REAL ANALYSIS
REAL ANALYSIS
Syllabus - A. Bucki
- Mathematical Logic and Set Theory.
- Tautologies; Polish Notation; Proofs; Boolean
Algebras
- Operations on Sets; Relations; Equivalence
Relations; Partitions of Sets
- Functions; Equivalent Sets; Cardinalities
of Sets
- Metric spaces.
- Open Balls; Topology of Metric Spaces, Open,
Closed, Derived Sets; Convergence
- Continuity of Functions
- Metrics in $R$ and $R^2$; Equivalent metrics;
Compact sets; Cantor set
- Riemann Integrals.
- Upper and lower sums; Cauchy criterion for
integrability of functions
- Properties of integrable functions; Fundamental
Theorem of Calculus