Fall 2010: Math 131A section 1
Analysis

Class: MWF at 10am in MS 5138
Instructor: Inwon Kim
Office hours: Monday and Friday 1:30-2:30pm or by appointment  in MS 7620E

Discussion section: T at 10am in MS 5138.
TA:  Wenhua Gao
TA Office hours: TBA
Attendance to discussion section, as well as active participation, is strongly encouraged. 

Textbook: 
K. A. Ross, Elementary Analysis: The Theory of Calculus,  Springer (required).


Prerequisites: Mathematics 32B and 33B


Material:  We will cover Sections 1 - 34 of the book, excluding the starred (*) sections. 
Mathematical rigor will be emphasized. 
The aim of this course is to learn how to formulate and write a correct mathematical proof.  
At the end of the course you should be able to derive every theorem in the course 
(with a few clearly indicated exceptions), from the axioms for the real numbers given in the first chapter. 


Grades: It will be the maximum of either
Homework 20%, final 40%, midterms 40% (each 20%)
or
Homework 15%, final 65%, best midterm 20%.

*In order to pass this class, you must take the final exam.

Homework: There will be weekly homework assignments. The lowest homework set score will be dropped.  
Homeworks will be assigned on this webpage one week prior to the due date. Homeworks will be due
at the beginning of the Tuesday section, beginning October 5th. Working in groups are encouraged, but
to make the most out of the homework and to prepare for the exams you must (a) spend some time 
on each problem by yourself before discussing it with others and (b) write up your solutions by yourself. 


Midterms: There will be two in-class midterms: 
                                 October 20th, on Sections 1 - 10 and November 17th, on Sections 10 - 20. 
Some questions will ask for proofs of theorems from class.  No books, notes or calculators are allowed.

Practice exam for Midterm I is Here.

Final Exam:  December 9th, 11:30am-2:30pm. Comprehensive.




Homework Assignment 1, due Tuesday October 5th: 
Section 1: Ross 1.3, 1.8, 1.10.
Section 2: Show that the square root of 3 is not a rational number. Using this fact, then show 2.4.
Section 3-4: Ross 3.3, 3.4, 3.6, 4.1 (i)(k)(n),  4.6, 4.10, 4.12. Added: 4.8

Homework Assignment 2, due Tuesday October 12th: 
Section 5-8: 5.6; 7.3(f,h,s,p,o), 7.4; 8.2 (a)(b)(d),  8.3, 8.6, 8.9,8.10. Added: 8.5.
One more question: Show that for any real number x, there is a sequence of rational numbers converging to x. 

Homework Assignment 3, due Tuesday October 19th: 

Section 9-10:  9.11, 9.13; 10.2, 10.6, 10.8, 10.10.

 Homework Assignment 4, due Tuesday October 26th: 

9.9; 10.7; 11.2, 11.5, 11.6, 11.7, 11.8, 11.9; 12,1.

 Homework Assignment 5, due Tuesday November 2nd: 

12.2, 12.3 (a)(b)(d)(e), 12.4, 12.5, 12.8, 12.10. 

 Homework Assignment 6, due Tuesday November 9th: 
14,6, 14.7, 14.9, 14.12; 15.6, 15.7; 17.2, 17.8, 17.9 (b)(c), 17.10 (b)(c), 17.11, 17.13, 17.14.

 Homework Assignment 7, due Tuesday November 16th: 
18. 2, 18.4, 18.10, 18.12; 19.1 (b)(d)(e)(f), 19. 4, 19.6, 19.8

 Homework Assignment 8, due Tuesday November 23th: 
20.10, 20.12, 20.16; 28.1 (b)(d)(f), 28.3 (b)(c), 28.4, 28.6, 28.8, 28.15.

 Homework Assignment 9, due Friday December 3rd: 
 29.2, 29.12, 29.14, 29.16; 32.2, 32.4, 32.6; 33.4, 33.6, 33.10.