
Professor Francis Su
Section 2, Summer 2025
Meetings: (zoom) MWF 8:00am – 10:30am,
May 28 – July 2
(except Fri Jun 13 and Mon June 22).
Zoom link can be found in an email from me, or on the course Canvas site.
Course Webpage: https://math.hmc.edu/su/math55/
My Email: (my last name) at math.hmc.edu
Grutor: Joshua Zhong (jozhong) can be reached at g.hmc.edu
Office Hours: online, with me or Joshua (same Zoom link as class)
Mon-Tue-Wed-Thu-Fri 3pm.
Course Description
This course is an introduction to combinatorics, number theory, and graph theory with an emphasis on creative problem solving and learning to read and write rigorous proofs. Topics include: combinations, permutations, inclusion-exclusion, strong induction, recurrences, Bayes’ theorem, the Euclidean algorithm, unique factorization, modular arithmetic, Euler’s theorem, RSA encryption, planar and Eulerian graphs, and graph coloring. My goal is to create an inclusive classroom climate where everyone feels responsible for the participation and the joy that others experience in learning.
Text
There is no required textbook to buy.
We will use portions of Oscar Levin’s Discrete Mathematics: An Open Introduction (4th edition), which is available both as a PDF and in an interactive online ebook.
Coursework
Homeworks will be assigned and due each class day at 8am via Gradescope. There will be one midterm (due Jun 13 at 5pm) and one final exam (due Jul 3 at 5pm). Each component (homework, midterm, final) is worth at least 30% of your final grade, with the “best” component worth 40%.
Every assignment has an automatic 24 hour extension–you do not need to formally request this extension. Since this is a summer course, I cannot accommodate homeworks later than this unless you are excused by the Dean.
The learning you are doing in this class takes place in a larger framework of school and life. Sometimes life takes precedence. Similarly, ‘success’ by whatever measure is not the most important thing in this course either. Every assessment of your work in this class is a measure of mathematical progress, not a measure of your mathematical promise. Joy, wonder, and expanding your mind through struggle—these are more important!
Honor Code
The HMC Honor Code applies in all matters of conduct concerning this course. Though cooperation on homework assignments is encouraged, you are expected to write up all your solutions individually to ensure your own understanding. Your solutions should acknowledge the assistance of other people or resources of any kind.
AI Policy
(1) Online resources, including artificial intelligence, may be consulted for general learning that is not directly related to assigned problems. However, such resources, especially AI, should be viewed with a healthy skepticism–they can be wrong, or they may rely on ideas we have not covered in this class. Moreover, an over-reliance on them can be detrimental to your learning if the ideas do not “pass through your brain” or give you a deeper understanding.
(2) You should not use AI or other resources to locate solutions for any assigned work. You may check your answers using the ‘Activate’ button in the Levin e-text, but you may not use published solutions for the text. Doing any of these things will be regarded as a violation of the HMC honor code. In addition, you will miss the joy of discovering a solution for yourself, which is one of the best feelings in the world.
Lecture Notes and Zoom
I will not be recording lectures, but zoom link and lecture notes will be linked from the course Canvas site.
Homeworks
Due on Gradescope each class day at 8am.
Some of you may find LaTeX helpful in typesetting your homework. If so, there is a LaTeX class for homework here.