geometric group theory, stochastic differential geometry: probabilistic approaches to geometric problems, projects in computational topology, projects in combinatorial geometry, nonlinear partial differential equations and geometric evolution equations, geometric pde: prescribed curvature problems, the ricci flow, and yang-mills theory, dynamical systems and ergodic theory, the 2-factorisation problem for complete graphs, hamilton cycle decompositions of cayley graphs and related topics, quasi exactly solvable quantum mechanical systems, computational approaches to geometric evolution equations, perfect one-factorisations.
Pure Mathematics Research
Pure Mathematics Fields
- Algebra & Algebraic Geometry
- Algebraic Topology
- Analysis & PDEs
- Geometry & Topology
- Mathematical Logic & Foundations
- Number Theory
- Probability & Statistics
- Representation Theory
Pure Math Committee
Mathematics at MIT is administratively divided into two categories: Pure Mathematics and Applied Mathematics. They comprise the following research areas:
Pure Mathematics
- Algebra & Algebraic Geometry
- Algebraic Topology
- Analysis & PDEs
- Mathematical Logic & Foundations
- Number Theory
- Probability & Statistics
- Representation Theory
Applied Mathematics
In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications.
- Combinatorics
- Computational Biology
- Physical Applied Mathematics
- Computational Science & Numerical Analysis
- Theoretical Computer Science
- Mathematics of Data
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- View all journals
Pure mathematics articles from across Nature Portfolio
Pure mathematics uses mathematics to explore abstract ideas, mathematics that does not necessarily describe a real physical system. This can include developing the fundamental tools used by mathematicians, such as algebra and calculus, describing multi-dimensional space, or better understanding the philosophical meaning of mathematics and numbers themselves.
Latest Research and Reviews
Interval-valued bipolar complex fuzzy soft sets and their applications in decision making.
- Abdul Jaleel
- Tahir Mahmood
Max-mixed EWMA control chart for joint monitoring of mean and variance: an application to yogurt packing process
- Seher Malik
- Muhammad Hanif
- Jumanah Ahmed Darwish
Computation and convergence of fixed-point with an RLC-electric circuit model in an extended b-suprametric space
- Sumati Kumari Panda
- Vijayakumar Velusamy
- Shafiullah Niazai
Spectral shifted Chebyshev collocation technique with residual power series algorithm for time fractional problems
- Saad. Z. Rida
- Anas. A. M. Arafa
- Marwa. M. M. Mostafa
A novel group decision making method based on CoCoSo and interval-valued Q-rung orthopair fuzzy sets
Entropy for q-rung linear diophantine fuzzy hypersoft set with its application in MADM
- Mohd Asif Shah
News and Comment
The real value of numbers
- Mark Buchanan
Machine learning to guide mathematicians
- Fernando Chirigati
A different perspective on the history of the proof of Hall conductance quantization
- Matthew B. Hastings
e is everywhere
From determining the compound interest on borrowed money to gauging chances at the roulette wheel in Monte Carlo, Stefanie Reichert explains that there’s no way around Euler’s number.
- Stefanie Reichert
Imagination captured
Imaginary numbers have a chequered history, and a sparse — if devoted — following. Abigail Klopper looks at why a concept as beautiful as i gets such a bad rap.
- Abigail Klopper
Prime interference
- David Abergel
Quick links
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- Guide to authors
- Editorial policies
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- St Andrews Research Repository
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Main areas of research activity are algebra, including group theory, semigroup theory, lattice theory, and computational group theory, and analysis, including fractal geometry, multifractal analysis, complex dynamical systems, Kleinian groups, and diophantine approximations.
For more information please visit the School of Mathematics and Statistics home page.
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.
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Groups defined by language theoretic classes , rearrangement groups of connected spaces , modern computational methods for finitely presented monoids , finiteness conditions on semigroups relating to their actions and one-sided congruences , on constructing topology from algebra .
