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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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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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[100+] Mathematics Research Topics With Free [Thesis Pdf] 2023
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Mathematics Research for the Beginning Student, Volume 1
Accessible Projects for Students Before Calculus
- © 2022
- Eli E. Goldwyn 0 ,
- Sandy Ganzell 1 ,
- Aaron Wootton 2
Mathematics, University of Portland, Portland, USA
You can also search for this editor in PubMed Google Scholar
Mathematics & Computer Science, St. Mary’s College of Maryland, St. Mary’s City, USA
- Focuses on mathematics research topics suitable for students who have not yet taken calculus
- Equips students with the tools needed to begin their own mathematics research projects, with or without faculty advisors
- Provides substantial background material and recommendations for further reading in each chapter
Part of the book series: Foundations for Undergraduate Research in Mathematics (FURM)
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Table of contents (9 chapters)
Front matter, games on graphs: cop and robber, hungry spiders, and broadcast domination.
- Joshua Carlson, Pamela E. Harris, Peter Hollander, Erik Insko
Mathematics for Sustainable Humanity: Population, Climate, Energy, Economy, Policy, and Social Justice
Mosaics and virtual knots.
Sandy Ganzell
Graph Labelings: A Prime Area to Explore
- Elizabeth A. Donovan, Lesley W. Wiglesworth
Acrobatics in a Parametric Arena
- Therese Shelton, Bonnie Henderson, Michael Gebhardt
But Who Should Have Won? Simulating Outcomes of Judging Protocols and Ranking Systems
- Ann W. Clifton, Allison L. Lewis
Modeling of Biological Systems: From Algebra to Calculus and Computer Simulations
- Alexander Dimitrov, Giovanna Guidoboni, William Hall, Raul Invernizzi, Sergey Lapin, Thomas McCutcheon et al.
Population Dynamics of Infectious Diseases
- Glenn Ledder, Michelle Homp
Playing with Knots
- Allison Henrich
- Undergraduate Mathematics Research
- Mathematics Research Topics
- Mathematical Modeling
- Mathematics for Sustainability
- Mathematical Epidemiology
About this book
- games on graphs
- modeling of biological systems
- mosaics and virtual knots
- mathematics for sustainable humanity
- mathematical epidemiology
Editors and Affiliations
Eli E. Goldwyn, Aaron Wootton
Mathematics & Computer Science, St. Mary’s College of Maryland, St. Mary’s City, USA
About the editors, bibliographic information.
Book Title : Mathematics Research for the Beginning Student, Volume 1
Book Subtitle : Accessible Projects for Students Before Calculus
Editors : Eli E. Goldwyn, Sandy Ganzell, Aaron Wootton
Series Title : Foundations for Undergraduate Research in Mathematics
DOI : https://doi.org/10.1007/978-3-031-08560-4
Publisher : Birkhäuser Cham
eBook Packages : Mathematics and Statistics , Mathematics and Statistics (R0)
Copyright Information : The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN : 978-3-031-08559-8 Published: 25 November 2022
Softcover ISBN : 978-3-031-08562-8 Published: 25 November 2023
eBook ISBN : 978-3-031-08560-4 Published: 24 November 2022
Series ISSN : 2520-1212
Series E-ISSN : 2520-1220
Edition Number : 1
Number of Pages : IX, 318
Number of Illustrations : 108 b/w illustrations, 103 illustrations in colour
Topics : Mathematics, general , Mathematics Education
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Mathematics PhD theses
A selection of Mathematics PhD thesis titles is listed below, some of which are available online:
2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991
Melanie Kobras – Low order models of storm track variability
Ed Clark – Vectorial Variational Problems in L∞ and Applications to Data Assimilation
Katerina Christou – Modelling PDEs in Population Dynamics using Fixed and Moving Meshes
Chiara Cecilia Maiocchi – Unstable Periodic Orbits: a language to interpret the complexity of chaotic systems
Samuel R Harrison – Stalactite Inspired Thin Film Flow
Elena Saggioro – Causal network approaches for the study of sub-seasonal to seasonal variability and predictability
