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Mathematics project report topics — UG (B.A. / B.Sc. / B.Com.)

250 topics for Mathematics students of Pandit Deendayal Upadhyay Shekhawati University (PDUSU), Sikar. Each names its own study area, and each can be written in Hindi or English. Choose one to read a free sample; the complete project report is ₹599 and arrives as an editable Word file with your name, college and university on it.

General

1. Abstract harmonic analysis on locally compact groups and Peter-Weyl theorem expansions.
2. Algebraic K-theory of rings: K_0, K_1, K_2 stability theorems and Higher K-theory.
3. Algebraic K-theory of schemes: Localization, Agreement theorems, and motivic cohomology.
4. Algebraic aspects of integrable systems: Lax pairs, R-matrices, and Frobenius manifolds.
5. Algebraic aspects of quantum error-correcting codes and stabilizer codes.
6. Algebraic code generation for non-linear optical signal processing.
7. Algebraic curves and Jacobians: Riemann-Roch theorem, Abel-Jacobi map, and moduli.
8. Algebraic formulation of finite state machines for formal language parsing.
9. Algebraic geometry of Calabi-Yau threefolds: Picard-Fuchs equations and mirror maps.
10. Algebraic geometry of Fano varieties and K-stability bounds.
11. Algebraic geometry of Higgs bundles and Hitchin fibration integrable systems.
12. Algebraic geometry of abelian varieties: Polarization, theta functions, and endomorphisms.
13. Algebraic geometry of hyperkähler manifolds and Beauville-Bogomolov decomposition.
14. Algebraic geometry of rational varieties: Lüroth’s problem and unirationality.
15. Algebraic geometry of stacks: Artin stacks, Deligne-Mumford stacks, and Keel-Mori theorem.
16. Algebraic geometry of toric varieties: Fans, divisors, and toric momentum polytopes.
17. Algebraic modeling of DNA sequence alignment using dynamic programming matrices.
18. Algebraic modeling of Rubik’s Cube permutations using Group Theory concepts.
19. Algebraic modeling of biological neural network connectivity matrices.
20. Algebraic properties and combinatorial analysis of Young Tableaux.
21. Algebraic properties of Quaternions and implementation of 3D rotational physics.
22. Algebraic structure modeling of Sudoku puzzle generation and solvability bounds.
23. Algebraic theory of quadratic forms, Witt rings, and Milnor K-theory.
24. Algebraic topology: Stable homotopy theory, spectra, and Adams spectral sequence.
25. Algorithmic generation and maze solving using Minimum Spanning Trees (Kruskal, Prim).
26. Algorithmic generation of L-systems for botanical structure modeling.
27. Algorithmic generation of Penrose tiling and non-periodic space-filling structures.
28. Algorithmic generation of Voronoi-based structural lattices for 3D printing.
29. Algorithmic generation of architectural freeform grid shells using catenary curves.
30. Algorithmic generation of hyper-dimensional shapes (Tesseract) projections into 3D.
31. Algorithmic generation of minimal surfaces (Helicoid, Catenoid) via differential geometry.
32. Algorithmic generation of procedural terrain heightmaps using Perlin noise mathematics.
33. Algorithmic generation of self-similar fractals (Mandelbrot, Julia sets, Barnsley Fern).
34. Algorithmic generation of spatial bounding volume hierarchies (BVH, Octrees).
35. Algorithmic generation of spatial space-filling curves (Hilbert, Peano curves).
36. Algorithmic generation of sphere packing configurations (Kepler conjecture setups).
37. Analysis of Cahn-Hilliard and Phase-Field equations: Gamma-convergence of energies.
38. Analysis of Fourier multipliers and Littlewood-Paley theory on L^p spaces.
39. Analysis of Hamilton-Jacobi equations: Viscosity solutions and KAM theory.
40. Analysis of Ramsey Numbers R(k, l) via computational lower-bound searches.
41. Analysis of bifurcation phenomena in non-linear dynamical systems (Logistic map).
42. Analysis of chaos and strange attractors in the Lorenz system of differential equations.
43. Analysis of chaotic dynamics in forced Duffing oscillator systems.
44. Analysis of chaotic modern climate models (Saltzman non-linear dynamical model).
45. Analysis of concentration of measure phenomena in high-dimensional probability spaces.
46. Analysis of convergence properties of Taylor series vs. Padé approximants.
47. Analysis of cross-diffusion systems in population dynamics: Global weak solutions.
48. Analysis of degenerate elliptic equations: Grushin operators and Hörmander's vector fields.