251+ Math Research Topics [2024 Updated]
Mathematics, often dubbed as the language of the universe, holds immense significance in shaping our understanding of the world around us. It’s not just about crunching numbers or solving equations; it’s about unraveling mysteries, making predictions, and creating innovative solutions to complex problems. In this blog, we embark on a journey into the realm of math research topics, exploring various branches of mathematics and their real-world applications.
How Do You Write A Math Research Topic?
Writing a math research topic involves several steps to ensure clarity, relevance, and feasibility. Here’s a guide to help you craft a compelling math research topic:
- Identify Your Interests: Start by exploring areas of mathematics that interest you. Whether it’s pure mathematics, applied mathematics, or interdisciplinary topics, choose a field that aligns with your passion and expertise.
- Narrow Down Your Focus: Mathematics is a broad field, so it’s essential to narrow down your focus to a specific area or problem. Consider the scope of your research and choose a topic that is manageable within your resources and time frame.
- Review Existing Literature: Conduct a thorough literature review to understand the current state of research in your chosen area. Identify gaps, controversies, or unanswered questions that could form the basis of your research topic.
- Formulate a Research Question: Based on your exploration and literature review, formulate a clear and concise research question. Your research question should be specific, measurable, achievable, relevant, and time-bound (SMART).
- Consider Feasibility: Assess the feasibility of your research topic in terms of available resources, data availability, and research methodologies. Ensure that your topic is realistic and achievable within the constraints of your project.
- Consult with Experts: Seek feedback from mentors, advisors, or experts in the field to validate your research topic and refine your ideas. Their insights can help you identify potential challenges and opportunities for improvement.
- Refine and Iterate: Refine your research topic based on feedback and further reflection. Iterate on your ideas to ensure clarity, coherence, and relevance to the broader context of mathematics research.
- Craft a Title: Once you have finalized your research topic, craft a compelling title that succinctly summarizes the essence of your research. Your title should be descriptive, engaging, and reflective of the key themes of your study.
- Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap for your study and justify the significance of your research topic.
By following these steps, you can effectively write a math research topic that is well-defined, relevant, and poised to make a meaningful contribution to the field of mathematics.
251+ Math Research Topics: Beginners To Advanced
- Prime Number Distribution in Arithmetic Progressions
- Diophantine Equations and their Solutions
- Applications of Modular Arithmetic in Cryptography
- The Riemann Hypothesis and its Implications
- Graph Theory: Exploring Connectivity and Coloring Problems
- Knot Theory: Unraveling the Mathematics of Knots and Links
- Fractal Geometry: Understanding Self-Similarity and Dimensionality
- Differential Equations: Modeling Physical Phenomena and Dynamical Systems
- Chaos Theory: Investigating Deterministic Chaos and Strange Attractors
- Combinatorial Optimization: Algorithms for Solving Optimization Problems
- Computational Complexity: Analyzing the Complexity of Algorithms
- Game Theory: Mathematical Models of Strategic Interactions
- Number Theory: Exploring Properties of Integers and Primes
- Algebraic Topology: Studying Topological Invariants and Homotopy Theory
- Analytic Number Theory: Investigating Properties of Prime Numbers
- Algebraic Geometry: Geometry Arising from Algebraic Equations
