Math H104 Home Page

Math H104: Honors introduction to analysis (Fall 2005)

Instructor Yuval Peres, 341 Evans Hall.

Class time Tuesday and Thursday, 9:30-11:00 AM (334 Evans Hall).

Lecture notes

Lecture 1 PDF , latex , Lectures 1 to 17 and two midterms PDF Lecture of Nov 2 PDF Lecture of Nov 10 PDF Lecture of Nov 15 PDF Lecture of Nov 17 PDF Lecture of Nov 22 PDF Lecture of Nov 29 PDF

Home work solutions

Home work 1 PDF ,

Course description

The real number system. Uncountable sets. Sequences and limits. Continuous functions of one and several real variables. Metric spaces: Complete, compact and connected. Uniform convergence, Infinite series. Cantor sets. Taylor polynomials and Taylor series. The Riemann integral.

Text

Required text: "Real Mathematical Analysis", by Charles Pugh, Springer (2002). Another Recommended text (no need to purchase): "Principles of Mathematical Analysis" by Walter Rudin, Third Edition, Mcgraw-Hill.

Prerequisites

Undergraduate courses in Calculus and Linear algebra (Math 53 and 54) and enjoyment of solving challenging problems.

Grading Students taking the course for credit will be graded based on

Group homework (10%);
Writeup of Lecture (10%);
Midterm (30%);
Final Exam (50%);
In addition, up to 10 bonus points can be obtained for making a 15 minute presentation of an advanced topic.

Each student will be graded based on his/her performance, rather than on how it compares to the work of other students. Hence collaboration in studying, and in doing homework, is encouraged and expected.