Fall 2011: Math 131AH
Honors Analysis 

Class: MWF, 11am-11:50am, MS 5137
Instructor: Inwon Kim
Office hours: Monday and Fridays 1:30-2:30pm 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 cover Chapter 1-5.  

Prerequisite: Mathematics 32B, 33B   

Discussion section: T at 11am in MS 5138.
TA:  Guy David
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 Sep. 28th.

 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 shouldwrite up the solution yourself after understanding it thoroughly, without following 
 someone else's written version.  Otherwise, the homework does you no good.
 
 
Exam There will be one midterm, on wednesday, Nov. 2nd. The final exam is on Thursday, Dec. 8th, 8-11am.

 Midterm solutions are  Here   


Grading: Final (50%), midterm(30%) and homework (20%).

Homework

Homework 1 (Due Sep. 28th) is  Here 

Homework 2 (Due Oct. 5th) is  Here   

Homework 3 (Due Oct. 12th) is  Here   

Homework 4 (Due Oct. 19th) : Rudin p43 #11 (only check for the last metric d_5), #12, 13, 15,16, 18, 22, 23, AND an extra problem
Homework 5 (Due Oct. 26th): Rudin p43 #19, 24, 26. p78: #2,3 AND #20. 

Homework 6 (Due Nov. 2nd): Rudin p78 #5, 23, 24. 

Homework 7 (Due Nov. 9th) is  Here   

Homework 8 (Due Nov. 16th) is  Here 

Homework 9 (Due Nov. 23rd) is  Here 

Homework 10 (Due Dec.2nd) is  Here