Description
This course covers real numbers, topology of the real line, sequences and series, continuity, differentiation, series and sequences of functions, Riemann integration, and an introduction to differential equations. The course emphasizes rigorous mathematical reasoning and proof techniques.
Textbook: Principles of Mathematical Analysis by Walter Rudin. McGraw-Hill, 1976.
Resources
Recitation problems (no solutions provided) can be found here.
Homework assignments and (brief) solutions:
| Assignment | Problems | Solutions |
|---|---|---|
| Homework 1 | Problems | Solutions |
| Homework 2 | Problems | Solutions |
| Homework 3 | Problems | Solutions |
| Homework 4 | Problems | Solutions |
| Homework 5 | Problems | Solutions |
| Homework 6 | Problems | Solutions |
| Homework 7 | Problems | Solutions |
Some of these problems are original, but many are adapted from the textbook (Baby Rudin) and/or from the following sources:
- Problems in Mathematical Analysis by W. J. Kaczor and M. T. Nowak, American Mathematical Society, 2000 (Volumes I, II, and [III).
- A Problem Book in Real Analysis by A. G. Aksoy and M. A. Khamsi, Springer 2010.