- Galois Theory: Understanding Field Extensions and Solvability of Equations
- Representation Theory: Studying Symmetry in Linear Spaces
- Harmonic Analysis: Analyzing Functions on Groups and Manifolds
- Mathematical Logic: Foundations of Mathematics and Formal Systems
- Set Theory: Exploring Infinite Sets and Cardinal Numbers
- Real Analysis: Rigorous Study of Real Numbers and Functions
- Complex Analysis: Analytic Functions and Complex Integration
- Measure Theory: Foundations of Lebesgue Integration and Probability
- Topological Groups: Investigating Topological Structures on Groups
- Lie Groups and Lie Algebras: Geometry of Continuous Symmetry
- Differential Geometry: Curvature and Topology of Smooth Manifolds
- Algebraic Combinatorics: Enumerative and Algebraic Aspects of Combinatorics
- Ramsey Theory: Investigating Structure in Large Discrete Structures
- Analytic Geometry: Studying Geometry Using Analytic Methods
- Hyperbolic Geometry: Non-Euclidean Geometry of Curved Spaces
- Nonlinear Dynamics: Chaos, Bifurcations, and Strange Attractors
- Homological Algebra: Studying Homology and Cohomology of Algebraic Structures
- Topological Vector Spaces: Vector Spaces with Topological Structure
- Representation Theory of Finite Groups: Decomposition of Group Representations
- Category Theory: Abstract Structures and Universal Properties
- Operator Theory: Spectral Theory and Functional Analysis of Operators
- Algebraic Number Theory: Study of Algebraic Structures in Number Fields
- Cryptanalysis: Breaking Cryptographic Systems Using Mathematical Methods
- Discrete Mathematics: Combinatorics, Graph Theory, and Number Theory
- Mathematical Biology: Modeling Biological Systems Using Mathematical Tools
- Population Dynamics: Mathematical Models of Population Growth and Interaction
- Epidemiology: Mathematical Modeling of Disease Spread and Control
- Mathematical Ecology: Dynamics of Ecological Systems and Food Webs
- Evolutionary Game Theory: Evolutionary Dynamics and Strategic Behavior
- Mathematical Neuroscience: Modeling Brain Dynamics and Neural Networks
- Mathematical Physics: Mathematical Models in Physical Sciences
- Quantum Mechanics: Foundations and Applications of Quantum Theory
- Statistical Mechanics: Statistical Methods in Physics and Thermodynamics
- Fluid Dynamics: Modeling Flow of Fluids Using Partial Differential Equations
- Mathematical Finance: Stochastic Models in Finance and Risk Management
- Option Pricing Models: Black-Scholes Model and Beyond
- Portfolio Optimization: Maximizing Returns and Minimizing Risk
- Stochastic Calculus: Calculus of Stochastic Processes and Itô Calculus
- Financial Time Series Analysis: Modeling and Forecasting Financial Data
- Operations Research: Optimization of Decision-Making Processes
- Linear Programming: Optimization Problems with Linear Constraints
- Integer Programming: Optimization Problems with Integer Solutions
- Network Flow Optimization: Modeling and Solving Flow Network Problems
- Combinatorial Game Theory: Analysis of Games with Perfect Information
- Algorithmic Game Theory: Computational Aspects of Game-Theoretic Problems
- Fair Division: Methods for Fairly Allocating Resources Among Parties
- Auction Theory: Modeling Auction Mechanisms and Bidding Strategies
- Voting Theory: Mathematical Models of Voting Systems and Social Choice
- Social Network Analysis: Mathematical Analysis of Social Networks
- Algorithm Analysis: Complexity Analysis of Algorithms and Data Structures
- Machine Learning: Statistical Learning Algorithms and Data Mining
- Deep Learning: Neural Network Models with Multiple Layers
- Reinforcement Learning: Learning by Interaction and Feedback
- Natural Language Processing: Statistical and Computational Analysis of Language
- Computer Vision: Mathematical Models for Image Analysis and Recognition
- Computational Geometry: Algorithms for Geometric Problems
- Symbolic Computation: Manipulation of Mathematical Expressions