Cathie A Wells – Reformulating aircraft routing algorithms to reduce fuel burn and thus CO 2 emissions
Jennifer E. Israelsson – The spatial statistical distribution for multiple rainfall intensities over Ghana
Giulia Carigi – Ergodic properties and response theory for a stochastic two-layer model of geophysical fluid dynamics
André Macedo – Local-global principles for norms
Tsz Yan Leung – Weather Predictability: Some Theoretical Considerations
Jehan Alswaihli – Iteration of Inverse Problems and Data Assimilation Techniques for Neural Field Equations
Jemima M Tabeart – On the treatment of correlated observation errors in data assimilation
Chris Davies – Computer Simulation Studies of Dynamics and Self-Assembly Behaviour of Charged Polymer Systems
Birzhan Ayanbayev – Some Problems in Vectorial Calculus of Variations in L∞
Penpark Sirimark – Mathematical Modelling of Liquid Transport in Porous Materials at Low Levels of Saturation
Adam Barker – Path Properties of Levy Processes
Hasen Mekki Öztürk – Spectra of Indefinite Linear Operator Pencils
Carlo Cafaro – Information gain that convective-scale models bring to probabilistic weather forecasts
Nicola Thorn – The boundedness and spectral properties of multiplicative Toeplitz operators
James Jackaman – Finite element methods as geometric structure preserving algorithms
Changqiong Wang - Applications of Monte Carlo Methods in Studying Polymer Dynamics
Jack Kirk - The molecular dynamics and rheology of polymer melts near the flat surface
Hussien Ali Hussien Abugirda - Linear and Nonlinear Non-Divergence Elliptic Systems of Partial Differential Equations
Andrew Gibbs - Numerical methods for high frequency scattering by multiple obstacles (PDF-2.63MB)
Mohammad Al Azah - Fast Evaluation of Special Functions by the Modified Trapezium Rule (PDF-913KB)
Katarzyna (Kasia) Kozlowska - Riemann-Hilbert Problems and their applications in mathematical physics (PDF-1.16MB)
Anna Watkins - A Moving Mesh Finite Element Method and its Application to Population Dynamics (PDF-2.46MB)
Niall Arthurs - An Investigation of Conservative Moving-Mesh Methods for Conservation Laws (PDF-1.1MB)
Samuel Groth - Numerical and asymptotic methods for scattering by penetrable obstacles (PDF-6.29MB)
Katherine E. Howes - Accounting for Model Error in Four-Dimensional Variational Data Assimilation (PDF-2.69MB)
Jian Zhu - Multiscale Computer Simulation Studies of Entangled Branched Polymers (PDF-1.69MB)
Tommy Liu - Stochastic Resonance for a Model with Two Pathways (PDF-11.4MB)
Matthew Paul Edgington - Mathematical modelling of bacterial chemotaxis signalling pathways (PDF-9.04MB)
Anne Reinarz - Sparse space-time boundary element methods for the heat equation (PDF-1.39MB)
Adam El-Said - Conditioning of the Weak-Constraint Variational Data Assimilation Problem for Numerical Weather Prediction (PDF-2.64MB)
Nicholas Bird - A Moving-Mesh Method for High Order Nonlinear Diffusion (PDF-1.30MB)
Charlotta Jasmine Howarth - New generation finite element methods for forward seismic modelling (PDF-5,52MB)
Aldo Rota - From the classical moment problem to the realizability problem on basic semi-algebraic sets of generalized functions (PDF-1.0MB)
Sarah Lianne Cole - Truncation Error Estimates for Mesh Refinement in Lagrangian Hydrocodes (PDF-2.84MB)
Alexander J. F. Moodey - Instability and Regularization for Data Assimilation (PDF-1.32MB)
Dale Partridge - Numerical Modelling of Glaciers: Moving Meshes and Data Assimilation (PDF-3.19MB)
Joanne A. Waller - Using Observations at Different Spatial Scales in Data Assimilation for Environmental Prediction (PDF-6.75MB)
Faez Ali AL-Maamori - Theory and Examples of Generalised Prime Systems (PDF-503KB)
Mark Parsons - Mathematical Modelling of Evolving Networks
Natalie L.H. Lowery - Classification methods for an ill-posed reconstruction with an application to fuel cell monitoring
David Gilbert - Analysis of large-scale atmospheric flows
Peter Spence - Free and Moving Boundary Problems in Ion Beam Dynamics (PDF-5MB)
Timothy S. Palmer - Modelling a single polymer entanglement (PDF-5.02MB)
Mohamad Shukor Talib - Dynamics of Entangled Polymer Chain in a Grid of Obstacles (PDF-2.49MB)
