Mathematics Projects

Overview

Mathematics is the logical study of abstract structures and relationships.

Math Projects

Elementary

  1. Algebraic equations.
  2. Algebraic expressions.
  3. Analytic geometry of points and lines.
  4. Angle measurement.
  5. Angles.
  6. Angles in segments of circles.
  7. Approximations of functions.
  8. Arc length.
  9. Arcs.
  10. Area.
  11. Area under a curve.
  12. Arithmetic operations.
  13. Binomials.
  14. Chords.
  15. Circles.
  16. Combinations.
  17. Complex numbers.
  18. Cones.
  19. Conic sections.
  20. Continuous functions.
  21. Cubes.
  22. Cubic equations.
  23. Curves.
  24. Cylinders.
  25. Decimal calculations.
  26. Denominate numbers.
  27. Derivatives.
  28. Differentials.
  29. Differentiation rules.
  30. Distance.
  31. Divisors.
  32. Equations.
  33. Estimation.
  34. Euclidean algorithm.
  35. Exponential equations.
  36. Exponential functions.
  37. Factoring.
  38. Factors.
  39. Fermat's last theorem.
  40. Field of complex numbers.
  41. Four color problem.
  42. Fractals.
  43. Fractional equations.
  44. Fractional exponents.
  45. Fractions.
  46. Functions.
  47. Functions of a complex variable.
  48. Functions of several variables.
  49. Geometric constructions.
  50. Goldbach conjecture.
  51. Graphs.
  52. Greatest common divisor.
  53. Groups.
  54. Growth.
  55. Inequalities.
  56. Imaginary numbers.
  57. Increment.
  58. Integrals.
  59. Intersecting circles.
  60. Knots.
  61. Laws of exponents.
  62. Leat common multiple.
  63. Limits.
  64. Linear algebra.
  65. Logarithmic functions.
  66. Logarithms.
  67. Logical statements.
  68. Matrices.
  69. Mathematical induction.
  70. Maxima and minima.
  71. Methods of integration.
  72. Minimal surfaces.
  73. Multiples.
  74. Natural numbers.
  75. Noneuclidean geometry.
  76. Number fields.
  77. Number theory.
  78. Oblique triangles.
  79. Ordered fields.
  80. Ordinary differential equations.
  81. Parallelograms.
  82. Parallels.
  83. Parametric equations.
  84. Partial differential equations.
  85. Percentage.
  86. Polar coordinates.
  87. Polygons.
  88. Polynomial functions.
  89. Polynomials.
  90. Powers.
  91. Prime divisors.
  92. Prime numbers.
  93. Probability.
  94. Progressions.
  95. Proofs.
  96. Projective geometry.
  97. Proportion.
  98. Pyramids.
  99. Pythagorean theorem.
  100. Quadratic equations.
  101. Quadrilaterals.
  102. Quartic equations.
  103. Radicals.
  104. Rates.
  105. Ratio.
  106. Real numbers.
  107. Regular pentagon.
  108. Regular polygons.
  109. Regular solids.
  110. Righ triangles.
  111. Roots.
  112. Secants.
  113. Sequences.
  114. Series.
  115. Set theory.
  116. Similar figures.
  117. Simultaneous equations.
  118. Solid figures.
  119. Spheres.
  120. Squaring the circle.
  121. Straight lines.
  122. Surface area.
  123. Surfaces.
  124. Symmetry.
  125. Tangents.
  126. Taylor's formula.
  127. The calculus of variations.
  128. The continuum hypothesis.
  129. The number e.
  130. The number system of mathematics.
  131. Topology.
  132. Triangles.
  133. Trigonometric functions.
  134. Trigonometric identities.
  135. Twin primes.
  136. Variation.
  137. Vectors.
  138. Volume.

