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)
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
.
Homework 1 (Due Wednesday Oct. 5):
Chapter 1 problems 1, 4, 5, 6, 7, 9. But in 6(c) change the definition
of B(x) to require t < x (instead of t <= x), and solve 6(c) by
applying 7(e). This change makes 6(d) easier.
Homework 2 (Due Wednesday Oct. 12): Chapter 1 problems 10, 13, 15, 17;
Chapter 2 problems 2, 11; and Problem A: Prove that the set of all
injections from the set of natural numbers to itself is uncountable.
Homework 3 (Due Sunday Oct. 23): Chapter 2 problems 6, 7, 8, 9, 10, 14, 22
Homework 4 (Due Friday Oct. 28): Chapter 2 problems 12, 13, 16, 23, 24, 29
Homework 5 (Due Wednesday Nov. 2): Chapter 2 problems 15, 17, 18, 19,
20, 21 and Chapter 3 problem 1 (Hint for problem 18: Mimick the
construction of the Cantor set)
Homework 6 (Due Wednesday Nov. 9): Chapter 3 problems 2, 3, 5, 16(a), 17(abc), 20, 23
Homework 7 (Due Sunday Nov. 20): Chapter 3 problems 4, 6, 7, 9, 10, 14(abcd)
Homework 8 (Due Wednesday Nov. 23): Chapter 3 problems 8, 11(a), 19, 21
Homework 9 (Due Friday Dec. 2): Chapter 4 problems 2, 3, 4, 5, 6, 7
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.
Approximate Course Schedule
Week
|
Monday
|
Wednesday
|
Friday
|
0
|
|
|
September 23 Ordered sets
|
1
|
September 26 Ordered sets
Fields
|
September 28 Fields
|
September 30
The Real field
The extended Real number system
The Complex field
|
2
|
October 3 The Complex field
Euclidean spaces
|
October 5 (HW 1 Due) The Complex Field, Euclidean spaces
|
October 7 Euclidean spaces
Finite, countable, and uncountable sets
Metric spaces
|
3
|
October 10 Metric spaces
|
October 12 (HW 2 Due)
Metric spaces
|
October 14
Metric spaces
|
4
|
October 17 Compact sets
|
October 19 First Midterm
Practice Midterm
|
October 21 (HW 3 Due Sunday)
Perfect sets
|
5
|
October 24
Connected sets
Convergent sequences
|
October 26
Convergent sequences
Subsequences
Cauchy sequences
|
October 28 (HW 4 Due) Cauchy sequences
Upper and lower limits
|
6
|
October 31
Upper and lower limits
Some special sequences
Series
|
November 2 (HW 5 Due)
Series
Series of non-negative terms
The number e
|
November 4
The number e
The Root and Ratio Tests
|
7
|
November 7
Power series
Summation by parts
Absolute convergence
|
November 9 (HW 6 Due) Addition and multiplication of series
Rearrangements
|
November 11
Veterans Day Holiday
|
8
|
November 14
Rearrangements
Limits of functions
|
November 16 Second Midterm
Practice Midterm
|
November 18 (HW 7 Due Sunday) Limits of functions
|
9
|
November 21
Continuous functions
|
November 23 (HW 8 Due)
Continuous functions
Continuity and compactness
|
November 25
Thanksgiving Holiday
|
10 |
November 28
Continuity and compactness
Continuity and connectedness
|
November 30
Discontinuities
Monotonic functions
|
December 2 (HW 9 Due)
Monotonic functions
Infinite limits and limits at infinity
|
11
|
Wednesday December 7, 8:00 AM -- 11:00 AM
Final Exam
Practice Final
|