# Spring 19 - Math 131A - Real Analysis

This is the course website for Math 131A in Spring 2019.

Please note that we are using Campuswire for this class (see below).

## Instructor, TAs and office hours

### Instructor

Jens Eberhardt (firstname@math.ucla.edu)
MS TBA (or in my office MS6304),TBA
MS TBA (or in my office MS6304),TBA

### TAs

TBA (TBA)
TBA

Please check back here as office hours and locations may change.

## Schedule

The lectures take place Monday, Wednesday and Friday at 11am-11:50am in MS 5137. Time and date of the discussions can be found here.

In the following table you can see the preliminary lecture schedule and find your weekly problems list and homework.

# Date Content Homework
1 M, 4/1 Induction and Natural Numbers (1.1) Week 1
Homework:
PDF
2 W, 4/3 Integers, Rational Numbers, Ordered Fields (1.2)
F, 4/5 Cauchy Sequences (1.7)
4 M, 4/8 Real Numbers (1.3), Completeness (1.4) Week 2
Homework:
PDF
5 W, 4/10 No Lecture!
6 F, 4/12 Limit Theorems (2.9)
7 M, 4/15 Least Upper Bound Theorem Week 3
Homework:
PDF
8 W, 4/17 Bolzano-Weierstraß (2.11)
9 F, 4/19 limsup, liminf (2.12)
10 M, 4/22 Midterm 1 Week 4
Homework:
PDF
11 W, 4/24 Infinite Series (2.14, 2.15)
12 F, 4/26 Continuity: Definition (3.17)
13 M, 4/29 Continuity: Examples (3.17) Week 5
Homework:
PDF
14 W, 5/1 Continuity: Properties (3.17)
15 F, 5/3 Uniform Continuity
16 M, 5/6 Uniform Continuity Week 6
Homework:
PDF Questions (3) and (4)
PDF Questions (1), (2) and (3)
17 W, 5/8 Uniform Continuity, Limits of Functions
18 F, 5/10 Limits of Functions
19 M, 5/13 Derivatives Week 7
Homework:
PDF
20 W, 5/15 Derivatives
21 F, 5/17 Mean Value Theorem
22 M, 5/20 Midterm 2 Week 8
Homework:
PDF
23 W, 5/22 Integration: Definition
24 F, 5/24 Integration: Integrability
Monday, 5/27: Memorial Day! Week 9
Homework:
PDF Questions (1) and (2)
25 W, 5/29 Integration: Linearity
26 F, 5/24 Integration: Inequalities
27 M, 6/3 Fundamental Theorem of Calculus I and II Week 10
Homework:
PDF Questions (3), (4), (5) and (6)
28 W, 6/5 Review
29 F, 6/7 Review

Hint: If you are using your phone, turning the screen horizontal makes the table easier to read.

# Course Notes

We are using Nickolas Andersen's lecture notes: MATH 131A: REAL ANALYSIS

## Homework

Solving problems on your own is one of the most important parts of this course. It will teach you how to apply your new knowledge and also be the best preparation for the midterms and final exam.

I encourage you to discuss the problems in teams but write up the solutions on your own. Simply copying your homework will not prepare you for the exams at all and is also not allowed (i.e. considered academic misconduct/cheating).

Every week you will be able to find a list of problems in the lecture schedule. They will be covering the material of the lectures and similar to exam questions.

You will have to solve these problems and hand them in at the beginning of the lecture every Friday. Your homework has to be submitted in a form obeying the following rules:

• In the upper right corner of the first page put:

First and last name
Student ID
Date, Homework number
TAs name
Number of discussion session

• In the upper right corner of every additional page, put your name.
• Write legible. No crumpled, torn paper.
• Label each solution with the section and problem number (e.g. 7.2 #2).
We will not accept your homework if it violates any of the above rules.

# Exams

There will be two midterms and a final exam. Apart from the exceptions mentioned below, only writing equipment will be allowed in exams. Exams must be written in pen.

• Midterm 1: TBA
• Midterm 2: TBA
• Final Exam: TBA

Cheatsheets: For each exam, students may bring a cheat sheet. Each student must prepare their own handwritten cheat sheet. For the midterms, the cheat sheet may consist of one side of half a standard (A4 or letter) sheet of paper (i.e. A5 or letter folded in half lengthways). For the final, the cheat sheet may consist of one side of a standard sheet of paper. Cheatsheets that do not meet these requirements will be confiscated at the beginning of the exam.

Calculators: You may use a non-programmable, non-graphing calculator in exams. Calculators not meeting this specification will be confiscated.

Study: Here I will post some practice exams which might aid your study.

The midterm scores will be adjusted to account for any difference in difficulty. Your final grade will be calculated using the maximum of the following two grading schemes. Your letter grade will then be determined by your rank in the class. Unless something very out of the ordinary occurs I expect to give approximately 20-30% A’s and 55-65% A’s and B’s combined.

Option 1:

10% (7 best homework scores) +
40% (combined midterm scores) +
50% (final exam score)

Option 2:

10% (7 best homework scores) +
30% (best midterm score) +
60% (final exam score)