Intermediate

  1. Accessibility
  2. Amicable Numbers
  3. Analysis of Variance
  4. Approximation
  5. Arc Length
  6. Arithmetic Functions
  7. Assignments and matchings
  8. Asymptotics
  9. Automata
  10. Autonomous Systems
  11. Axiom of Choice
  12. Bases
  13. Basis
  14. BCH Codes
  15. Bilinear Forms
  16. Binomial Distribution
  17. Bloch's Theorem
  18. Boolean Algebra
  19. Boundary Value Problems
  20. Burst-Error Correction
  21. Calculus of Variations
  22. Canonical Forms
  23. Cardinality
  24. Cartesian Products
  25. Catenary
  26. Cauchy-Riemann Equations
  27. Cauchys Integral
  28. Cayley's Theorem
  29. Central Limit Theorem
  30. Central Tendency
  31. Chaos
  32. Characteristic Functions
  33. Chi-Square Test
  34. Classical Cryptosystems
  35. Closed Sets
  36. Cofactors
  37. Combinatorial Designs
  38. Compactness
  39. Completeness
  40. Complex Arithmetic
  41. Complex Integration
  42. Complex Mappings
  43. Complex Numbers
  44. Complex Roots of Polynomials
  45. Complex Series
  46. Complex Variables
  47. Computational Methods for Constructing Irreducible Polynomials
  48. Computational Methods for Factoring Polynomials
  49. Computer Algebra
  50. Conditional Distributions
  51. Congruence
  52. Connectedness
  53. Connectivity
  54. Constrained Extrema
  55. Continuity
  56. Continuous Distribution Functions
  57. Continuous Functions
  58. Contour Integration
  59. Convergence of Random Variables
  60. Convergence Tests
  61. Convergence Theorems
  62. Convexity
  63. Convolutions
  64. Correlation
  65. Countability
  66. Counting
  67. Curvature
  68. Cycles
  69. Cyclic Codes
  70. De Moivre's Theorem
  71. Decoding Algorithms
  72. Decompositions
  73. Diagonalization
  74. Differentiability
  75. Dimension
  76. Diophantine Equations
  77. Directional Derivatives
  78. Discrete Logarithm Problem
  79. Discrete Probability
  80. Discrete Random Variables
  81. Divergence Theorem
  82. Dual Spaces
  83. Duality
  84. Eigenfunction Expansions
  85. Elliptical Geometry
  86. Equivalence Relations
  87. Error Analysis
  88. Estimation
  89. Euclidean Spaces
  90. Euler's Theorem
  91. Even and Odd Functions
  92. Existence and Uniqueness of Solutions
  93. Expectation
  94. Exponential Map
  95. Factoring
  96. Families of Distributions
  97. Fermat's Last Theorem
  98. Fields
  99. Finite State Machines
  100. First-Order Differential Equations
  101. Fourier Series
  102. Fourier Transforms
  103. Game Theory
  104. Generating Functions
  105. Geometry of Space
  106. Grammars
  107. Graph Colorings
  108. Graphs
  109. Green's Functions
  110. Groebner Bases over Fields
  111. Groups
  112. Green's Functions
  113. Green's Theorem
  114. Hamiltonicity
  115. Hamming and Golay Codes
  116. Higher-Order Linear Differential Equations with Constant Coefficients
  117. Hyperbolic Equations
  118. Hyperbolic Functions
  119. Hyperbolic Geometry
  120. Hyperbolic Identities
  121. Hypothesis Testing
  122. Ideals
  123. Implicit Function Theorem
  124. Induction
  125. Information Theory
  126. Initial Value Problems
  127. Inner Product Spaces
  128. Integer Programming
  129. Integral Domains
  130. Interpolation
  131. Interval Estimation
  132. Invariant Subspaces
  133. Inverse Function Theorem
  134. Isometries
  135. Isomorphism Theorems
  136. Isoperimetric Problems
  137. Iterative Methods for Linear Systems