- Numerical Analysis: Algorithms for Solving Numerical Problems
- Finite Element Method: Numerical Solution of Partial Differential Equations
- Monte Carlo Methods: Statistical Simulation Techniques
- High-Performance Computing: Parallel and Distributed Computing Techniques
- Quantum Computing: Quantum Algorithms and Quantum Information Theory
- Quantum Information Theory: Study of Quantum Communication and Computation
- Quantum Error Correction: Methods for Protecting Quantum Information from Errors
- Topological Quantum Computing: Using Topological Properties for Quantum Computation
- Quantum Algorithms: Efficient Algorithms for Quantum Computers
- Quantum Cryptography: Secure Communication Using Quantum Key Distribution
- Topological Data Analysis: Analyzing Shape and Structure of Data Sets
- Persistent Homology: Topological Invariants for Data Analysis
- Mapper Algorithm: Method for Visualization and Analysis of High-Dimensional Data
- Algebraic Statistics: Statistical Methods Based on Algebraic Geometry
- Tropical Geometry: Geometric Methods for Studying Polynomial Equations
- Model Theory: Study of Mathematical Structures and Their Interpretations
- Descriptive Set Theory: Study of Borel and Analytic Sets
- Ergodic Theory: Study of Measure-Preserving Transformations
- Combinatorial Number Theory: Intersection of Combinatorics and Number Theory
- Additive Combinatorics: Study of Additive Properties of Sets
- Arithmetic Geometry: Interplay Between Number Theory and Algebraic Geometry
- Proof Theory: Study of Formal Proofs and Logical Inference
- Reverse Mathematics: Study of Logical Strength of Mathematical Theorems
- Nonstandard Analysis: Alternative Approach to Analysis Using Infinitesimals
- Computable Analysis: Study of Computable Functions and Real Numbers
- Graph Theory: Study of Graphs and Networks
- Random Graphs: Probabilistic Models of Graphs and Connectivity
- Spectral Graph Theory: Analysis of Graphs Using Eigenvalues and Eigenvectors
- Algebraic Graph Theory: Study of Algebraic Structures in Graphs
- Metric Geometry: Study of Geometric Structures Using Metrics
- Geometric Measure Theory: Study of Measures on Geometric Spaces
- Discrete Differential Geometry: Study of Differential Geometry on Discrete Spaces
- Algebraic Coding Theory: Study of Error-Correcting Codes
- Information Theory: Study of Information and Communication
- Coding Theory: Study of Error-Correcting Codes
- Cryptography: Study of Secure Communication and Encryption
- Finite Fields: Study of Fields with Finite Number of Elements
- Elliptic Curves: Study of Curves Defined by Cubic Equations
- Hyperelliptic Curves: Study of Curves Defined by Higher-Degree Equations
- Modular Forms: Analytic Functions with Certain Transformation Properties
- L-functions: Analytic Functions Associated with Number Theory
- Zeta Functions: Analytic Functions with Special Properties
- Analytic Number Theory: Study of Number Theoretic Functions Using Analysis
- Dirichlet Series: Analytic Functions Represented by Infinite Series
- Euler Products: Product Representations of Analytic Functions
- Arithmetic Dynamics: Study of Iterative Processes on Algebraic Structures
- Dynamics of Rational Maps: Study of Dynamical Systems Defined by Rational Functions
- Julia Sets: Fractal Sets Associated with Dynamical Systems
- Mandelbrot Set: Fractal Set Associated with Iterations of Complex Quadratic Polynomials
- Arithmetic Geometry: Study of Algebraic Geometry Over Number Fields
- Diophantine Geometry: Study of Solutions of Diophantine Equations Using Geometry
- Arithmetic of Elliptic Curves: Study of Elliptic Curves Over Number Fields
- Rational Points on Curves: Study of Rational Solutions of Algebraic Equations
- Galois Representations: Study of Representations of Galois Groups
- Automorphic Forms: Analytic Functions with Certain Transformation Properties
- L-functions: Analytic Functions Associated with Automorphic Forms
