Math 142A, Winter 2025
Introduction to Analysis I
Lecture: MWF 2:00-2:50 in Peterson 102 (lecture recordings are on Canvas)
Professor: Brandon Seward (pronouns: they/them or he/him)
Email: bseward@ucsd.edu
Office Hours: Mondays 10-11 and 3-5 in AP&M 5739
Discussion B01: Thursdays 7:00-7:50 pm in HSS 2154
Discussion B02: Thursdays 8:00-8:50 pm in HSS 2154
Teaching Assistant: Greg Patchell
Email: gpatchel@ucsd.edu
Office Hours: Tuesdays 9-11 am and Thursdays 5-6:50 pm in HSS 4008
Course Description:
First course in an introductory two-quarter sequence on analysis. Topics include the
real number system, numerical sequences and series, infinite limits, limits of
functions, continuity, differentiation. Students may not receive credit for MATH 142A
if taken after or concurrently with MATH 140A.
Textbook:
Elementary Analysis: The Theory of Calculus by Kenneth A. Ross, 2nd edition.
This textbook is free to UCSD students; see Canvas.
We will cover chapters 1 - 3, excluding sections marked by * in the book's table of
contents.
Homework:
Homework will be due most weeks on Wednesday 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 WWEKBB.
- HW 1 (due Wed Jan 15): problems 2 and 6 from Section 1.1 and problems 2, 4, 7(b), and 8 from Section 1.2 (see the Hint at the back of the book for #7)
Note: For financial aid purposes, turning in this assignment will serve as verification of your participation in the class.
- HW 2 (due Wed Jan 22): problems 5 and 7 from Section 1.3 and problems 7, 14, 15, 16 from Section 1.4
- HW 3 (due Wed Jan 29): problems 1, 2, 4, 5, 8, 9, 10 from Section 2.8. (see Hints at the back of the book for #5, 9)
- HW 4 (due Wed Feb 5): problems 1, 2, 4, 6 from Section 2.9.
- HW 5 (due Wed Feb 12): problem 10, 16(a) from Section 2.9 and problems 6, 8, 10 from Section 2.10
- HW 6 (due Wed Feb 19): problem 10 from Section 2.11 and problems 2, 3(de), 4, and 10 from Section 2.12
- HW 7 (due Wed Feb 26): problems 2, 4, and 12 from Section 2.14 and problems 2 and 6 from Section 2.15
- HW 8 (due Wed March 5): problems 2, 3(cf), 4, and 10 from Section 3.17
- HW 9 (due Fri March 14): problems 6 and 10 from Section 3.18, problems 2 and 6 from Section 3.19, and problems 10 and 18 from Section 3.20
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: Friday January 31
- Second Midterm: Friday February 28
- Final Exam: Monday March 17, 3:00-6:00 PM
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 in need of special accommodations should provide the instructor an
Authorization for Accommodation (AFA) letter issued by the
Office for Students
with Disabilities (OSD).
Food Insecurity: If you are having difficutly affording food, the below programs may be able to help.
Support for Undocumented Immigrants:
Approximate Course Schedule:
| Week |
Monday |
Wednesday |
Friday |
| 1 |
Jan 6
1.1 The set of natural numbers
|
Jan 8
1.2 The set of rational numbers
|
Jan 10
1.3 The set of real numbers
|
| 2 |
Jan 13
1.4 The completeness axiom
|
Jan 15
1.5 The symbols +∞ and -∞
HW 1 Due
|
Jan 17
2.7 Limits of sequences
|
| 3 |
Jan 20
Martin Luther King Jr Holiday
|
Jan 22
2.8 A discussion about proofs
HW 2 Due
|
Jan 24
2.9 Limit theorems for sequences
|
| 4 |
Jan 27
2.9 Limit theorems for sequences
2.10 Monotone sequences and Cauchy sequences
|
Jan 29
Review
HW 3 Due
|
Jan 31
Midterm 1
|
| 5 |
Feb 3
2.10 Monotone sequences and Cauchy sequences
2.11 Subsequences
|
Feb 5
2.11 Subsequences
HW 4 Due
|
Feb 7
2.12 limsup and liminf
|
| 6 |
Feb 10
2.12 limsup and liminf
2.14 Series
|
Feb 12
2.14 Series
HW 5 Due
|
Feb 14
2.15 Alternating series and integral tests
|
| 7 |
Feb 17
President's Day Holiday
|
Feb 19
2.15 Alternating series and integral tests
3.17 Continuous functions
HW 6 Due
|
Feb 21
3.17 Continuous functions
|
| 8 |
Feb 24
3.18 Properties of continuous functions
|
Feb 26
Review
HW 7 Due
|
Feb 28
Midterm 2
|
| 9 |
March 3
3.18 Properties of continuous functions
3.19 Uniform continuity
|
March 5
3.19 Uniform continuity
HW 8 Due
|
March 7
3.20 Limits of functions
|
| 10 |
March 10
3.20 Limits of functions
Review
|
March 12
Review
|
March 14
Review
HW 9 Due
|
| 11 |
March 17
Final Exam
3:00-6:00 PM
|
March 19 |
March 21 |