  138. Joint Distributions
  139. Jordan Canonical Form
  140. Koch Snowflake
  141. Lagrange Multipliers
  142. Languages
  143. Laplace Transforms
  144. Laurent Series
  145. Least Squares Analysis
  146. Likelihood Ratio Tests
  147. Limit Proofs
  148. Line Integrals
  149. Linear Codes
  150. Linear Difference Equations
  151. Linear Groups
  152. Linear Independence
  153. Linear Operators
  154. Linear Programming
  155. Linear Spaces
  156. Linear Systems
  157. Linear Transformations
  158. Mandelbrot Set
  159. Matchings
  160. Mathematical Logic
  161. Mathematical Modeling
  162. Markov Chains
  163. Markov Processes
  164. Method of Frobenius
  165. Methods of Proof
  166. Metric Spaces
  167. Min-Cost Flows and Circulations
  168. Modules
  169. Moments of Random Variables
  170. Multilinear Algebra
  171. Multivariate Probability Distribution
  172. Network Flows
  173. Newton's Method
  174. Noneuclidean Geometry
  175. Nonlinear Difference Equations
  176. Nonlinear Differential Equations
  177. Nonlinear Programming
  178. Nonparametric Tests
  179. Null Space
  180. Numerical Differentiation
  181. Numerical Integration
  182. Numerical Solution of Linear Equations
  183. Numerical Solution of Nonlinear Equations
  184. Numerical Solution of Ordinary Differential Equations
  185. One-Way Functions
  186. Open Mapping Theorem
  187. Open Sets
  188. Optimization
  189. Order Relations
  190. Order Statistics
  191. Orthonormal Bases
  192. Orthogonal Curvilinear Coordinates
  193. Orthogonal Polynomials
  194. Orthogonal Projections
  195. Orthogonality
  196. Orthonormal Systems
  197. Out-of-Kilter Method
  198. Parallelism
  199. Partial Differential Equations
  200. Partial Orders
  201. Partitions
  202. Penalty Method
  203. Period Doubling
  204. Periodic Solutions
  205. Phase Plane Analysis
  206. Planarity
  207. Poincare-Bendixson Theory
  208. Point Estimation
  209. Point Sets
  210. Pointwise Convergence
  211. Poisson Distribution
  212. Polynomial Approximations
  213. Polynomial Data Fitting
  214. Posets
  215. Power Series Solutions of Differential Equations
  216. Primality Testing
  217. Principle Axes
  218. Principle of Inclusion and Exclusion
  219. Probability Models
  220. Product Spaces
  221. Projective Geometry
  222. Quadratic Forms
  223. Quotient Rings
  224. Ramsey Theory
  225. Random Error Detection and Correction
  226. Recurrence Relations
  227. Reduction of Order
  228. Regression Analysis
  229. Relations
  230. Riemann Integral
  231. Riemann Mapping Theorem
  232. Riemann Zeta Function
  233. Riemann-Stieltjes Integral
  234. Rings
  235. RSA and Other Public Key Cryptosystems
  236. Sampling Distributions
  237. Schottley's Theorem
  238. Schwarz-Christoffel Transformation
  239. Schwarz's Lemma
  240. Separation of Variables
  241. Shifting Orthogonal Coordinates
  242. Shortest Paths
  243. Similarity
  244. Simplex Method
  245. Span
  246. Spanning Trees
  247. Special Functions
  248. Stochastic Processes
  249. Stokes' Theorem
  250. Sturm-Liouville Problems
  251. Structure of Finite Fields
  252. Subspaces
  253. Sylow Theorems
  254. Systems of Polynomial Equations
  255. Tests of Hypotheses
  256. Tests of Statistical Significance
  257. Theory of Groebner Bases
  258. Topological Spaces
  259. Trees
  260. Uniform Continuity
  261. Uniform Convergence

