Professor: Brandon Seward (pronouns: they/them or he/him)
Email: bseward@ucsd.edu
Lecture: MWF 9:00-9:50 in Ridge Walk Academic Building (RWAC) room 0121
Lecture Recordings: On our Canvas page under the Media Gallery tab
Office Hours: Mon. 2-4 and Wed. 11-12 in AP&M 5739

Teaching Assistant: Juno Seong
Email: jseong@ucsd.edu
A01 Discussion: Mon. 5:00-5:50 in Center Hall room 217B
A02 Discussion: Mon. 6:00-6:50 in Center Hall room 217B
Office Hours: Tues. 12:00 - 4:00 in Humanities and Social Sciences Building (HSS) 4016

Course Description: First course in a rigorous three-quarter sequence on real analysis. Topics include: the real number system, basic topology, numerical sequences and series, continuity.

Textbook: Principles of Mathematical Analysis by Walter Rudin, 3rd edition. We will cover Chapters 1 through 4 (excluding the appendix to Chapter 1).

Additional Study Materials: (you will not be tested on these)

• A list of errata in the course textbook (by George Bergman)
  
• A supplement to the exercises in the course textbook (by George Bergman)
• Elementary Analysis: The Theory of Calculus by K. A. Ross, 2nd edition (standard textbook for 142A; less advanced but may be helpful. Available for free to UCSD students on the campus network, and can be found by searching in UCSD's Library Catalog).
• Understanding Analysis by Stephen Abbott
  
• 140A-B Lecture Notes (by Professor Todd Kemp). Note that these lecture notes do not follow our textbook and may cover different topics. This is for reference only.
• Construction of the real numbers by Dedikind cuts - see the appendix to chapter 1 of the course textbook
  
• Construction of the real numbers by Cauchy sequences (by Professor Todd Kemp - this will make more sense after we discuss Cauchy sequences in class)
• Uniqueness of the real number field and containment of the rationals.
  

Homework: Homework will be due most weeks on Wednesdays at 11:59 PM, except on weeks in which we have a midterm it will be due on Friday at 11:59 PM. No late homework will be accepted, but your lowest homework score will be dropped when computing your final grade. On each assignment, a few problems will be graded for correctness, while the others will be graded simply for completion. We will use Gradescope for turning in homework. When registering for gradescope, please register using your "@ucsd.edu" email address and use Entry Code 4VDVEN.

Exams: All exams will be in-person. If you miss a midterm no makeup exam will be given. Instead your final exam will count towards 60% of your final grade.

• First Midterm. [Practice Midterm] Wednesday Oct. 19. Will cover Chapter 1 and the first two sections of Chapter 2 ("Finite, Countable, and Uncountable Sets" and "Metric Spaces").
  
• Second Midterm. [Practice Midterm] Wednesday Nov. 16. Will cover the following sections from the book: Compact Sets, Perfect Sets, Connected Sets, Convergent Sequences, Subsequences, Cauchy Sequences, Upper and Lower Limits, and Some Special Sequences
  
• Final Exam. [Practice Final] Wednesday Dec. 7 from 8:00 AM to 11:00 AM. Will cover Chapter 1 (excluding the appendix), Chapter 2, Chapter 3, and the first two sections of Chapter 4 (Limits of Functions and Continuous Functions).
  

Grading: Your final grade will be the maximum of the following two weighted averages:

• 20% Homework, 20% First Midterm, 20% Second Midterm, 40% Final Exam.
• 20% Homework, 20% Best Midterm, 60% Final Exam

Special Accommodations: Students requiring accommodations should provide an OSD letter of certification and OSD accommodation recommendation as soon as possible.

---