Course: MATH 131B, Analysis 2, Lecture 1, Winter 2015
Prerequisite: MATH 131A, Analysis 1; MATH 115A, Linear algebra.
Course Content: This course is a continuation of MATH 131A. We will treat the topics in real analysis from a more general perspective. Topics include: metric spaces, point-set topology, function spaces, convergence of sequences of functions, power series, analytic functions, and Fourier analysis. This course should develop your ability to write rigorous proofs.
Last update: 17 February 2015

Instructor: Steven Heilman, heilman(@-symbol)ucla.edu
Office Hours: Mondays, 10AM-12PM, Wednesdays, 11AM-12PM, MS 7370
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 9AM-950AM, MS 5147
TA: Adam Azzam, adamazzam(@-symbol)gmail.com
TA Office Hours: Tuesdays 12PM-150PM, MS 6139
TA Course Website: here
Discussion Session Meeting Time/Location: Thursday, 9AM-950AM, MS 5147
Required Textbook: Mathematical Analysis, 2nd Ed, T. Apostol
Other Textbooks (not required): T. Tao, Analysis II, Hindustan Book Agency, 2009.
First Midterm: January 30th, 9AM-950AM, MS 5147
Second Midterm: February 23rd, 9AM-950AM, MS 5147
Final Exam: March 18, 8AM-11AM, MS 5147
Other Resources: 131BH, Tao, Spring 2003: I would highly recommend reading these lecture notes. 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). Note that we will probably not be covering the Lebesgue intergral.
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 than ours.

Homework Policy:

• Late homework is not accepted.
• The lowest homework grade will be dropped. This policy is meant to account for illnesses, emergencies, etc.
• Do not submit homework via email.
• There will be 8 homework assignments, assigned weekly on Thursday and turned in at the beginning of each discussion session on the following Thursday
• A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
• You may use whatever resources you want to do the homework, including computers, textbooks, friends, the TA, etc. However, I would discourage any over-reliance on search technology such as Google, since its overuse could degrade your learning experience. By the end of the quarter, you should be able to do the entire homework on your own, without any external help.
• All homework assignments must be written by you, i.e. you cannot copy someone else's solution verbatim. I would encourage you to understand carefully how the homework solutions work, and how you would find such a solution on your own. Overusing collaborations or search technology should result in poor performance on the exams.
• You are free to use any results in my lectures notes, up to the things that we have covered in class. If you use results from the book that are not in my notes, you must also produce the proof from the book, written in your own words.
• Label your homework with the lecture number and the discussion section number.
• Homework solutions will be posted ... (time)

• The final grade is given by the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%) The final grade will be curved. However, anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
• We will use the MyUCLA gradebook.
• If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
• You must attend the final exam to pass the course.

Tentative Schedule: (This schedule may change slightly during the course.)

Advice on succeeding in a math class:

• Review the relevant course material before you come to lecture. Consider reviewing course material a week or two before the semester starts.
• When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
• Come to class with questions, so you can get more out of the lecture. Also, finish your homework at least two days before it is due, to alleviate deadline stress.
• Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes. Also, consider typesetting your homework. Here is a template .tex file if you want to get started typesetting.
• If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

• HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 (solutions removed)

• 5: Metric Spaces, Topology, Continuity, Compactness
• 6: Sequences and Series of Functions, Convergence, Power Series, Special Functions
• 7: Inner Products, Fourier Series, Convolution
• 8: Differentiation in Several Variables
• Math 131B Full set of notes