Advanced

  1. Adjoints
  2. Algebraic Combinatorics
  3. Algebraic Extensions
  4. Algebraic Geometry
  5. Algebraic Topology
  6. Analytic Functions
  7. Analytic Number Theory
  8. Artinian Rings
  9. Asymptotic Behavior of Solutions to Ordinary Differential Equations
  10. Asymptotic Distributions
  11. Asymptotic Expansions
  12. Automorphic Forms
  13. Banach Algebras
  14. Banach Spaces
  15. Barrier Method
  16. Basis for a Topology
  17. Bessel Functions
  18. Bifurcations
  19. Block Cyphers
  20. Block Designs
  21. Boundary-Value Problems
  22. Bounded Arithmetic
  23. Bounded Operators
  24. Branching
  25. Brownian Motion
  26. Cantor Set
  27. Category Theory
  28. Change of Variables Formula
  29. Chaotic Dynamics on Fractals
  30. Chebyshev's Inequality
  31. Colorings
  32. Commutative Algebra
  33. Complex Integration
  34. Composition Series
  35. Computational Number Theory
  36. Computing Fractals
  37. Conformal Mapping
  38. Congruence Arithmetic
  39. Congruences
  40. Connectivity
  41. Continuous Stochastic Processes
  42. Convergence Theorems for Integrals
  43. Convex Functions
  44. Convex Sets
  45. Convexity
  46. Convolutional Codes with Trellis Decoding
  47. Covering Maps
  48. Covering Spaces
  49. Critical Behavior
  50. Cryptography
  51. Curvilinear Coordinates
  52. Data Compression
  53. Decision Models
  54. Descent Method
  55. Decomposition Principle
  56. Dependence on Initial Conditions
  57. Difference Sets
  58. Differential Manifolds
  59. Diffusion Equation
  60. Diffusion Processes
  61. Dirichlet Character
  62. Dirichlet Problem
  63. Disjoint Paths
  64. Dispersion
  65. Distribution of Quadtratic Forms
  66. Distribution Theory
  67. Distributions of Random Variables
  68. Divergence Theorem
  69. Dual Method
  70. Duality
  71. Dynamic Programming
  72. Eilenberg Steenrod Axioms
  73. Elliptic Equations
  74. Error Approximation
  75. Euler Tours
  76. Existence and Uniqueness of Solutions of Ordinary Differential Equations
  77. Extremal Graph Theory
  78. Fast Fourier Transform
  79. Finite Abelian Groups
  80. Finite Automata
  81. Finite Fourier Series
  82. Finite Geometries
  83. First-Order Quasilinear Partial Differential Equations
  84. Floquet Theory
  85. Fractal Dimension
  86. Fractal Structures
  87. Fractals
  88. Free Groups
  89. Free Modules
  90. Fubini's Theorem
  91. Fundamental Groups
  92. Galerkin Method
  93. Galois Theory
  94. Generalized Eigenvectors
  95. Generalized Inverse Matrices
  96. Generating Functions
  97. Geodesic Curves
  98. Geodesic Parallelism
  99. Geometric Algebra
  100. Geometric Analysis
  101. Geometric Measure Theory
  102. Geometric Programming
  103. Gödel's Incompleteness Theorems
  104. Goursat's Theorem
  105. Green's Theorem
  106. Group Actions
  107. Hahn Decomposition
  108. Hahn-Banach Theorem
  109. Hamilton Cycles
  110. Hamiltonian Dynamics
  111. Harmonic Analysis
  112. Harmonic Functions
  113. Heat Equation
  114. Hilbert Nullstellensatz
  115. Hilbert Spaces
  116. Homology Theory
  117. Homotopy Theory
  118. Hopf Bifurcations
  119. Hypergraphs
  120. Idempotents
  121. Infinite Groups
  122. Infinitely Divisible Distributions
  123. Information and Entropy
  124. Information Rate Optimization and Channel Capacity
  125. Integrable Systems
  126. Integral Transforms
  127. Interval Estimation
  128. Invariance Theory
  129. Invariant Basis Number
  130. Iterated Function Systems
  131. Jacobians
  132. Jump Processes
  133. Key Exchange
  134. Laplace's Equation
  135. Latin Squares
  136. Laurent Series
  137. Lebesgue Integral
  138. Lebesgue Measure
  139. Lie Algebras
  140. Lie Derivatives
  141. Lie Groups