49. Analysis of free boundary problems: Obstacle problem regularity and blow-up analysis.
50. Analysis of limit cycles and van der Pol oscillator dynamics.
51. Analysis of modular arithmetic applications in ISBN, UPC, and credit card validation.
52. Analysis of non-linear Dirac equations: Solitary wave solutions and Dirac-Coulomb stability.
53. Analysis of non-linear Schrödinger equations: Soliton stability and critical collapse.
54. Analysis of non-linear wave equations: Dispersive estimates and energy critical global solutions.
55. Analysis of non-linear wave steepening in compressible gas dynamics PDEs.
56. Analysis of non-local partial differential equations: Fractional Laplacian operators and regularity.
57. Analysis of perturbation techniques (Boundary layer theory) on singular ODEs.
58. Analysis of phase space trajectories in non-linear pendulum systems with damping.
59. Analysis of several complex variables: dbar-Neumann problem and pseudoconvexity.
60. Analysis of stability boundaries in Mathieu differential equations.
61. Analysis of stability regions for explicit vs. implicit numerical ODE solvers.
62. Analysis of structural beam deflection using Euler-Bernoulli fourth-order ODEs.
63. Analysis of wave maps: Gauge choices, critical energy estimates, and global existence.
64. Application of Green’s functions for solving non-homogeneous boundary value problems.
65. Asymptotic analysis of reaction-diffusion PDEs: Traveling wave solutions and front propagation.
66. Asymptotic behavior of solutions to parabolic conservation laws: Large time decay rates.
67. Auslander-Reiten theory of Artin algebras and representation types of finite dimensional algebras.
68. Backward Stochastic Differential Equations (BSDEs): Well-posedness and non-linear PDEs link.
69. Banach algebra theory: Gel'fand spectrum, commutative Banach algebras, and Silov boundary.
70. Banach lattices and positive operators: Riesz spaces, Order continuous norms, and Kaplansky theorem.
71. Banach space embeddings: Subspaces of L_p, Schatten von Neumann classes, and nuclear operators.
72. Banach space geometry: Radon-Nikodym property, local structure, and Dvoretzky’s theorem.
73. Bayesian estimation of species abundance using capture-recapture models.
74. Bayesian network modeling for medical diagnosis under uncertainty.
75. Bayesian parameter estimation for lifetime distributions (Weibull, Gamma).
76. Bayesian regression modeling using Markov Chain Monte Carlo (PyMC/JAGS proxies).
77. Bayesian updating algorithms for real-time sensor fusion systems.
78. Birational geometry of algebraic varieties: Minimal Model Program (MMP) and flops.
79. Boundary behavior of holomorphic functions in several complex variables.
80. Boundary element method (BEM) implementation for electrostatic potential problems.
81. Bézier curves and B-splines generation for computer-aided geometric design (CAGD).
82. C*-algebras: Classification of simple nuclear C*-algebras and Elliott program.
83. Calculus of variations application: Solving the Brachistochrone problem computationally.
84. Categorification of quantum invariants, Khovanov homology, and link homologies.
85. Category theory applications in computer science: Monads, comonads, and categorical semantics.
86. Category theory approach to higher structures: (inf, 1)-categories and quasi-categories.
87. Category theory foundations: Enriched categories, internal categories, and Topos theory.
88. Category theory of model categories, Quillen equivalences, and homotopy theories.
89. Category theory of monads and algebras over monads in functional programming foundations.
90. Category theory of sheaves, stacks, and gerbes in algebraic geometry.
91. Character theory of finite reductive groups and Deligne-Lusztig representations.
92. Characteristic classes of vector bundles: Chern, Pontryagin, Euler, and Stiefel-Whitney.
93. Chromatic homotopy theory: Morava K-theories and Nilpotence theorem (Devinatz-Hopkins-Smith).
94. Cluster algebras: Combinatorial structures, exchange graphs, and positivity conjectures.
95. Cohomology of Lie algebras and Chevalley-Eilenberg complex constructions.
96. Cohomology of groups, profinite groups, and Galois cohomology of local fields.
97. Comparative analysis of integer factorization algorithms for RSA security evaluation.
98. Comparative efficiency analysis of Monte Carlo integration techniques.
99. Comparative study of sorting algorithm time-complexities through empirical benchmarking.