- Selberg Trace Formula: Tool for Studying Spectral Theory and Automorphic Forms
- Langlands Program: Program to Unify Number Theory and Representation Theory
- Hodge Theory: Study of Harmonic Forms on Complex Manifolds
- Riemann Surfaces: One-dimensional Complex Manifolds
- Shimura Varieties: Algebraic Varieties Associated with Automorphic Forms
- Modular Curves: Algebraic Curves Associated with Modular Forms
- Hyperbolic Manifolds: Manifolds with Constant Negative Curvature
- Teichmüller Theory: Study of Moduli Spaces of Riemann Surfaces
- Mirror Symmetry: Duality Between Calabi-Yau Manifolds
- Kähler Geometry: Study of Hermitian Manifolds with Special Symmetries
- Algebraic Groups: Linear Algebraic Groups and Their Representations
- Lie Algebras: Study of Algebraic Structures Arising from Lie Groups
- Representation Theory of Lie Algebras: Study of Representations of Lie Algebras
- Quantum Groups: Deformation of Lie Groups and Lie Algebras
- Algebraic Topology: Study of Topological Spaces Using Algebraic Methods
- Homotopy Theory: Study of Continuous Deformations of Spaces
- Homology Theory: Study of Algebraic Invariants of Topological Spaces
- Cohomology Theory: Study of Dual Concepts to Homology Theory
- Singular Homology: Homology Theory Defined Using Simplicial Complexes
- Sheaf Theory: Study of Sheaves and Their Cohomology
- Differential Forms: Study of Multilinear Differential Forms
- De Rham Cohomology: Cohomology Theory Defined Using Differential Forms
- Morse Theory: Study of Critical Points of Smooth Functions
- Symplectic Geometry: Study of Symplectic Manifolds and Their Geometry
- Floer Homology: Study of Symplectic Manifolds Using Pseudoholomorphic Curves
- Gromov-Witten Invariants: Invariants of Symplectic Manifolds Associated with Pseudoholomorphic Curves
- Mirror Symmetry: Duality Between Symplectic and Complex Geometry
- Calabi-Yau Manifolds: Ricci-Flat Complex Manifolds
- Moduli Spaces: Spaces Parameterizing Geometric Objects
- Donaldson-Thomas Invariants: Invariants Counting Sheaves on Calabi-Yau Manifolds
- Algebraic K-Theory: Study of Algebraic Invariants of Rings and Modules
- Homological Algebra: Study of Homology and Cohomology of Algebraic Structures
- Derived Categories: Categories Arising from Homological Algebra
- Stable Homotopy Theory: Homotopy Theory with Stable Homotopy Groups
- Model Categories: Categories with Certain Homotopical Properties
- Higher Category Theory: Study of Higher Categories and Homotopy Theory
- Higher Topos Theory: Study of Higher Categorical Structures
- Higher Algebra: Study of Higher Categorical Structures in Algebra
- Higher Algebraic Geometry: Study of Higher Categorical Structures in Algebraic Geometry
- Higher Representation Theory: Study of Higher Categorical Structures in Representation Theory
- Higher Category Theory: Study of Higher Categorical Structures
- Homotopical Algebra: Study of Algebraic Structures in Homotopy Theory
- Homotopical Groups: Study of Groups with Homotopical Structure
- Homotopical Categories: Study of Categories with Homotopical Structure
- Homotopy Groups: Algebraic Invariants of Topological Spaces
- Homotopy Type Theory: Study of Foundations of Mathematics Using Homotopy Theory
In conclusion, the world of mathematics is vast and multifaceted, offering endless opportunities for exploration and discovery. Whether delving into the abstract realms of pure mathematics or applying mathematical principles to solve real-world problems, mathematicians play a vital role in advancing human knowledge and shaping the future of our world.
By embracing diverse math research topics and interdisciplinary collaborations, we can unlock new possibilities and harness the power of mathematics to address the challenges of today and tomorrow. So, let’s embark on this journey together as we unravel the mysteries of numbers and explore the boundless horizons of mathematical inquiry.
