Instructor: Ari Stern (stern@wustl.edu)

Office Hours: Tue 6-7 pm, Thu 12-1 pm Central Time (via Zoom, accessed
through Canvas)

Assistant
(AI): Atzimba Martinez
(martineza@wustl.edu)

Office Hours: Mon 6-7 pm, Wed 9-10 am Central Time (via Zoom, accessed
through Canvas)

There will be no lectures or office hours on the following days:

- Tuesday, February 9 (study day)
- Tuesday, March 2 (wellness day)
- Wednesday, March 3 (wellness day)
- Monday, March 22 (study day)
- Monday, April 12 (wellness day)

Although I hope it won't be necessary, it's possible that some aspects of the course may need to be adjusted to respond to changing circumstances of the COVID-19 pandemic during the semester. If that is the case, I will communicate any changes to you via email and/or Canvas announcements, and by updating this syllabus.

The Honors Mathematics I-II sequence (203-204) aims to give students a rigorous understanding of single-variable and multivariable calculus and linear algebra, together with their theoretical underpinnings. Along the way, students are introduced to the language and methods of modern mathematics, with a strong emphasis on proofs.

This second semester begins where Math 203 left off, with the study of linear transformations, matrices, and linear systems of equations. We will then go deeper into linear algebra, covering topics including determinants, eigenvalues and eigenvectors, diagonalization, and the spectral theorem. After a brief interlude on (some aspects of) linear differential equations, we will spend the second half of the term developing the theory of multivariable differential and integral calculus, including vector calculus and the fundamental theorems of Green, Stokes, and Gauss in two and three dimensions.

By the conclusion of this course, I expect students to have a
firm grounding in the key theoretical ideas and techniques of
linear algebra and multivariable calculus. Unlike last term with
the material on single-variable calculus, it is *not*
assumed that students have previous experience with linear
algebra or multivariable calculus from a computational point of
view. Therefore, in addition to theory, I also expect students
to gain some experience with computational techniques that are
used in applications (e.g., in science and engineering).

Synchronous remote lectures will be held Monday-Thursday,
11:00-11:50 am Central Time, live via Zoom. These lectures will
also be recorded to the cloud for later viewing. Live and recorded
lectures will both be accessed
through Canvas using
the Zoom link in the navigation bar. Synchronous attendance at
lectures is *strongly encouraged* but not mandatory.

Synchronous remote discussion sections, led by the AI, will be held on Fridays from 6:00-6:50 pm Central Time, also via Zoom. In these sessions, students will work together on problems in small groups, discuss them, and submit their written solutions afterwards.

*Participation in discussion sections is mandatory*. If
you cannot attend a particular meeting due to illness or other
unforeseen circumstances,
email the AI at
least one hour before the start of that meeting to request an
alternative way to receive credit for discussion problems. This
is at the discretion of the AI, and you may need to provide
documentation for an excused absence. (This policy is intended
for rare emergencies. If you already know that you will be
unable to attend discussion section meetings, please contact the
instructor and AI as soon as possible.)

*Scheduling Note:* Discussion sections were originally
scheduled for 11:00-11:50 am, but due to time zone issues, this
would have required about 1/3 of the class to attend in the
middle of the night. After surveying students to determine an
acceptable alternative time, we chose one that both US and
international students could attend synchronously.

Problem sets will be posted
to Canvas
approximately weekly, and students will submit their solutions
electronically by uploading them before the specified due date and
time. You are encouraged to discuss the homework with your fellow
students, but *your final write-up must be your
own*. Please make sure that your solutions are written clearly
and legibly.

In lieu of exams, each student will present an individual final project on a mathematical topic of their choice related to the course. Midway through the term, students will submit a short written proposal of the topic they plan to cover; this proposal is due Thursday, March 18. In the last 4 class meetings (April 28-29 and May 3-4), students will give a brief remote presentation on this topic to the class and hand in a written report.

Grades will be based on a weighted average of homework (50%, lowest score dropped), discussion section problems (25%, lowest score dropped), and the final project (25% = 5% proposal + 10% final presentation + 10% final report).

The corresponding letter grade will be assigned using the following scale:

A |
A- |
B+ |
B |
B- |
C+ |
C |
C- |
D |
F |
---|---|---|---|---|---|---|---|---|---|

≥90% | ≥85% | ≥80% | ≥75% | ≥70% | ≥65% | ≥60% | ≥55% | ≥50% | <50% |

The scale may be adjusted upward based on the class's cumulative averages. However, it will not be adjusted downward, so your letter grade is guaranteed to be at least that corresponding to your score on this scale. The grade of A+ is given at the instructor's discretion.

Pass/Fail policy: You must earn at least a letter grade of C- to get a P.

The required text for this course is *Calculus*,
vol. II (second edition), by Tom M. Apostol, published
by Wiley.

The following schedule of topics is preliminary and may be adjusted during the term, since some topics may take more or less time to cover than predicted.

Weeks 1-2: Linear transformations and matrices (Apostol 2)

Week 3: Determinants (Apostol 3)

Weeks 4-5: Eigenvalues and eigenvectors (Apostol 4-5)

Week 6: Linear differential equations (select topics from Apostol 6-7)

Weeks 7-8: Multivariable differential calculus (Apostol 8-9)

Week 9: Line integrals (Apostol 10)

Weeks 10-11: Multiple integrals and Green's theorem (Apostol 11)

Weeks 12-13: Surface integrals, Stokes's and Gauss's theorems (Apostol 12)

Week 14: Student presentations

All students are expected to adhere to high standards of academic integrity, as specified in the undergraduate student academic integrity policy. Since this course is offered through the College of Arts & Sciences, any violations of this policy will be referred to the College’s Academic Integrity Officer. Violations of this policy include, but are not limited to:

- homework collaboration exceeding that permitted in the Homework Assignments section above (e.g., preparing your final write-up side-by-side with another student rather than independently, copying another student's solutions);
- submitting the work of others as your own (e.g., copying homework solutions found online, including outside material in your final project without citing the source).

If you have any questions, or are unsure about what is permitted/prohibited by this policy, please ask me.

*In many cases, academic integrity violations are the result
of getting behind in coursework and making bad decisions under
pressure. Keep up with your assignments, ask questions when you
are unsure what is expected of you, and do not give in to the
temptation to cut corners.*