Cassandra A.J. Moran - Wave scattering by harbours and offshore structures
Ashley Twigger - Boundary element methods for high frequency scattering
David A. Smith - Spectral theory of ordinary and partial linear differential operators on finite intervals (PDF-1.05MB)
Stephen A. Haben - Conditioning and Preconditioning of the Minimisation Problem in Variational Data Assimilation (PDF-3.51MB)
Jing Cao - Molecular dynamics study of polymer melts (PDF-3.98MB)
Bonhi Bhattacharya - Mathematical Modelling of Low Density Lipoprotein Metabolism. Intracellular Cholesterol Regulation (PDF-4.06MB)
Tamsin E. Lee - Modelling time-dependent partial differential equations using a moving mesh approach based on conservation (PDF-2.17MB)
Polly J. Smith - Joint state and parameter estimation using data assimilation with application to morphodynamic modelling (PDF-3Mb)
Corinna Burkard - Three-dimensional Scattering Problems with applications to Optical Security Devices (PDF-1.85Mb)
Laura M. Stewart - Correlated observation errors in data assimilation (PDF-4.07MB)
R.D. Giddings - Mesh Movement via Optimal Transportation (PDF-29.1MbB)
G.M. Baxter - 4D-Var for high resolution, nested models with a range of scales (PDF-1.06MB)
C. Spencer - A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table.
P. Jelfs - A C-property satisfying RKDG Scheme with Application to the Morphodynamic Equations (PDF-11.7MB)
L. Bennetts - Wave scattering by ice sheets of varying thickness
M. Preston - Boundary Integral Equations method for 3-D water waves
J. Percival - Displacement Assimilation for Ocean Models (PDF - 7.70MB)
D. Katz - The Application of PV-based Control Variable Transformations in Variational Data Assimilation (PDF- 1.75MB)
S. Pimentel - Estimation of the Diurnal Variability of sea surface temperatures using numerical modelling and the assimilation of satellite observations (PDF-5.9MB)
J.M. Morrell - A cell by cell anisotropic adaptive mesh Arbitrary Lagrangian Eulerian method for the numerical solution of the Euler equations (PDF-7.7MB)
L. Watkinson - Four dimensional variational data assimilation for Hamiltonian problems
M. Hunt - Unique extension of atomic functionals of JB*-Triples
D. Chilton - An alternative approach to the analysis of two-point boundary value problems for linear evolutionary PDEs and applications
T.H.A. Frame - Methods of targeting observations for the improvement of weather forecast skill
C. Hughes - On the topographical scattering and near-trapping of water waves
B.V. Wells - A moving mesh finite element method for the numerical solution of partial differential equations and systems
D.A. Bailey - A ghost fluid, finite volume continuous rezone/remap Eulerian method for time-dependent compressible Euler flows
M. Henderson - Extending the edge-colouring of graphs
K. Allen - The propagation of large scale sediment structures in closed channels
D. Cariolaro - The 1-Factorization problem and same related conjectures
A.C.P. Steptoe - Extreme functionals and Stone-Weierstrass theory of inner ideals in JB*-Triples
D.E. Brown - Preconditioners for inhomogeneous anisotropic problems with spherical geometry in ocean modelling
S.J. Fletcher - High Order Balance Conditions using Hamiltonian Dynamics for Numerical Weather Prediction
C. Johnson - Information Content of Observations in Variational Data Assimilation
M.A. Wakefield - Bounds on Quantities of Physical Interest
M. Johnson - Some problems on graphs and designs
A.C. Lemos - Numerical Methods for Singular Differential Equations Arising from Steady Flows in Channels and Ducts
R.K. Lashley - Automatic Generation of Accurate Advection Schemes on Structured Grids and their Application to Meteorological Problems
J.V. Morgan - Numerical Methods for Macroscopic Traffic Models
M.A. Wlasak - The Examination of Balanced and Unbalanced Flow using Potential Vorticity in Atmospheric Modelling
M. Martin - Data Assimilation in Ocean circulation models with systematic errors
K.W. Blake - Moving Mesh Methods for Non-Linear Parabolic Partial Differential Equations
J. Hudson - Numerical Techniques for Morphodynamic Modelling
A.S. Lawless - Development of linear models for data assimilation in numerical weather prediction .