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Department of Mathematical Sciences
The Pure Mathematics cluster consists of three research groups in Algebraic Geometry, Dynamical Systems and Geometry and Topology
Pure Mathematics studies the properties of abstract objects and concepts (such as numbers, functions, spaces, graphs and even reasoning itself), usually motivated by their own intrinsic interest or beauty rather than by specific applications outside of mathematics. This is not to say that Pure Mathematics is not applicable indeed, it has a long history of making a fundamental impact on society. For example, the invention of complex numbers by Cardano in 16 th century made possible the quantum mechanical vision of reality in 20 th century, which in turn led to the development of semiconductors and modern computers, and hence the internet and our modern information-based society. The development of number theory and algebraic geometry up until the end of 19 th century provided the level of cryptography needed to secure internet banking in the beginning of 21 st century. The invention of Riemannian geometry during the 19 th century provided the mathematical tools for Einstein's theory of general relativity, which describes space-time as an intrinsically curved four-dimensional object whose geometry is determined by the distribution of mass within it. More recently, discoveries in the theory of dynamical systems have considerable applications in other fields, such as biology, and we can expect further impact of pure mathematics on many areas of science and society in the future. In addition to eventual applications, the deepest problems studied by pure mathematics, such as the Riemann hypothesis or the Poincaré conjecture, shed light at the very basic principles of our world.
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A Project-Based Guide to Undergraduate Research in Mathematics
Starting and Sustaining Accessible Undergraduate Research
- © 2020
- Pamela E. Harris 0 ,
- Erik Insko 1 ,
- Aaron Wootton 2
Mathematics, Williams College, Williamstown, USA
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Mathematics, Florida Gulf Coast University, Fort Myers, USA
Mathematics, university of portland, portland, usa.
- Provides students with all the tools and information they will need to pursue undergraduate research within concise and accessible chapters
- Guides faculty through creating sustainable research programs by offering helpful hints and tips
- Contains a unique chapter on pursuing research in mathematics education
Part of the book series: Foundations for Undergraduate Research in Mathematics (FURM)
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Mentoring Undergraduate Research in Mathematical Modeling
Proving the “Proof”: Interdisciplinary Undergraduate Research Positively Impacts Students
A brief summary of my scientific work and highlights of my career
- Undergraduate research in mathematics
- Phylogenetic networks
Tropical Geometry
- Numerical Semigroups
- Squigonometry
- Mathematical Epidemiology
- combinatorics
Table of contents (11 chapters)
Front matter, folding words around trees: models inspired by rna.
- Elizabeth Drellich, Heather C. Smith
Phylogenetic Networks
- Elizabeth Gross, Colby Long, Joseph Rusinko
- Ralph Morrison
Chip-Firing Games and Critical Groups
- Darren Glass, Nathan Kaplan
Counting Tilings by Taking Walks in a Graph
- Steve Butler, Jason Ekstrand, Steven Osborne
Beyond Coins, Stamps, and Chicken McNuggets: An Invitation to Numerical Semigroups
- Scott Chapman, Rebecca Garcia, Christopher O’Neill
Lateral Movement in Undergraduate Research: Case Studies in Number Theory
- Stephan Ramon Garcia
Projects in (t, r) Broadcast Domination
- Pamela E. Harris, Erik Insko, Katie Johnson
Squigonometry: Trigonometry in the p -Norm
- William E. Wood, Robert D. Poodiack
Researching in Undergraduate Mathematics Education: Possible Directions for Both Undergraduate Students and Faculty
- Milos Savic
Undergraduate Research in Mathematical Epidemiology
- Selenne Bañuelos, Mathew Bush, Marco V. Martinez, Alicia Prieto-Langarica
Editors and Affiliations
Pamela E. Harris
Aaron Wootton
About the editors
Bibliographic information.
