Spring 2025: Math 131BH
Honors Analysis
Class: MTF, 10am-10:50am, MS 5117
Instructor: Inwon Kim
Office hours: M 2-3 W 1-2 or by appointment in MS 7923
131AH-BH is an honors-level introduction to real analysis. Real analysis is the theoretical foundation which underlies calculus. Many of the subjects in class 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. Continuing from last quarter, we will start from covering compactness from chapter 2, and cover Chapter 4, 5, 6, and
(if time permits) some of Chapter 7 and 9.
Note from last quarter’s 131AH
Prerequisite: Math 131AH.
Discussion section: T at 10am in Geology 4645.
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 on Gradescope on Fridays and is due on every thursday, starting from April 10th. 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 Friday, May 9th, in class. The final exam is on Tuesday June 10th.
Grading: Final (50%), midterm(30%) and homework (20%): we will drop one lowest homework score).