Math 110.416: Honors Analysis 2, Spring 2020

Course description:
This course continues 110.415 Honors Analysis I, with an emphasis on the fundamental notions of modern analysis. Topics covered will include functions of bounded variation, Riemann-Stieltjes integration, Riesz representation theorem, along with measures, measurable functions, and the lebesgue integral, properties of Lp spaces, and Fourier series.

Where and when:
Lecture will be held Mondays and Wednesdays 1:30-2:45 in Bloomberg 176 (NOTE WE CHANGED THE ROOM). Discussions will be held Fridays 1:30-2:20 in Gilman 277.

Instructor: Alex Mramor, amramor1 'at'
Office hours 3-5 Thursdays at Krieger hall 311
Teaching Assistant: Junyan Zhang, jzhan182 'at'

Main text:
Real Analysis, by Carothers, Cambridge, ISBN:9780521497565. Please let me know if you are having trouble getting the book.

There will be an in class final worth 40% of your grade, an in class midterm worth 20% ( Update, 2/19: we will have the test 3/25 ), weekly 20-30 minute long quizzes in discussion worth 25%, and weekly homework of 7-10 problems assigned Wednesdays and due the following Fridays in discussion worth the last 15%.

Academic integrity:
The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

Report any violations you witness to the instructor. You may consult the associate dean of students and/or the chairman of the Ethics Board beforehand. Read the “Statement on Ethics” at the Ethics Board website for more information.

Disability accommodations policy:
Students with documented disabilities or other special needs who require accommodation must register with Student Disability Services. After that, remind the instructor of the specific needs at two weeks prior to each exam; the instructor must be provided with the official letter stating all the needs from Student Disability Services.

Course schedule and assignments (updated often!):

Week 1:
We'll begin the new semester with the last material covered in honors analysis 1 in the fall semester: Chapter 11, "the space of continuous of functions," out of Carothers.

Homework due Friday: Nothing due, but spend the week reviewing what you covered in math 415, and pick out and try a few problems from the book.

Week 2:
We covered chapter 13 on Monday, and Wednesday will be from chapter 14.

Homework due this Friday (posted Monday, 2/3/20 - typically homework will be assigned Wednesday and due the Friday after. l'll list homework under the week it is due for future reference): problems 47, 52, 54, 55, 56 from Chapter 11 of Carothers. NEW HOMEWORK IS POSTED BELOW.

Week 3:
We covered (nearly) all of what we wanted to cover in chapter 14, up through "integrators of bounded variation"

Homework due Friday (posted Wednesday, 2/5, due Friday 2/14: Valentines day): do problems 1, 4, 6, 12 from chapter 13, and problems 1, 2, 5, 8, 11, 22 from chapter 14.

Week 4:
We wrapped up chapter 14 (the fundamental theorem of calculus parts 1 and 2) and did chapter 15, up through Dirichlet and Fejer kernels.

Homework due Friday (posted Wednesday, 2/12, due Friday 2/21): do problems 10, 25, 26, 27, 36, 38, 40, 41, 46 out of chapter 14.

Week 5:
In chapter 16 we covered the section "Lebesgue outer measure," skipped (we'll come back to this) "Riemann integrability," and started the section "measurable sets." We gave the definition (Carother's definition, not the original one) of measurable set, and showed the collection of measurable sets was an algebra of sets.

Homework due Friday (posted Wednesday, 2/19, due Friday 2/28): do problems 4,5, 7, 8, 11 out of chapter 15 (yes, a light assignment this week!)

Week 6:
We will continue on with chapter 16.

Homework due Friday (posted Wednesday, 2/26, due Friday 3/6): do problems 3,4,5,6,8,9,16,17,20, 21 out of chapter 16.