Fundamentals of Mathematics: an Introduction to Analysis

Basic information

Workload: 

45 hours

Syllabus: 

Elements of language and mathematical logic: propositional logic (examples, counterexamples, reciprocal, contrapositive); predicates, logical connectives, negation and quantifiers; demos. Natural numbers; Peano's axioms, the principle of good ordering, the principle of induction. Real numbers; sequence limits; completeness of the real numbers. Limits and continuity. 

Bibliography

Mandatory: 

  • Mattuck, A (1999). Introduction to analysis. Prentice Hall.
  • Lima, E. L. (2003). Análise Real, Volume 1. IMPA.