PhD COURSES
 

Introductory (Mandatory) Courses

Algebra

1. Basic Algebra 1
2. Basic Algebra 2
3. Basic Algebra 3

Analysis

4. Real Analysis
5. Complex Function Theory
6. Functional Analysis and Differential Equations
 

Additional Introductory Courses

7. Enumeration
8. Extremal Combinatorics
9. Random Methods in Combinatorics
10. Convex Geometry
11. Non-Euclidean Geometries
12. Differential Geometry
13. Homological Algebra
14. Smooth Manifolds and Differential Topology
15. Algebraic Topology
16. Function Spaces and Distributions
17. Nonlinear Functional Analysis
18. Introduction to Mathematical Logic
19. Modern Set Theory
20. Algebraic Logic and Model Theory
21. Elementary Prime Number Theory
22. Combinatorial Number Theory
23. Probabilistic Methods in Number Theory
24. Probability
25. Mathematical Statistics
26. Information Theory
27. Introduction to the Theory of Computing
28. Algorithms
29. Complexity Theory
30. Ergodic Theory
31. Mathematical Methods of Statistical Physics
32. Fractals and Dynamical Systems
  

Advanced Courses

[These will be offered as needed, depending on the interests of the students  participating in the program.]

33. Higher Linear Algebra
34. Representation Theory I
35. Representation Theory II
36. Universal Algebra and Category Theory
37. Topics in Group Theory
38. Topics in Ring Theory I
39. Topics in Ring Theory II
40. Permutation Groups
41. Lie Groups and Lie Algebras
42. Commutative Algebra
43. Algebraic Number Theory
44. Geometric Group Theory
45. Residually Finite Groups
46. Invariant Theory
47. Semigroup Theory
48. Basic Algebraic Geometry
49. The Language of Schemes
50. Galois Groups in Geometry
51. Algebraic Curves and Jacobian Varieties
52. The Arithmetic of Elliptic Curves
53. Hodge Theory
54. Introduction to Classification Theory
55. Toric Varieties
56. Dynamical Systems
57. Approximation Theory
58. Partial Differential Equations
59. Nonlinear Evolution Equations and Applications
60. Functional Methods in Differential Equations
61. Complex Manifolds
62. Geometric Analysis
63. Block Designs
64. Hypergraphs, Set Systems, Intersection Theorems
65. Selected Topics in Graph Theory
66. Finite Packing and Covering
67. Packing and Covering
68. Convex Polytopes
69. Combinatorial Geometry
70. Geometry of Numbers
71. Stochastic Geometry
72. Brunn-Minkowski Theory
73. Hyperbolic Manifolds
74. Characteristic Classes
75. Singularities of Differentable Maps: Local and Global Theory
76. Four Manifolds and Kirby Calculus
77. Symplectic Manifolds, Lefschetz Fibration
78. Advanced Intersection Theory
79. Descriptive Set Theory
80. Advanced Set Theory
81. Logical Systems
82. Set-Theoretic Topology
83. Logic and Relativity
84. Frontiers of Algebraic Logic
85. Classical Analytic Number Theory
86. Probabilistic Number Theory
87. Probabilistic Number Theory, Level II
88. Modern Prime Number Theory
89. Exponential Sums in Combinatorial Number Theory
90. Information Theoretical Methods in Mathematics
91. Selected Topics in Probability
92. Invariance Principles in Probability and Statistics
93. Stochastic Processes
94. Stochastic Analysis
95. Path Properties of Stochastic Processes
96. Nonparametric Statistics
97. Multivariate Statistics
98.  Information Theoretical Methods in Statistics
99.  Numerical Methods in Statistics
100. Ergodic Theory and Dynamical Systems
101. Ergodic Theory and Combinatorics
102. Data Compression
103. Cryptology
104. Combinatorial Optimization
105. Quantum Computing
106. Computational Geometry
107. Random Computation
108.  Logic of Programs
 

Courses offered to other CEU departments

[Mathematics students need permission to receive credit toward the Mathematics Ph.D.]

109. Topics in Mathematical Analysis
110. Calculus of Variations and Optimal Control
 

Note : For short descriptions of  the courses listed above click on Syllabi