Math 140B (Spring 2026)
Summary
Math 140B is a second course in the 140ABC series, giving a rigorous introduction to mathematical analysis. Math 140A is a prerequisite for the course.
The topics covered include differential and integral calculus, sequences and series of functions, power series and Fourier series.
The course textbook is Principles of Mathematical Analysis by Walter Rudin, 3rd Edition. The course material corresponds to chapters 5–8.
Contacts
The instructor is Freddie Manners (email fmanners); my office is AP&M 7343. The TA is Leo Liu (email yil350).
Class and section
Lectures are held on Tuesdays and Thursdays 1230–1350 (i.e., 12:30pm–1:50pm). They will be held in-person in HSS 1315. The course will not be generally available as a podcast, and lecture attendance is mandatory. I will take lecture attendance, and some portion of your grade is assigned to class attendance.
Section is held in-person, on Tuesdays, at 1800–1850 (6:00pm–6:50pm) in SOLIS 105. Section attendance is very strongly encouraged and attendance will be taken. Some course grade is tied to attend section at least once and office hours (with either TA or the instructor) at least once over the quarter.
Exams
There will be two evening midterm exams, on Wednesday April 22 (Week 4) and Wednesday May 13 (Week 7), 1900–2030 (i.e., 7pm to 8:30pm), in AP&M B402A (in the basement).
The final exam is on Monday June 8, at 1130–1430 (11:30am–2:30pm). It is also in-person, in HSS 1315.
You should ensure at the start of the quarter that you can attend these exams. In general, alternative modalities, dates or times (in particular, remote exams) will not be offered.
(Note: it is standard practice in the Mathematics Department to use multiple versions of exams where necessary.)
Exams will be closed-book. Use of any outside resources or communication in exams is, of course, strictly forbidden.
Homework
Homework is due every Saturday at 23:59 (11:59pm), starting in Week 1 (April 4). Deadlines may change as circumstances require.
You may collaborate in discussing and thinking about homework problems; indeed this is often beneficial. However, if you do, you must list your collaborators on your assignment when you turn it in. Moreover, you must not simply show another student a written solution to a problem, and when you write your own solutions, you must do so alone and in your own words, without looking at another solution. You may use outside resources, including the internet, other textbooks or AI tools, to help you understand the subject material. However, you may not attempt to find a solution to a specific homework problem using such resources. In particular, you may not post any homework problem as a question on the internet, or to an AI system.
Your lowest homework grade for the quarter will be dropped, to allow for disruptions that may arise. Beyond this, I will not grant extensions or accept late homework, unless there are truly exceptional circumstances. Good-faith technical or logistical issues in turning in your homework (which result in very short delays) may be forgiven, on a case-by-case basis.
Grading
Your combined grade for the course is calculated as follows. First, you worst homework grade will be dropped. Then, take
- 15% homework;
- 23% midterm 1;
- 23% midterm 2;
- 35% final exam;
- 3% class attendance (capped at 80% attendance rate, then 0.0375% grade remvoved for every 1% attendance below that);
- 1% for both attending section at least once, and attending office hours at least once.
The requirement to attend office hours at least once is intended to be fun and encourage dialogue. You don't have to have a specific question – it's ok to show up and chat in general terms.
Letter grade boundaries are chosen based on how well I think students have performed, relative to historical norms, rather than by fixed percentages. Exams in 140B will generally be challenging, so percentage scores which would be low by many standards do not necessarily imply low letter grades.
If for some reason the course scores are much higher than expected, it is nevertheless guaranteed that the letter grade cutoffs will be at least as generous as the following table. However, it is extremely likely that they will be more generous: this serves as a minimum guarante only.
| A+ | A | A- | B+ | B | B- | C+ | C | C- | F |
|---|---|---|---|---|---|---|---|---|---|
| 97 | 93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 | < 70 |
Accommodations
Students in need of special accommodations should provide me with an Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (OSD).
Resources
In addition to this website, the course has a Canvas page, a Gradescope page and a Piazza site. The sign-up codes for Gradescope and Piazza are listed on the Canvas home page.
Provisional schedule
A rough provisional course schedule is given below. It is subject to change.
| Week | Tue | Thu | Topic |
|---|---|---|---|
| 1 | L1 | L2 | Derivatives. Mean value theorems. Continuity. L'Hopital's rule. |
| 2 | L3 | L4 | Taylor's theorem. Derivatives of vector-valued functions. |
| 3 | L5 | L6 | Integration. Definition, existence and properties. |
| 4 | L7 | L8 | Integration and differentiation. Midterm 1 review. |
| 5 | L9 | L10 | Rectifiable curves. Uniform convergence. |
| 6 | L11 | L12 | Uniform convergence and calculus. Equicontinuous functions; Stone—Weierstrass. |
| 7 | L13 | L14 | Stone—Weierstrass. Midterm 2 review. Power series. |
| 8 | L15 | L16 | Power series. |
| 9 | L17 | L18 | Exponential and logarithmic functions. Trigonometric functions. Fourier series. |
| 10 | L19 | L20 | [If time] More Fourier series. The Gamma function. |
Office hours
Regular office hours and locations are listed in the table below. However, please check the calendar below for any one-off changes or cancellations.
| Instructor / TA | Location | Regular hours |
|---|---|---|
| Freddie Manners | APM-7343 | Thursdays 4:30-5:30pm, Fridays 1:00-2:00pm |
| Leo Liu | HSS 4044 | Wednesdays & Fridays 3:30-4:30pm |
Course calendar
A link to add this calendar is available on the course's Canvas page.