Math 55b Honors Real and Complex Analysis
Spring 2012

Place: Science Center 310
Time: Mondays, Wednesdays, Fridays, 10 a.m. - 11 a.m.

Instructor: Professor Yum-Tong Siu   (e-mail: siu@math.harvard.edu)
Office Hours: Mondays, Wednesdays, Fridays, noon - 1 p.m., Science Center 511

Textbooks:    Michael Artin: Algebra Prentice Hall
C.H. Edwards, Jr.: Advanced Calculus of Several Variables, Dover Publications

Course Assistant: Levent Alpoge   (e-mail: levent.alpoge@gmail.com)
Section: Thursday, 4 p.m. to 5 p.m., Science Center 411
Office Hours: Thursday, 5 p.m. to 6 p.m., Science Center 411

Syllabus:  This is the second term of Math 55 which is a one-year course.  Math 55b presents a rigorous treatment of real and complex analysis.

Lecture Notes of Augustin-Louis Cauchy in 1823 at École Polytechnique (Résumé des leçons sur le calcul infinitésimal) where for the very first time in history the epsilon-delta formulation was introduced (see p.44 after the word "Démonstration" in the middle of the page).

LECTURE NOTES: Logical Foundation of Real Analysis (Part 1)

LECTURE NOTES: Logical Foundation of Real Analysis (Parts 1 and 2) Note that the formulation here for the commutation of limit-taking is stronger than that given in class though the arguments are the same.

LECTURE NOTES: Logical Foundation of Real Analysis (Parts 1, 2, and 3)

HOMEWORK: Homework Assignment due February 3, 2012

LECTURE NOTES: Logical Foundation of Real Analysis (Complete Version)

HOMEWORK: Homework Assignment due February 10, 2012

LECTURE NOTES: Differentiation and Integration in Hihger Dimension (Part 1)

LECTURE NOTES: Differentiation and Integration in Hihger Dimension (Parts 1 and 2)

LECTURE NOTES: Differentiation and Integration in Hihger Dimension (Complete Version)

LECTURE NOTES: Leibniz's Notations, Differentials, and Vectors as Differential Operators

HOMEWORK: Homework Assignment due February 17, 2012