Fundamentals of analysis

Course Content
- Fundamental mathematical logic
- Set theory, sets of numbers
- The concept of function, elementary functions
- Direct and indirect proof, proof by contradiction
- Sequences and recursion, proof by induction
- Supremum and infimum, the supremum axiom
- Convergence of sequences
- Limits and continuity of functions
- Properties of continuous functions
- Derivative and differentiability
- Properties of differentiable functions
- The Riemann integral, the fundamental theorem of calculus

For doctoral student in