C.J.Smith - The semi lagrangian method in atmospheric modelling
T.C. Johnson - Implicit Numerical Schemes for Transcritical Shallow Water Flow
M.J. Hoyle - Some Approximations to Water Wave Motion over Topography.
P. Samuels - An Account of Research into an Area of Analytical Fluid Mechnaics. Volume II. Some mathematical Proofs of Property u of the Weak End of Shocks.
M.J. Martin - Data Assimulation in Ocean Circulation with Systematic Errors
P. Sims - Interface Tracking using Lagrangian Eulerian Methods.
P. Macabe - The Mathematical Analysis of a Class of Singular Reaction-Diffusion Systems.
B. Sheppard - On Generalisations of the Stone-Weisstrass Theorem to Jordan Structures.
S. Leary - Least Squares Methods with Adjustable Nodes for Steady Hyperbolic PDEs.
I. Sciriha - On Some Aspects of Graph Spectra.
P.A. Burton - Convergence of flux limiter schemes for hyperbolic conservation laws with source terms.
J.F. Goodwin - Developing a practical approach to water wave scattering problems.
N.R.T. Biggs - Integral equation embedding methods in wave-diffraction methods.
L.P. Gibson - Bifurcation analysis of eigenstructure assignment control in a simple nonlinear aircraft model.
A.K. Griffith - Data assimilation for numerical weather prediction using control theory. .
J. Bryans - Denotational semantic models for real-time LOTOS.
I. MacDonald - Analysis and computation of steady open channel flow .
A. Morton - Higher order Godunov IMPES compositional modelling of oil reservoirs.
S.M. Allen - Extended edge-colourings of graphs.
M.E. Hubbard - Multidimensional upwinding and grid adaptation for conservation laws.
C.J. Chikunji - On the classification of finite rings.
S.J.G. Bell - Numerical techniques for smooth transformation and regularisation of time-varying linear descriptor systems.
D.J. Staziker - Water wave scattering by undulating bed topography .
K.J. Neylon - Non-symmetric methods in the modelling of contaminant transport in porous media. .
D.M. Littleboy - Numerical techniques for eigenstructure assignment by output feedback in aircraft applications .
M.P. Dainton - Numerical methods for the solution of systems of uncertain differential equations with application in numerical modelling of oil recovery from underground reservoirs .
M.H. Mawson - The shallow-water semi-geostrophic equations on the sphere. .
S.M. Stringer - The use of robust observers in the simulation of gas supply networks .
S.L. Wakelin - Variational principles and the finite element method for channel flows. .
E.M. Dicks - Higher order Godunov black-oil simulations for compressible flow in porous media .
C.P. Reeves - Moving finite elements and overturning solutions .
A.J. Malcolm - Data dependent triangular grid generation. .
Pure Mathematics Research
Pure mathematics fields.
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Mathematics, Pure and Applied Math | Explore the latest full-text research PDFs, articles, conference papers, preprints and more on MATHEMATICS. Find methods information, sources, references or ...
PDF. Research In Short Term Actuarial Modeling, Elijah Howells. PDF. Hyperbolic Triangle Groups, ... PDF. BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS, ... Simple Groups and Related Topics, Manal Abdulkarim Marouf Ms. PDF. Elliptic Curves, ...
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.
2. Wavelet-Galerkin technique for solving certain numerical differential equations and inverse Ill-posed problems. Download. 3. Some study on edge geodetic number of a graph. Download. 4. Haar wavelet technique for solving certain differential integral and integro differential equations. Download.
