Winter 2018: Math 131AH
Honors Analysis
Class: MWF, 10am-10:50am, MS 6627
Instructor: Inwon Kim
Office hours: MW 3-4 and F 1-2 in MS 7905
This course is an honors-level introduction to real analysis. Real analysis is the theoretical foundation which underlies calculus. Many of the subjects we will be discussing will be familiar to you
from previous calculus classes, however the emphasis is quite different here. While calculus classes focuses on computational aspects, in this class we will focus
on the underlying theory and mathematical rigor. The goal is to understand mathematical concepts and to construct careful mathematical arguments to prove
properties about them.
Text: Principles of Mathematical Analysis (3rd edition) by W. Rudin. We will cover Chapter 1-4 and a bit of Chapter 5 if time permits.
Prerequisite: Mathematics 131AH (consult with me if you took 131A), 115 (only for multivariable functions appearing later in the quarter).
Discussion section: T at 11am in MS 6627
TA: Sangchul Lee
TA Office hours: TBA
Attendance to discussion section, as well as active participation, is strongly encouraged: the section will give you an opportunity to discuss proofs of problems in different aspects, broadening one's point of view.
Homework: Homeworks will be posted below on thursdays and is due on every wednesday, starting from January 17th. We will drop one lowest homework score.
In this class you will be required to write precise mathematical statements in a clear logical order, and present pictures or examples as necessary to illustrate
your work. Acquiring these skills is impossible without a steady practice: it is essential that you do the homework problems carefully and promptly.
You may discuss homework problems with other students, the TA or me before they are turned in. I do expect though that: (i) you should make a serious effort
to do the exercise yourself before discussing it with anyone, and (ii) you should write up the solution yourself after understanding it thoroughly, without following
someone else's written version. Otherwise homework will not help you to prepare for the exams. Identical solutions to a source will get zero credit.
Exam There will be one midterm, on Monday, Feb 12th, in class. The final exam is on Friday Mar. 23rd, 11:30am-2:30pm.
Grading: Final (50%), midterm(30%) and homework (20%): we will drop one lowest homework score.
Homework
Homework 1 (Due January 17th)
Homework 2 (Due January 24th)
Homework 3 (Due January 31th)
Homework 4 (Due February 7th)
Homework 5: Rudin Chapter 2 Exercises 22,23,24,25,26
Homework 6 (Due February 28th)
Homework 7 (Due March 7th)
Homework 8 (Due March 16th)