100. Complex algebraic surfaces: Enriques-Kodaira classification and invariants.
101. Complex analysis of coherent analytic sheaves and Cartan’s Theorems A and B.
102. Complex analytic spaces: Singularities, normal spaces, and Remmert’s proper mapping theorem.
103. Complex approximation theory: Runge’s theorem, Mergelyan’s theorem, and several variables.
104. Complex dynamics in several variables: Henon maps, Fatou components, and Green functions.
105. Complex dynamics: Fatou and Julia sets, iteration of rational functions, and Mandelbrot structure.
106. Complex geometry of Calabi-Yau manifolds and Yau’s proof of the Calabi conjecture.
107. Complex manifold theory: Kähler manifolds, Hodge decomposition, and Kodaira embedding.
108. Complex potential theory: Plurisubharmonic functions and complex Monge-Ampère equations.
109. Computational analysis of Happy Numbers and digital invariant loops in base-10.
110. Computational analysis of continued fraction expansions for irrational number approximations.
111. Computational analysis of the distribution of prime gaps up to 10^12.
112. Computational analysis of the partition function p(n) and Ramanujan congruences.
113. Computational evaluation of fractal dimensions of coastline geometry using box-counting.
114. Computational evaluation of special functions (Bessel, Gamma, Zeta) via series expansions.
115. Computational exploration of Farey sequences and Ford circles geometry.
116. Computational exploration of Pythagorean triples and generalized Hilbert spaces.
117. Computational exploration of the Collatz Conjecture dynamics and trajectory trees.
118. Computational exploration of the distribution of twin primes up to high numerical limits.
119. Computational geometry algorithms for 2D Convex Hull generation (Graham Scan, Jarvis March).
120. Computational geometry algorithms for 3D convex hull generation (Quickhull algorithm).
121. Computational geometry algorithms for computing 3D alpha shapes of molecular structures.
122. Computational geometry algorithms for computing Minkowski sums of 2D polygons.
123. Computational geometry algorithms for computing visibility polygons in 2D environments.
124. Computational geometry algorithms for line clipping in 2D and 3D (Cohen-Sutherland, Liang-Barsky).
125. Computational geometry algorithms for line segment intersection detection (Bentley-Ottmann).
126. Computational geometry algorithms for point-in-polygon queries (Ray casting, Winding number).
127. Computational geometry algorithms for polygon triangulation (Ear Clipping algorithm).
128. Computational geometry methods for map map-matching algorithms in GPS tracking.
129. Computational geometry methods for robot motion planning using Configuration Spaces (C-Space).
130. Computational implementation of Spectral Methods for high-accuracy PDE solving.
131. Computational investigation of perfect numbers, Mersenne primes, and aliquot sequences.
132. Computational optimization of shape contours using Level Set methods.
133. Computational simulation of targeted drug delivery kinetics using compartment models.
134. Computational simulation of tsunami wave propagation using Shallow Water Equations.
135. Computational solution of reaction-diffusion equations for Turing pattern generation.
136. Computational solution of stochastic differential equations (SDEs) via Euler-Maruyama method.
137. Computational solution of the Cahn-Hilliard equation for phase separation dynamics.
138. Computational solution of the Poisson equation using Multigrid iterative methods.
139. Computational solution of the time-dependent Schrödinger equation in 1D.
140. Computational solving of delay differential equations in epidemiological systems.
141. Computational solving of non-linear differential equations using Runge-Kutta 4th Order.
142. Computational solving of the heat equation on irregular 2D spatial geometries.
143. Computational study of Bernoulli numbers, Euler numbers, and sum of powers formulas.
144. Computational study of Diophantine equations and integer lattice solutions.
145. Computational study of Fibonacci numbers, Lucas numbers, and Golden Ratio convergents.
146. Computational topology analysis of vector field singularities in fluid flows.
147. Computational topology implementation: Persistent Homology for 2D point cloud data.
148. Concentration of measure inequalities: Talagrand’s concentration, Transportation-cost bounds.
149. Construction and convergence rate analysis of Fourier series for discontinuous signals.
