Course: MATH 131A, Analysis, Lecture 5, Fall 2014
Prerequisite: MATH 32B, Multivariable Calculus, MATH 33B, Differential Equations.
Recommended course: MATH 115A, Linear algebra.
Course Content: Rigorous treatment of the foundations of real analysis, including construction of the rationals and reals; metric space topology, including compactness and its consequences; numerical sequences and series; continuity, including connections with compactness; rigorous treatment of the main theorems of differential calculus. This course should develop your ability to write rigorous proofs.
Last update: 15 December 2014

Lecture Meeting Time/Location: Monday, Wednesday and Friday, 2PM-250PM, Geology 4645
Instructor: Steven Heilman, heilman(@-symbol)
Office Hours: Mondays, 930AM-1130AM, Fridays, 1030AM-1130AM, MS 7370
TA: Sangchul Lee, sos440(@-symbol)
TA Office Hours: Tuesdays, 1PM-230PM, MS 2963
Discussion Session Meeting Time/Location: Thursday, 2PM-250PM, Geology 4645
Required Textbook: Elementary Analysis: The Theory of Calculus, 2nd Ed., K.A. Ross. Note: You can download the textbook from the UCLA library, by searching for the book and looking up the eBook copy, or by searching for Springerlink, and then searching for the book within Springerlink.
Other non-required textbooks: T. Tao, Analysis I, Hindustan Book Agency, 2006. 2nd Ed. R.S. Strichartz, The Way of Analysis, 2000. Revised Ed.
TA Course Website: here
First Midterm: October 27, 2PM-250PM, WGYOUNG 4216
Second Midterm: November 21, 2PM-250PM, BOELTER 5249
Final Exam: December 19, 1130AM-230PM, GEOLOGY 3656
Other Resources: 131AH, Tao, Winter 2003: I would highly recommend reading these lecture notes. These notes are also available in book form, which is cited above. Note that these resources correspond to the honors version of the course, so we will not be covering the material in as much detail. My own lecture notes below are meant to be a more condensed presentation of similar material. So, if you prefer a more thorough treatment, I recommend these notes (and the book by Ross).
An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Exam Procedures: Students must bring their UCLA ID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam.
Exam Resources: Here is a page with past exams for the course. Here is another page with past exams for the course. Note that the content of these other courses may be slightly different.
Here is a list of practice final questions (skip Q1,8,9,14,16,17b,21,24,25). Here are solutions.

Homework Policy:

Grading Policy:

Tentative Schedule: (Sections of the book listed below only approximate what we will cover.) (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
0Sep 29 Oct 2: No homework dueOct 3: Introduction
1Oct 6: S1, Natural numbers, induction Oct 8: S2, Integers, rationalsOct 9: Homework 1 due Oct 10: S10, Cauchy sequences of rationals
2Oct 13: S3,S4,S5, Real numbers Oct 15: Sets and functionsOct 16: Homework 2 due Oct 17: Cardinality of sets
3Oct 20: Countable and uncountable sets Oct 22: S7,S8 Sequences and convergence Oct 23: Homework 3 due Oct 24: S9,S10,S12 Limit points, lim sup, lim inf
4Oct 27: Midterm #1 Oct 29: S14, Standard sequences, series, absolute convergenceOct 30: Homework 4 dueOct 31: S15, Convergence tests
5Nov 3: S15, Root and ratio tests Nov 5: S11,Subsequences, Bolzano-Weierstrass theoremNov 6: Homework 5 due Nov 7: S20, Limiting values of functions
6Nov 10: S17, Continuity Nov 12: S18, Maximum principle, intermediate value theoremNov 13: Homework 6 dueNov 14: S19, Uniform continuity
7Nov 17: S28, Differentiability Nov 19: S28, Properties of differentiable functionsNov 20: Homework 7 dueNov 21: Midterm #2
8Nov 24: S32, Riemann integral definition Nov 26: S33, Riemann integral, existenceNov 27: No classNov 28: No class
9Dec 1: S33, Riemann integral, properties Dec 3: S29, Mean value theoremDec 4: Homework 8 dueDec 5: S34, Fundamental theorem of calculus
10Dec 8: Catch up, review Dec 10: Catch up, reviewDec 11: Homework 9 dueDec 12: Catch up, review

Advice on succeeding in a math class:

Homework Homework Solutions Exams Supplementary Notes