Math 131B: Analysis

Spring 2017

Material: this course can be seen as a continuation of Math 131A. We will deal with similar concepts in more abstract settings, in particular we will try to cover the following topics: some topological notions in metric spaces; continuous functions on metric spaces; sequences and series of functions; power- and Fourier series; several variable differential calculus; Lebesgue mesure and integral (if time permits). During the course there will be a big accent on writing and understanding rigorous proofs.

Instructor: Alpár R. Mészáros, MS 5230 (check the e-mail address on my webpage or on CCLE)

Schedule of classes: MWF - 9-9h50AM

Location: Geology 6704

Office hours: MW, 10h00-11h30AM (or by appointment)

TA: Younghak Kwon (check e-mail address on CCLE)

Discussion: Tuesday, 9-9h50PM, same room as the lecture

TA's office hour: TBA

Textbook: T. Tao, Analysis II, Hindustan Book Agency, Third Edition, (2014).

Requisites: Math 131A (or an equivalent course) is enough to follow this course.

There will be 9 sets of homework sheets assigned, and I will collect them always at the beginning of the lecture on Wednesday. The purpose of the homework exercises is to deepen the notions and the concepts learned during the lectures and sometimes it will be asked to complete some proofs started during the lectures. Please note that late- or no homework papers will be graded as zero, but the lowest homework score will be dropped in the computation of your final grade (see 'Grading' section below). The homework sheets will appear on this webpage, approximately 1 weak before their deadlines. There is a possibility to work in groups on the homework papers. In this case, everybody from the group has to submit her/his own homework paper and should write the names of the other students from her/his group on the top of the papers.

Exams: there will be one midterm roughly on the fourth or fifth week of the instruction period (see the precise dates below) and a written final exam at the end. No make-up exams will be provided, a missed exam is graded as zero. You must take the final in order to pass the class!

Grading: the final score is computed as follows (I will choose the scheme which gives you higher score):
20% HG + 30% MG + 50% FG,
or
20% HG + 80% FG, where

HG = the average of the homework scores, except the lowest one

MG = the score of the midterm

FG = the score of the final exam

Date of the midterm: Wednesday, April 26, 2017; same time as the lectures; place: MS 5200

Date of the final exam: Wednesday, June 14, 2017, 8-11AM

Regrading for the homework, midterm and final papers should be requested within 2 weeks of their due date and exam dates respectively. Any requests after this period will be not taken into consideration.

Homework sheets