Foundations of Analysis, Fall 2026

Foundations of Analysis

Vladimir Ivanov

Syllabus of the course

Lecture 1 notes – Maps of sets

Lecture 2 notes – Inverse Map

Recommended textbooks

Real Analysis

1. S.Abbott, Understanding Analysis
2. W. Rudin, Principles of Mathematical Analysis
3. T.Tao, Analysis I
4. V.Zorich, Mathematical Analysis I

Preparation for Real Analysis

1. D. Velleman, How to Prove It: A Structured Approach
2. M. Aigner, G. Ziegler, Proofs from THE BOOK
3. G. Polya, How to Solve It

Additional resources.

1. Youtube channel of professor Richard E. Borcherds