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Doctor of Philosophy in Mathematics
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Course Outline
10 sections
1. Probability Theory
90 mins
9 topics
Introduction to Probability Theory
Probability Distributions
Bayes' Theorem
Conditional Probability
Combinatorics and Probability
2. Linear Algebra
90 mins
9 topics
Introduction to Vectors
Vector Spaces
Matrix Operations
Determinants and Inverses
Systems of Linear Equations
3. Real Analysis
80 mins
8 topics
Introduction to Real Analysis
Sequences and Series
Continuity and Differentiability
The Riemann Integral
Sequences of Functions
4. Abstract Algebra
90 mins
9 topics
Introduction to Groups
Subgroups and Lagrange's Theorem
Group Homomorphisms and Isomorphisms
Rings and Fields
Polynomial Rings
5. Topology
90 mins
9 topics
Introduction to Topology
Topological Properties
Continuity and Homeomorphisms
Topological Constructions
Metric Spaces and Topology
6. Mathematical Logic
90 mins
9 topics
Introduction to Mathematical Logic
Propositional Logic
Predicate Logic
Inference Rules and Proofs
Logical Equivalences
7. Number Theory
80 mins
8 topics
Prime Numbers
Divisibility Rules
Modular Arithmetic
Greatest Common Divisor (GCD) and Least Common Multiple (LCM)
Diophantine Equations
8. Advanced Calculus
80 mins
8 topics
Limits and Continuity
Differentiation Techniques
Applications of Derivatives
Integration Methods
Differential Equations
9. Differential Geometry
80 mins
8 topics
Introduction to Differential Geometry
Curves in Space
Surfaces in Euclidean Space
Curvature and Torsion
Geodesics and Minimal Surfaces
10. Functional Analysis
70 mins
7 topics
Introduction to Functional Analysis
Metric Spaces and Normed Spaces
Banach Spaces and Hilbert Spaces
Linear Operators and Functionals
Distributions and Sobolev Spaces