Book Title : A Project-Based Guide to Undergraduate Research in Mathematics
Book Subtitle : Starting and Sustaining Accessible Undergraduate Research
Editors : Pamela E. Harris, Erik Insko, Aaron Wootton
Series Title : Foundations for Undergraduate Research in Mathematics
DOI : https://doi.org/10.1007/978-3-030-37853-0
Publisher : Birkhäuser Cham
eBook Packages : Mathematics and Statistics , Mathematics and Statistics (R0)
Copyright Information : Springer Nature Switzerland AG 2020
Hardcover ISBN : 978-3-030-37852-3 Published: 18 April 2020
Softcover ISBN : 978-3-030-37855-4 Published: 18 April 2021
eBook ISBN : 978-3-030-37853-0 Published: 17 April 2020
Series ISSN : 2520-1212
Series E-ISSN : 2520-1220
Edition Number : 1
Number of Pages : XI, 324
Number of Illustrations : 61 b/w illustrations, 81 illustrations in colour
Topics : Combinatorics
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Mathematics Research Proposals Samples For Students
24 samples of this type
Regardless of how high you rate your writing abilities, it's always an appropriate idea to check out an expertly written Research Proposal example, especially when you're dealing with a sophisticated Mathematics topic. This is exactly the case when WowEssays.com database of sample Research Proposals on Mathematics will prove useful. Whether you need to brainstorm a fresh and meaningful Mathematics Research Proposal topic or survey the paper's structure or formatting peculiarities, our samples will provide you with the required data.
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Research Proposal On Whiteboard on Mathematics Classroom
Virtual architecture model, smashing research proposal about research questions, impacts of interactive boards in mathematics classrooms..
- What are the effects of white board technology on mathematics student’s performance and attention? - Do mathematics students engage better while using interactive white boards than without the white board?
Research description
Purpose statement research proposals example, impact of interactive board in mathematics classroom.
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Example Of Research Proposal On The Correlation Between Student Anxiety And Academic Performance In Low-Level College
This paper examines the correlative effects of stress levels on examination results, particularly in areas of academic study where students are already struggling. The research examines the test scores and stress levels of remedial and basic-level mathematics students in the undergraduate level, tracking their changes in stress level over time and the effects that changes in stress level has on a student’s academic performance in in-class mathematics examinations.
Introduction
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Introduction Hippocrates made mathematical advancement during the Golden Age in which fundamental concepts of geometry began thriving in the social dynamics (Huffman, and Filolaos 197). Some of the two core mathematic techniques that occurred during this era include axiomatic techniques to geometry and introduction of paradoxes by the Zeno of Elea (Bell 138). Principally, the paradoxes were concerned with the determination of infinite and infinitesimal mathematic concepts (Klette, and Azriel 455).
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This research proposal will employ a longitudinal experimental design to investigate student learning using Project-based learning for middle school literature classrooms within the same school. The results will be measured by IOWA testing every term over a 3 year time period and compared to the results of the students from traditional classroom setting. Assessment scores will be the dependent variables. The literature review of six peer-reviewed articles is included. The purpose of the study, hypotheses, methodology, participants, procedure, instruments and data analysis will be described.
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Introduction The application of computers is widespread in the current generation. Computers form a fundamental part of our daily lives as well as activities. The application of computers ranges from simple mathematical computations in devices like calculators to complex mathematical computations in industries. Virtually everything depends on computers for operation and completion of various tasks and processes in equal measure. The use of computer presents a variety of advantages over other alternative methods of accomplishing tasks (Krishnamoorthy, et al, 2009).
Background Research
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Old age is associated with several mental illnesses, which culminate into other psychosocial issues. For example, dementia and other related conditions such as the Creutzfeudz Jacob’s disease – as caused by advanced senility – have become common in the modern world. Usually, these diseases affect old people, which become more and more problematic as the age advances. The role of caring for the old people has therefore become very vital, usually requiring increased care and special treatment to these people.
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Home > College of Natural Sciences > Mathematics > Mathematics Theses, Projects, and Dissertations
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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Massachusetts Institute of Technology Department of Mathematics Headquarters Office Simons Building (Building 2), Room 106 77 Massachusetts Avenue
1. When applying for PhD programs outside your home university, the university you apply to usually requires a research statement from you. However, this isn't the case when you reach out for a Bachelor's or Master's thesis topic to a professor you know from your home university (in mathematics). You would just approach a supervisor and express ...
Mathematics in a Research Proposal Emily Clader Good proposal writing is, in many ways, just good math-ematical writing, which is just good writing, period. Nei-ther of these equivalences is entirely true, however, and examining their nuances is a helpful way to probe the question of what exactly makes a strong research proposal in mathematics.