  142. Limit Sets
  143. Limiting Distributions
  144. Line Integrals
  145. Locally Convex Spaces
  146. Low Dimensional Topology
  147. LP Spaces
  148. Lyapunov Stability
  149. Manifolds
  150. Martingales
  151. Matched Asymptotics
  152. Matchings
  153. Matrix Rings
  154. Maximization in Random Systems
  155. Maximum Likelihood Decoding
  156. Maximum Principle
  157. Measure Theory
  158. Method of Characteristics
  159. Minimax Theory for Convex Functions
  160. Modular Congruencies
  161. Modular Forms
  162. Moment Generating Functions
  163. Mutually Orthogonal Latin Squares
  164. Nest Algebras
  165. Network Flows
  166. Network Models
  167. Network Optimization
  168. Network Reliability
  169. Neyman-Pearson Lemma
  170. Nilpotent Groups
  171. Noetherian Rings
  172. Normal Operators
  173. Optimization of Functionals
  174. Orthogonal and Perpendicular Arrays
  175. Orthogonal Operators
  176. p-adic Representations
  177. Period Doubling
  178. Periodic Solutions of Systems
  179. Permutation Groups
  180. Permutations and Combinations
  181. Picard Theorem
  182. Planar Graphs
  183. Poincaré-Bendixson Theorem
  184. Point Estimation
  185. Poisson Processes
  186. Poisson Queues
  187. Polya Theory
  188. Polycyclic Groups
  189. Polynomial Rings
  190. Pontryagin's Principle
  191. Postoptimality Analysis
  192. Potential Theory
  193. Power Series Expansions
  194. Preparata Codes
  195. Primitive Roots
  196. Probabilistic Combinatorics
  197. Probability Density Function
  198. Probability Set Functions
  199. Product Spaces
  200. Projection Modules
  201. Pseudoinverses
  202. Public Key Cryptosystems
  203. Push-Down Automata
  204. Quadratic Functionals on Finite-Dimensional Vector Spaces
  205. Quadratic Reciprocity
  206. Queueing Theory
  207. Quotient Spaces
  208. Radon-Nikodym Theorem
  209. Ramsey Theory
  210. Random Graphs
  211. Random Matrices
  212. Random Permutations
  213. Random Phenomena
  214. Random Variables
  215. Rayliegh-Ritz Method
  216. Real Line
  217. Recurrence Relations
  218. Reed-Muller Codes
  219. Reed-Solomon Codes
  220. Renewal Processes
  221. Representation of a Lie Group
  222. Representation Theory
  223. Residue Theory
  224. Riemann-Hilbert Problems
  225. Riesz Representation Theorem
  226. Saddle Functions
  227. Scheduling Problems
  228. Self-Adjoint Operators
  229. Self-Similar Structures
  230. Semi-Direct Products
  231. Separation Axioms
  232. Separation of Variables
  233. Shannon's Noisy Channel Theorem
  234. Sierpinski Sets
  235. Similarity Solutions
  236. Singular Perturbations
  237. Singular Value Decomposition
  238. Singular Values
  239. Smale-Birkhoff Theorem
  240. Sobolev Spaces
  241. Solvable Groups
  242. Spanning Trees
  243. Spectral Density
  244. Spectral Theorem
  245. Spectral Theory
  246. Spherical Geometry
  247. Spherical Harmonics
  248. Spline Functions
  249. Stability
  250. Stationary Distributions
  251. Steiner Triple Systems
  252. Stiff Equations
  253. Stokes' Theorem
  254. Strange Attractors
  255. Stream Cyphers
  256. Subharmonic Functions
  257. Surface Integrals
  258. Symbolic Dynamics
  259. Symmetry Groups
  260. Tangent Spaces
  261. Tauberian Theorems
  262. Taylor Series
  263. Tensor Algebra
  264. Tensor Calculus
  265. Torsion
  266. Tower of Hanoi
  267. Transfinite Numbers
  268. Transformation Groups
  269. Transformation of Random Variables
  270. Two-Dimensional Order Processes
  271. Unique Factorization Theorem
  272. Using Generating Functions to do Sophisticated Counting
  273. Using Polya Theory to do Sophisticated Counting
  274. Variable Length Codes
  275. Wave Equation
  276. Wavelets