150. Construction and properties analysis of Voronoi Diagrams and Delaunay Triangulations.
151. Construction and property analysis of magic squares, cubes, and hypercubes.
152. Construction and property verification of Hadamard matrices and orthogonal designs.
153. Construction and visual mapping of cellular automata models for biological pattern formation.
154. Construction of Genetic Algorithms for constrained function optimization problems.
155. Construction of public-key cryptographic prototypes using lattice-based problems.
156. Construction of zero-knowledge proof protocols using discrete logarithm primitives.
157. Contact geometry: Legendrian knots, contact structures in 3D, and tight vs. overtwisted.
158. Convergence speed analysis of numerical integration techniques (Simpson, Gaussian Quadrature).
159. Deformation theory of algebraic structures and L_inf-algebra formalisms.
160. Deformation theory of complex structures and Kodaira-Spencer theory.
161. Derived algebraic geometry: Derived schemes, spectral schemes, and derived moduli.
162. Derived categories of coherent sheaves on smooth algebraic varieties and Fourier-Mukai transforms.
163. Design and simulation of multi-armed bandit algorithms for online decision making.
164. Design of customized error-correcting codes (Hamming, Reed-Solomon) for noisy channel simulation.
165. Differential geometry of CR manifolds (Cauchy-Riemann) and Levi pseudo-convexity.
166. Differential geometry of Einstein manifolds and Yamabe problem solutions.
167. Differential geometry of Lie algebroids and Poisson geometry.
168. Differential geometry of minimal submanifolds: Bernstein's problem and Simons’ cones.
169. Differential topology: Morse theory, handlebody decompositions, and h-cobordism theorem.
170. Elliptic partial differential equations: De Giorgi-Nash-Moser estimates and Hölder continuity.
171. Empirical investigation of Benford’s law in financial audit data and fraud detection.
172. Empirical verification of Goldbach’s conjecture for large even integers.
173. Ergodic theory and additive combinatorics: Szemerédi’s theorem via ergodic averages.
174. Ergodic theory of dynamical systems: Measure-preserving transformations and mixing properties.
175. Ergodic theory of geodesic flows on negatively curved Riemannian manifolds.
176. Ergodic theory of interval exchange transformations and translation surfaces.
177. Etale cohomology of schemes: Weil conjectures, Deligne’s proof, and purity theorems.
178. Financial Black-Litterman model implementation for incorporating subjective views into portfolios.
179. Financial convertible bond valuation using jump-diffusion trees.
180. Financial credit default swap (CDS) pricing using copula models for joint default timing.
181. Financial credit scoring models using penalized logistic regression (Lasso, Ridge).
182. Financial derivative pricing using Monte Carlo simulation under Heston stochastic volatility.
183. Financial exotic option pricing (Asian, Barrier options) using binomial tree models.
184. Financial high-frequency order book modeling using Hawkes processes.
185. Financial implied volatility surface construction using thin-plate spline interpolation.
186. Financial interest rate swap valuation using multi-curve framework mathematical models.
187. Financial mortgage-backed security (MBS) cash flow yield modeling under prepayment risks.
188. Financial optimal trade execution strategies using Almgren-Chriss market impact models.
189. Financial portfolio risk attribution using Risk Parity allocation mathematical models.
190. Financial risk modeling using Value at Risk (VaR) and Expected Shortfall (CVaR).
191. Financial term structure modeling using Vasicek and Cox-Ingersoll-Ross (CIR) interest rate models.
192. Financial yield curve construction using Svensson and Nelson-Siegel parametric models.
193. Finite Difference Time Domain (FDTD) modeling of electromagnetic wave propagation.
194. Finite Element Method (FEM) implementation for 2D thermal distribution modeling.
195. Finite Volume Method (FVM) implementation for 1D advection-diffusion-reaction equations.
196. Finsler geometry: Berwald spaces, Chern connections, and flag curvatures.
197. Floer homology theories: Lagrangian Floer homology and instanton Floer homology.
198. Fractional calculus applications: Modeling anomalous diffusion processes.
199. Free analysis and non-commutative function theory over operator algebras.