Try to find some survey papers that give a broad overview of the field. Pay particular attention to open problems given in the survey and in the conclusions of papers. One of my colleagues, Prof ...
Pure Mathematics Research. We have a wide range of research opportunities in the four groups that make up the Pure section of the Department of Mathematics, namely the Analysis, Geometry, Number Theory and Probability groups. We recommend that you identify a broad research area that you are interested in and explore the webpages of the relevant ...
Find methods information, sources, references or conduct a literature review on PURE MATHEMATICS. Science topics: Mathematics Algebra Pure Mathematics. ... Research Proposal. Full-text available ...
Projects in combinatorial geometry. Supervisor: Professor Benjamin Burton. Perfect one-factorisations. Supervisor: Dr Barbara Maenhaut. Nonlinear Partial Differential Equations and Geometric Evolution Equations. Supervisor: Professor Joseph Grotowski. Hamilton cycle decompositions of Cayley graphs and related topics.
Massachusetts Institute of Technology Department of Mathematics Headquarters Office Simons Building (Building 2), Room 106 77 Massachusetts Avenue
RESEARCH PROPOSAL 1. Background The central goal of the proposed research is a proof of Cherlin's Conjecture for nite binary primitive groups [5]. Conjecture 1. A nite primitive binary permutation group must be one of the following: (1) a symmetric group Sym(n) acting naturally on nelements; (2) a cyclic group of prime order acting regularly ...
given by a mathematics department with a strong background in pure research. The course module is one of four mathematics courses required for an elementary education qualification, apart from the teaching methods component. It took place bi-weekly, and was given to 37 students, 33 of which were female. The majority of the
So you have to make a few points in your proposal: [ WHY] that the problem you're studying is interesting and worthwhile. [ HOW] that your line of attack (briefly sketched) is plausible. [ WHO] and that you have the right skills to execute this plan. and all of this in 2 pages !
In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications. Combinatorics. Computational Biology. Physical Applied Mathematics. Computational Science & Numerical Analysis.
Research Open Access 15 Apr 2024 Scientific Reports Volume: 14, P: 8683 A novel group decision making method based on CoCoSo and interval-valued Q-rung orthopair fuzzy sets
Al Kohli, Raad Sameer Al Sheikh (2024-06-11) - Thesis. In this thesis we shall study classes of groups defined by formal languages. Our first main topic is the class of groups defined by having an ET0L co-word problem; i.e., the class of co-ET0L groups.
Dive into the world of 251+ math research topics, from pure mathematics to applied fields, uncovering real-world applications. ... Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap ...
PDF | This paper considers the role of projects in teaching pure mathematics - their nature and issues of using them in practice. | Find, read and cite all the research you need on ResearchGate
The Pure Mathematics cluster consists of three research groups in Algebraic Geometry, Dynamical Systems and Geometry and Topology Pure Mathematics studies the properties of abstract objects and concepts (such as numbers, functions, spaces, graphs and even reasoning itself), usually motivated by their own intrinsic interest or beauty rather than ...
This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs. The chapters in this work span a variety of topical areas of pure and applied mathematics and mathematics education.
Jan 19, 2022 at 10:19. 2. Universities in UK do not usually ask for a full research proposal, but rather a short summary of what topic/questions you are interested in (although it might be different in the university you are applying to). - S R Maiti. Jan 19, 2022 at 12:50. 2. With the caveat that (within UK system) I have only observed ...
Good Research Proposal On P (G,S,R)= P (G/S,R)P (S/R)P (R) The Bayesian method, also known as Bayesian method, is an inferential rule that is commonly used whenever an update is required within any probability estimate (Cohen et al. 12-57).
bio-mathematics: introduction to the mathematical model of the hepatitis c virus, lucille j. durfee. pdf. analysis and synthesis of the literature regarding active and direct instruction and their promotion of flexible thinking in mathematics, genelle elizabeth gonzalez. pdf. life expectancy, ali r. hassanzadah. pdf