This research aims to uncover current trends and key issues by examining the research in mathematics education during the period 2017-2021. For this purpose, five major peer reviewed academic journals ... see the details of different topics, ask new questions, and even see alternative ways/possibilities (Ernest et al., 2016). Schoenfeld (2000 ...
Pavel Etingof is professor of mathematics at Massachusetts Institute of Technology and the PRIMES chief research ad-viser. His email is [email protected]. Slava Gerovitch is a lecturer in history of mathematics at Massachusetts Institute of Technology and the PRIMES program director. His email is [email protected]. All
Before the pandemic (2019), we asked: On what themes should research in mathematics education focus in the coming decade? The 229 responses from 44 countries led to eight themes plus considerations about mathematics education research itself. The themes can be summarized as teaching approaches, goals, relations to practices outside mathematics education, teacher professional development ...
Each chapter gives a self-contained introduction on a research topic with an emphasis on the specific tools and knowledge needed to create and maintain fruitful research programs for undergraduates. Some of the topics discussed include: • Disease modeling • Tropical curves and surfaces • Numerical semigroups • Mathematics Education
Research in Mathematics is a broad open access journal publishing all aspects of mathematics including pure, applied, and interdisciplinary mathematics, and mathematical education and other fields. The journal primarily publishes research articles, but also welcomes review and survey articles, and case studies. Topics include, but are not limited to:
The high school dropout. rate in 2006 was 6.3% while the chronic truancy rate was at 7.4%. The financial earnings of the teachers and administrators at this district average at. $62, 452 per year. The teachers in this district have been working for an average for 12.5. years.
Strategies and interventions employed by teachers in supporting students with mathematics learning difficulties in Kenya. James Alan Oloo. Published online: 3 May 2024. Explore the current issue of Research in Mathematics Education, Volume 26, Issue 1, 2024.
Some topics covered include: games on graphs; modeling of biological systems; mosaics and virtual knots; mathematics for sustainable humanity; mathematical epidemiology; Mathematics Research for the Beginning Student, Volume 1 will appeal to undergraduate students at two- and four-year colleges who are interested in pursuing mathematics ...
A selection of Mathematics PhD thesis titles is listed below, some of which are available online: 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991. 2023. Melanie Kobras - Low order models of storm track variability Ed Clark - Vectorial Variational Problems in L∞ and Applications ...
Research in Mathematics, Volume 11, Issue 1 (2024) See all volumes and issues. Volume 11, 2024 Vol 10, 2023 Vol 9, 2022 Vol 8, 2021 Vol 7, 2020 Vol 6, 2019 Vol 5, 2018 Vol 4, 2017 Vol 3, 2016 Vol 2, 2015 Vol 1, 2014. Download citations Download PDFs Download issue. Browse by section (All)
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.
Pure Mathematics Research Pure Mathematics Fields The E 8 Lie group. Algebra & Algebraic Geometry; Algebraic Topology; Analysis & PDEs; Geometry & Topology; Mathematical Logic & Foundations; ... Department of Mathematics Headquarters Office Simons Building (Building 2), Room 106 77 Massachusetts Avenue Cambridge, MA 02139-4307 Campus Map (617 ...
Browse the list of issues and latest articles from Research in Mathematics Education. All issues. Special issues. Latest articles. Volume 26 2024. Volume 25 2023. Volume 24 2022. Volume 23 2021. Volume 22 2020.
Mathematics learning is particularly vul-nerable in a disrupted school year (Kuhfeld and Tarasawa 2020), so mathematics teaching and learning must be prioritized in any plan. Questions and processes are described in this document to facilitate the collaborations needed around issues influencing how to move mathematics learning forward.
particular topic for the EE, the need to identify a well -thought-out research question and the requirement to search for the mathematical problems that require a solution. Students must be advised that mathematical research is a longterm and open- -ended exploration of a set of related mathematical problems that are based on personal observations.
enrolled in high school (often en route to college) took courses in algebra, geometry, and physics. Schoenfeld: Research in Mathematics Education 499. The late 19th and early 20th centuries ...