Mathematics Projects

Overview

Mathematics is the logical study of abstract structures and relationships.

Math Projects

Elementary

1. Algebra
2. Area
3. Binomial Expansion
4. Binomial Theorem
5. Centroids
6. Change of Variables
7. Circles
8. Combinations
9. Complex Numbers
10. Conditional Probablity
11. Conic Sections
12. Continuity
13. Coordinate Geometry
14. Counting
15. Cubic Equations
16. Curve Sketching
17. Data Analysis
18. Definite Integrals
19. Derivatives
20. Descriptive Statistics
21. Determinants
22. Difference Equations
23. Differentials
24. Differentiation of Functions
25. Discrete Mathematics
26. Divisibility
27. Eigenvalues
28. Eigenvectors
29. Elementary Number Theory
30. Enumeration
31. Equations with Absolute Values
32. Euclidean Constructions
33. Euclidean Geometry
34. Exponential Equations
35. Exponential Functions
36. Exponents
37. Extrema
38. Factoring Polynomials
39. Fibonacci Sequences
40. Field Properties of Real Numbers
41. Figurate Numbers
42. Finite Mathematics
43. Finite Sequences and Series
44. First-Order Logic
45. Functions
46. Fundamental Theorem of Arithmetic
47. Fundamental Theorems of Calculus
48. Geometric Figures
49. Geometric Transformations
50. Graphs of Functions
51. Homogeneous Linear Equations
52. Improper Integrals
53. Inequalities
54. Infinite Series
55. Integration
56. Inverse Hyperbolic Functions
57. Inverse Trigonometric Functions
58. Irrational Numbers
59. L'Hôpital's Rule
60. Limits of Functions
61. Linear Approximation
62. Linear Equations
63. Linear Functions
64. Linear Inequalities
65. Linear Programming
66. Linear Transformations
67. Location of Roots of Equations
68. Logarithmic Equations
69. Logarithmic Functions
70. Logarithms
71. Logic
72. Maclaurin's Series
73. Magic Squares
74. Mappings and Relations
75. Mathematical Induction
76. Mathematical Proof
77. Matrices
78. Matrix Inversion
79. Maxima and Minima
80. Mean Value Theorems
81. Methods of Integration
82. Multiple Integrals
83. Multivariable Functions
84. Natural Numbers
85. Nonlinear Inequalities
86. Number Representation in Various Bases
87. Number Systems
88. Number Theory
89. Numbers
90. Numerical Differentiation
91. Numerical Integration
92. Ordinary Differential Equations
93. Parabolic Equations
94. Parameterized Curves
95. Parametric Equations
96. Partial Derivatives
97. Partial Differentiation
98. Perfect Numbers
99. Periodic Functions
100. Permutations
101. Pi
102. Plane Geometry
103. Polar Coordinates
104. Polygons
105. Polynomial Functions
106. Polynomials
107. Power Series
108. Powers
109. Prime Numbers
110. Probability
111. Proof Methods
112. Proportion
113. Propositional Logic
114. Pythagorean Theorem
115. Quadratic Equations
116. Quadratic Formula
117. Quadratic Functions
118. Quadrature
119. Quadric Surfaces
120. Quartic Equations
121. Quadrilaterals
122. Radical Equations
123. Radicals
124. Range
125. Ratio
126. Rational Expressions
127. Rational Functions
128. Rational Numbers
129. Rational Roots of Polynomials
130. Real Numbers
131. Recursion
132. Relations
133. Riemann Integration
134. Roots
135. Sequences
136. Sequences of Functions
137. Series
138. Series Expansions of Functions
139. Set Theory
140. Solid Geometry
141. Solving Triangles
142. Statistics
143. Sums of Squares
144. Surface Integrals
145. Surface of Revolution
146. Systems of Linear Equations
147. Systems of Numeration
148. Taylor Series
149. Techniques of Integration
150. The Jacobian
151. Translation of Axes
152. Trigonometric Equations
153. Trigonometric Functions
154. Trigonometric Identities
155. Triangles
156. Vector Calculus
157. Vector Functions
158. Vector Spaces
159. Vectors
160. 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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