Winter 2012: Math 131BH
Honors Analysis 

Class: MWF, 11am-11:50am, MS 6201
Instructor: Inwon Kim
Office hours: Mon. and Wed. 1-2pm or by appointment  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: Chapter 5, p110 (Taylor's theorem).
 We will then cover Chapter 6,7, some of Chapter 8 (Power series and Fourier series) and Chapter 9.

Prerequisite: Mathematics 131AH. If you have taken 131A instead of 131AH please check with me.

Discussion section: T at 11am in MS 6201
TA:  Sungjin Kim
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.18th.

 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. 15th. The final exam is on Thursday, March 22nd, 3pm-6pm.


Grading: Final (50%), midterm(30%) and homework (20%: we will drop one lowest homework score).

Homework

Homework 1 (Due Jan. 18th): p.116, #15,17,19, 20,21,22,28.

Homework 2 (Due Jan. 25th) is  Here.

Homework 3 (Due Feb. 1st) is  Here.

Homework 4 (Due Feb. 8th) is  Here.

Homework 5 (Due Feb. 15th) is  Here.

Homework 6 (Due Feb. 22nd): p. 168,  #15,16,18 20, 22, 25.

Homework 7 (Due Feb. 29th) is  Here.

Homework 8 (Due Mar.7th): p. 200,  #9,12,14,15,16, 17(a),19.

Homework 9 (Due Mar. 14th): p. 200, #17 (b)-(d), p.239 #7, 9, 10, 14,15, 16.