Winter 2013: Math 131BH
Honors Analysis
Class: MWF, 11am-11:50am, MS 5233
Instructor: Inwon Kim
Office hours: Tues 3-4pm and Fri. 1:30-2:30pm in MS 7620E
This course is an honors-level (and thus highly theoretical) introduction to real analysis. Real analysis is the theoretical foundation which underlies calculus:
we will study real numbers, sequences and series of real numbers, and real-valued functions. Many of the subjects we will be discussing will be familiar to you
from previous calculus classes, however the emphasis is quite different here. While calculus classes focuses on computational aspects, in this class we will focus
on the underlying theory and mathematical rigor. The goal is to understand mathematical concepts and to construct careful mathematical arguments to prove
properties about them.
Text: Principles of Mathematical Analysis (3rd edition) by W. Rudin. We will continue from where we finished last quarter.
We will cover Chapter 6,7, some of Chapter 8 (Power series and Fourier series) and Chapter 9, and if time permits Chapter 10.
Prerequisite: Mathematics 131AH. If you have taken 131A instead of 131AH please check with me.
Discussion section: T at 11am in MS 5233
TA: Jacques Benatar
TA Office hours: TBA
Attendance to discussion section, as well as active participation, is strongly encouraged: the section will give you an opportunity to discuss proofs of problems in
different aspects, broadening one's point of view.
Homework: Homeworks will be posted below on wednesdays and is due on every wednesday, starting from Jan.16th.
In this class you will be required to write precise mathematical statements in a clear logical order, and present pictures or examples as necessary to illustrate
your work. Acquiring these skills is impossible without a steady practice: it is essential that you do the homework problems carefully and promptly.
You may discuss homework problems with other students, the TA or me before they are turned in. I do expect though that: (i) you should make a serious effort
to do the exercise yourself before discussing it with anyone, and (ii) you should write up the solution yourself after understanding it thoroughly, without following
someone else's written version. Otherwise homework will not help you to prepare for the exams. Identical solutions to a source will get zero credit.
Exam There will be one midterm, on Wednesday, Feb. 13th. The final exam is on Tuesday, March 19th, 3pm-6pm.
A sample Midterm is here
Grading: Final (50%), midterm(30%) and homework (20%: we will drop one lowest homework score).
Homework
Homework 1 (Due Jan. 16th) is here
Homework 2 (Due Jan. 23rd) is here
Homework 3 (Due Jan. 30th) is here
Homework 4 (Due Feb. 6th): Rudin p. 167, 13,16,18,20,22,25.
Homework 5 (Due Feb. 13th) is here
Homework 6 (Due Feb. 27th): Rudin p. 196, problem 9,12,14,15,16, 17(a),19.
Homework 7 (Due Mar. 6th): Rudin p239, problem 7,8,9,10, 13,14.
Homework 8 (Due Mar. 15th): Rudin p239, problems 15, 16, 17, 20, 21, 23.