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