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math104-s21:start

Math 104: Introduction to Real Analysis (Spring 2021)

Instructor: Peng Zhou
Email: pzhou.math@berkeley.edu

Welcome to Math 104, introduction to real analysis. We plan to cover the following topics:

The real number system. Sequences, limits, and continuous functions in R and R. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Mean value theorem and applications. The Riemann integral.

I am planning to use two textbooks. Most likely, I will follow Ross and assign problems from it.

  • Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross. You can download a copy of this book here (UC account login required).
  • Principles of Mathematical Analysis, by Walter Rudin

Here is a problem book with solutions. The scope of this book does not exactly match with this course, which follows closely with Rudin.

I will be teaching two sections, at Tuesday and Thursday 9:30 - 11:00 (section 5) and 12:30 - 14:00 (section 6). You can attend either of the lectures, they are supposedly to be the same. ( We are going to use 'Berkeley time', so the actual lecture starts at 10 minutes later. )

  • Zoom link: here (Meeting ID: 972 1343 0388, Passcode: 591757).

Logistic

A tentative grading policy: 20% homework, two midterms each 20%, and final (accumulative) 40%. If you didn't do well in one of the midterm, you have the option to drop it, and final will have a 60% weight. The lowest homework grades will be dropped.

Midterms (Feb 18, Apr 1) and final (May 12 or 13) will be done through gradescope. Midterm will be 90 minutes, and final will be 3 hours. 10 minutes extra will be given for scanning and uploading. If you are in a different time zone and prefer an alternative time slot, please contact me in advance.

There will be weekly homework, to be submitted on gradescope. Entry code is BPKBXR

Office Hours and Q&A

Time: By appointment (everyday after 9pm, or Wednesday 1-2pm, Friday morning 9-12noon)
Zoom: https://berkeley.zoom.us/j/98628027987

We also have a GSI (Graduate Student Instructor) Rahul Dalal, he is available at 10:30-12:30 M, 11am-1pm WF and 5:30p-7:30p TuTh. zoom link 96793003738 and the password is epsilon.

A faster way to communicate is through online platform, we can do either

  • Piazza. Sign Up (access code: cauchy). You can ask questions anonymously here.
  • Zoom chat channel . You may join the channel “Math 104, by Peng Zhou”, and ask question there.
  • Zoom direct message: you can search for my name “Peng Zhou” in zoom chat, and ask me questions directly there. Email is also fine.

Homeworks

There are weekly homeworks, grades will be published the next Wednesday night. There is always a late due date, 24h after the normal due date, only for emergency use.

Lectures

Here I put lecture video (valid for 30 days) and notes. 1 means section 9:30 and 2 means section 12:30. They are more or less the same. video will expire after 30 days . Videos can also be found on bcourse, which will not be deleted.

Date Content Notes Videos
Jan 19, Tue Logistic and Number system 1, 2 1, 2
Jan 21, Thu Completeness Axiom and Sequence 1, 2 1, 2
Jan 26, Tue Ross §7,§9 1, 2 1, 2
Jan 28, Thu Ross §10, Monotone sequence 1, 2 1, 2
Feb 2, Tue Cauchy Sequence, limsup and liminf 1, 2 1, 2
Feb 4, Thu Subsequence 1, 2 1, 2
Feb 9, Tue Subsequence(2) 1, 2 1 2
Feb 11, Thu §12 limsup, liminf and review 1, 2 1, 2
Feb 16, Tue §13 Metric Space and Topology 1, 2 1, 2
Feb 18, Thu Midterm 1 and suggestions A, B solution stat
Feb 23, Tue §13 Compactness 1, 2 1, 2
Feb 25, Thu §14, 15 Series 1, 2 1, 2
Mar 2, Tue Continuity of functions[Ru, p83-89] 1, 2 1, 2
Mar 4, Thu Continuity and Compactness 1, 2 1, 2
Mar 9, Tue Uniform Continuity, Connectedness 1, 2 1, 2
Mar 11, Thu Finishing Connectedness, Discussion and Examples 1, 2 1, 2
Mar 16, Tue Sequence and Convergence of functions 1, 2 1, 2
Mar 18, Thu Uniform Convergence and Continuity 1, 2 1, 2
Mar 23, 25 Spring Break!
Mar 30, Tue Review 1, 2 1, 2
Apr 1, Thu Midterm 2 A, B solution stat
Apr 6, Tue Differentiation, Mean Value Theorem 1, 2 1, 2
Apr 8, Thu Mean Value Theorem, L'Hopital Rule 1, 2 1, 2
Announcement: drop-in tutor available
Apr 13, Tue Taylor's Theorem 1, 2 1, 2
Announcement: 10 pts extra credits available: sharing notes and questions
Apr 15, Thu Finish Taylor Series. Begin Riemann integral 1, 2 1, 2
Apr 20, Tue Discussion of Integrability 1, 2 1, 2
Apr 22, Thu More on integrability 1, 2 1, 2
In the last 20 minutes of video #2 above, I discuss Rudin 6.13 - 6.17. People from morning session please also watch it.
Apr 27, Tue Integration and Differentiation 1, 2 1, 2
Apr 29, Thu Uniform Convergence and review 1, 2 1, 2
May 12-13 Final Exam exam solution stat

Other instances of Math 104

math104-s21/start.txt · Last modified: 2022/01/17 15:55 by pzhou