**Schedule**

Mondays 9-10 (15:40-17:10), Room B014, San Joaquín Campus (TA)

Tuesdays 3-4 (10:00-11:30), Room A016, San Joaquín Campus

Thursdays 3-4 (10:00-11:30), Room B031, San Joaquín Campus

**Office Hours**

Tuesdays and Thursdays 5 (11:45-13:15), Office A061, San Joaquín Campus

**Course Content & Evaluation
**

**Unit I:** Metric spaces

Definitions and examples, sequences, completeness, compactness, continuity

Assignment I, due April 13

Group work I, April 4

Exam I (25%), April 13

**Unit II:** Normed spaces

Definitions and examples, function spaces, Hilbert spaces, differential calculus

Assignment II, due May 27

Group work II, April 25

Group work III, May 11

Exam II (25%), May 27

**Unit III:** Topological spaces

Definitions and examples, product space, compactness, functions, topological vector spaces, connectedness

Assignment III, due June 26

Practice group work I, May 25

Practice group work II, June 6

Group work III, June 22

Exam III (30%), June 27

**Final Exam**

A final oral exam will be available for students with grades between 45 and 54.

Date:

**Bibliography**

H.L. Royden: Real Analysis. Prentice Hall, New Jersey, 1988

A.N. Kolmogorov & S.V. Fomin: Introductory Real Analysis. Dover, New York, 1970

H. Cartan: Cálculo Diferencial. Omega, Barcelona, 1978

G. Choquet: Topology. Academic Press, New York, 1966

M.A. Armstrong: Basic Topology. Springer, New York-Berlin, 1983

C.S. Honig: Aplicações da topologia á análise, second edition. IMPA, 2012

**Supplementary Material **(2016/01)

Unit I: Exercises - Assignment I – Exam I

Unit II: Exercises – Assignment II – Exam II

Unit III: Exercises – Assignment III - Exam III

**Latex**

T. Oetiker, H. Partl, I. Hyna, E. Schlegl: The not so short introduction to Latex 2e

Compiler: MiKTeX

Free MiKTeX compatible editor: TeXstudio