Math 204

Honors Mathematics II, Spring 2021

Contact Information

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

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

Wellness and Study Days

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

Syllabus Note

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.

Course Overview and Learning Objectives

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.

Discussion Sections

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.

Homework Assignments

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.

Final Projects

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.

Schedule of Topics

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

Academic Integrity

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:

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.