200. Functional analysis foundations of quantum mechanics: Rigged Hilbert spaces and KMS states.
201. Galois representations associated to Hilbert modular forms and abelian varieties.
202. Galois representations, modular forms, and Serre’s modularity conjecture formulations.
203. Galois theory of differential fields, Picard-Vessiot extensions, and differential Galois groups.
204. Gauge theory on 8-manifolds: Spin(7) and G2 instantons.
205. Gauge theory: Donaldson invariants of 4-manifolds and Yang-Mills instantons.
206. Geometric algorithms for collision detection between 3D convex polyhedra (GJK algorithm).
207. Geometric functional analysis: Convex bodies, John’s ellipsoid, and Isoperimetric inequalities.
208. Geometric group theory: Hyperbolic groups (Gromov), boundaries, and quasi-isometries.
209. Geometric measure theory: Minimal surfaces, currents, and Plateau’s problem solutions.
210. Geometric modeling of 3D mesh surface simplification using quadric error metrics.
211. Geometric modeling of camera lens distortion parameters using rational polynomials.
212. Geometric modeling of conformal mappings using Schwarz-Christoffel transformations.
213. Geometric modeling of folding structures via Computational Origami principles.
214. Geometric modeling of implicit surfaces using Marching Cubes algorithms.
215. Geometric modeling of non-Euclidean spaces (Poincaré disk model of hyperbolic geometry).
216. Geometric modeling of perspective transformation matrices for augmented reality alignment.
217. Geometric modeling of space curves: Frenet-Serret frame visualization and curvature.
218. Geometric modeling of spatial interpolations using Thin Plate Splines.
219. Geometric modeling of spherical harmonics for global illumination calculations.
220. Geometric topology: 3-manifold geometry, Thurston’s Geometrization Conjecture.
221. Geometric transformation matrices for 3D graphics camera projections and viewports.
222. Global Riemannian geometry: Sphere theorem (Bredon-Berger) and Differentiable Sphere theorem.
223. Graph centrality metrics for social network influence and community detection.
224. Graph coloring optimization algorithms for automated university timetabling.
225. Graph connectivity analysis and vulnerability metrics in electrical power grids.
226. Graph matching algorithms for bipartite matching in resource allocation problems.
227. Graph planarity testing algorithms and linear-time embedding implementations.
228. Graph spectral theory applications: Laplacian eigenvalues for network partition.
229. Graph theoretical methods for detecting money laundering cycles in banking networks.
230. Graph theory applications in sports tournament scheduling and venue allocation.
231. Graph theory approaches to solving the Traveling Salesperson Problem (TSP) using heuristics.
232. Graph tree-decomposition algorithms for low-treewidth graph solving.
233. Graph-theoretic analysis of local road networks for traffic congestion minimization.
234. Graph-theoretic modeling of epidemic spreading dynamics on complex networks.
235. Gromov-Witten invariants and Quantum Cohomology rings of symplectic manifolds.
236. Grothendieck categories, localization theory, and sheaf cohomology foundations.
237. Harmonic analysis on Euclidean spaces: Calderón-Zygmund singular integral operators.
238. Harmonic analysis on discrete groups: Kazhdan’s Property (T) and amenability.
239. Harmonic analysis on reductive Lie groups: Orbital integrals and Plancherel formula.
240. Hochschild and cyclic homology of non-commutative algebras and non-commutative geometry.
241. Holomorphic vector bundles over compact complex manifolds and Chern classes.
242. Holonomy groups of Riemannian manifolds and Berger classification theorem.
243. Homogenization theory for partial differential equations in strongly heterogeneous media.
244. Homological algebra of persistent homology: Barcodes, quiver representations, and stability.
245. Homological algebra: Ext and Tor functors, spectral sequences, and derived functors.
246. Homological dimensions of rings: Global dimension, Krull dimension, and weak dimension.
247. Homological properties of commutative Noetherian rings and Cohen-Macaulay module theory.
248. Homology and cohomology theories: Eilenberg-Steenrod axioms, cobordism, and K-theory.
249. Homotopy algebra structures (A_inf, C_inf, P_inf) and bar-cobar dualities.
250. Homotopy theory of simplicial sets, Kan complexes, and model category of spaces.

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