Foundations of Analysis
Vladimir Ivanov
Syllabus of the course
Lectures 1-4 notes – Natural numbers.
Lecture 5 notes – Maps of sets, Problem Set 5
Lecture 6 notes – Integers
Lecture 7 notes – Rational numbers
Lecture 8 notes – Real numbers
An Addendum to Lectures 4 and 8
Lecture 9 notes – Ordering real numbers
Lecture 10 notes – The least upper bound
An Addendum to Lecture 10
Lecture 11 notes – Real exponentiation, part 1
Lecture 12 notes – Real exponentiation, part 2
Lecture 13 notes – Limits of sequences, Problem Set 13
Lecture 14 notes – Limit points of sequences
Recommended textbooks
Real Analysis
- T.Tao, Analysis I
- S.Abbott, Understanding Analysis
- V.Zorich, Mathematical Analysis I
Preparation for Real Analysis
- D. Velleman, How to Prove It: A Structured Approach
- M. Aigner, G. Ziegler, Proofs from THE BOOK
- G. Polya, How to Solve It
Additional resources.