Frontier

  1. Abelian Varieties
  2. Algebraic Graph Theory
  3. Algebraic K-Theory
  4. Approximate Algorithms
  5. Arithmetic Algebraic Geometry
  6. Bounded Linear Operators on Hilbert Spaces
  7. Boundedness of Solutions of Differential Equations
  8. C* Algebras
  9. Center Manifolds
  10. Characteristic Classes
  11. Cohomology
  12. Compact Operators on Hilbert Spaces
  13. Complexity Classes
  14. Computation of Ext. Groebner Bases over Rings
  15. Computational Elliptic Equations
  16. Computational Hyperbolic Equations
  17. Computational Parabolic Equations
  18. Conformal Field Theory
  19. Conjugate Gradient Method
  20. Constrained Nonlinear Optimization
  21. Curves of Low Genus
  22. Cutting Plane Method
  23. de Rham Representations
  24. Degree Theory
  25. Dense Graphs
  26. Dictionary Methods of Encoding
  27. Dimension Theory
  28. Distributions
  29. Edge Colorings
  30. Embeddings
  31. Entire Functions
  32. Exponential Structures
  33. Fredholm Theory
  34. Function Spaces
  35. Gradient Projection Method
  36. Graph Designs
  37. Greedy Algorithms
  38. Groebner Bases for Modules
  39. Hadamard Designs
  40. Heuristics
  41. Hilbert-Schmidt Theory
  42. Homological Algebra
  43. Huffman and Arithmetic Encoding
  44. Improved Buchberger's Algorithm
  45. Interval and Recency Rank Encoding
  46. Krylov Methods
  47. Landau-Lifshitz Equations
  48. Lattices
  49. Line Search Algorithms
  50. Linear Integral Equations
  51. Lossless Compression Methods
  52. Lossy Compression Methods
  53. Martingales
  54. Matroid Algorithms
  55. Meromorphic Functions
  56. Moduli Spaces of Curves
  57. Multifractal Measures
  58. Multigrid Methods
  59. Multiscale Problems
  60. Network Flow Algorithms
  61. Nonlinear Partial Differential Equations
  62. Numeric Algorithms
  63. Numerical Solution of Stiff Differential Equations
  64. Orthogonal Arrays
  65. Penalty Methods
  66. Perturbation Theory
  67. Physical Systems with Many Degrees of Freedom
  68. Polynomial Time Approximations
  69. Preconditioning
  70. Primal-Dual Algorithm
  71. Primary Decomposition of Ideals
  72. Products of Fractals
  73. Punctured Lines
  74. Q-Curves
  75. QR Algorithm
  76. Quadruple Systems
  77. Quasi-Newton Methods
  78. Randomized Algorithms
  79. Reductions
  80. Riemann Mapping Theorem
  81. Riemann Surfaces
  82. Search Techniques
  83. Sieberg-Witten Theory
  84. Sieve Methods
  85. Singularities
  86. Smooth 4-Manifolds
  87. Sobolev Spaces
  88. Sparse Graphs
  89. Spectral Methods for Partial Differential Equations
  90. Stochastic Geometric Systems
  91. Symmetric Functions
  92. Symplectic Geometry
  93. Syzygy Computations
  94. Theory of NP-Completeness
  95. 3-Manifolds
  96. Topological Quantum Field Theories
  97. Unconstrained Nonlinear Minimization
  98. Weighted Matchings
  99. Wilson's Constructions

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