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)ucla.edu
Office Hours: Mondays, 930AM-1130AM, Fridays, 1030AM-1130AM, MS 7370
TA: Sangchul Lee, sos440(@-symbol)math.ucla.edu
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.
Tentative Schedule: (Sections of the book listed below only approximate what we will cover.) (This schedule may change slightly during the course.)
|0||Sep 29||Oct 2: No homework due||Oct 3: Introduction|
|1||Oct 6: S1, Natural numbers, induction||Oct 8: S2, Integers, rationals||Oct 9: Homework 1 due||Oct 10: S10, Cauchy sequences of rationals|
|2||Oct 13: S3,S4,S5, Real numbers||Oct 15: Sets and functions||Oct 16: Homework 2 due||Oct 17: Cardinality of sets|
|3||Oct 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|
|4||Oct 27: Midterm #1||Oct 29: S14, Standard sequences, series, absolute convergence||Oct 30: Homework 4 due||Oct 31: S15, Convergence tests|
|5||Nov 3: S15, Root and ratio tests||Nov 5: S11,Subsequences, Bolzano-Weierstrass theorem||Nov 6: Homework 5 due||Nov 7: S20, Limiting values of functions|
|6||Nov 10: S17, Continuity||Nov 12: S18, Maximum principle, intermediate value theorem||Nov 13: Homework 6 due||Nov 14: S19, Uniform continuity|
|7||Nov 17: S28, Differentiability||Nov 19: S28, Properties of differentiable functions||Nov 20: Homework 7 due||Nov 21: Midterm #2|
|8||Nov 24: S32, Riemann integral definition||Nov 26: S33, Riemann integral, existence||Nov 27: No class||Nov 28: No class|
|9||Dec 1: S33, Riemann integral, properties||Dec 3: S29, Mean value theorem||Dec 4: Homework 8 due||Dec 5: S34, Fundamental theorem of calculus|
|10||Dec 8: Catch up, review||Dec 10: Catch up, review||Dec 11: Homework 9 due||Dec 12: Catch up, review|
Advice on succeeding in a math class: