# Course Info

**Time and Place:** TTh 12:00-01:15pm UNIV 119

**Instructor:** Arshak Petrosyan

**Office Hours:** TTh 11:00-12:00noon, or by appointment, in MATH 610

**Course Description:** MA44200 covers the foundations of real analysis in several variables, assuming the single variable notions of these concepts.
*Prerequisite:* MA44000

**Textbook:**

[B] R. Bartle, *The Elements of Real Analysis*, Second Edition, John Wiley & Sons, New York, 1975.

Additional texts:

[R] W. Rudin, *Principles of mathematical analysis*, Third edition, McGraw-Hill, New York, 1976

[M] J. Munkres, *Analysis on Manifolds*, Addison-Wesley, 1991.

**Course Outline:**

- [B], Ch. II, (2 wks.): Topology of
**R**^{p}: Heine-Borel, connectedness, etc. - [B], Ch. III, §§14-17 (1 wk): Sequences, Bolzano-Weierstrass thm., Cauchy criterion.
- [B], Ch. IV, §§20-22 (1 wks): Continuity (with emphasis on the equivalence of different definitions).
- [B], Ch. VII, §§39-41 (5 wks.): Differentiation, mapping theorems.
- [B], Ch. VIII (4 wks.): Riemann integration, including “content”, Lebesgue’s criterion for integrability, and careful treatment of change of variables.

The final two weeks will be spent on additional topics, such as integration on manifolds.

**Homework** will be collected weekly on Thursdays. The assignments will be posted on this website at least one week prior the due date.

**Exams:** There well be two midterm exams (in-class or evening) and a final project. The exact times and places will be specified due course.