Fall 2021: Math 170, Ideas in Mathematics


Key info

Lectures: Section 2: MWF, DRLB A2, Livestream, 1:45pm-2:45pm

Section 601: MW, DRLB 2C4, 7:00pm-8:30pm

Instructor: Truong-Son Van,   Email: tsvan+170@sas.upenn.edu,   Office: DRL 3N8C

Office Hours (Instructor): M: 12:30p - 1:30p (in person), W: 5:00p-6:00p (Zoom)

TA: TBD,   Office Hours (TA):

Midterm 1: Oct 4

Midterm 2: Nov 1

Midterm 3: Dec 8 for Section 601 and Dec 10 for Section 2

Prerequisites: being curious.

Penn’s COVID-19 guidance

  • Masks are required indoors in public and shared spaces for ALL, including those who are fully vaccinated.
    • Exceptions to the masking requirement include single occupancy offices and shared spaces where 6ft distancing can be maintained, with roommates in our college house suites/rooms, and by permission in instructional settings for academic reasons.

Important dates

  • First day of class: Aug 31
  • Course selection period ends: Sep 14
  • Drop period ends: Oct 11
  • Fall break: Oct 14-17
  • Last day to withdraw: Nov 8
  • Thanksgiving: Nov 25-28
  • Final for this class: TBA

Textbook(s) and References

There is no official textbook for this course as any one book would limit the amount of creativity and fun we would have. I will provide readings one week (or two) before a new topic is discussed so that you have time to read the materials. Lecture notes will be provided after each class.

That said, there are a few books that I highly recommend if you are motivated.

  • Infinite Descent by Newstead. This book was written by my pal Clive Newstead for a course similar to Math 170 (but slightly more demanding and standardized) and it was an instant hit at Carnegie Mellon University. It is free and will be the main reference for a lot of the materials I plan to cover.
  • What is mathematics? by Courant, Robbins and Stewart. This is a classic written by two giants in modern mathematics. It was written to help teachers and students “look beyond mathematical formalism and manipulation and to grasp the real essence of mathematics.”
  • Wikipedia. In my opinion, this is the best source to learn about basic concepts in general (not just mathematics) if you know what you are looking for.

Course description

This course, if successful, will help students explore what mathematics really is. At its best, mathematics contains all of the following: creativity, beauty and, of course, precision. A masterpiece in mathematics could be compared to a great drawing or a classic novel. As an example, Martin Hairer’s regularity structure is compared to Lord of the Rings on Quanta Magazine.

We will start with the basic language of modern mathematics, logic and set theory. Then, depending on the interests of students, we will talk about some (but not limited to) of the following topics: infinity, number theory, combinatorics, probability, game theory, linear algebra, discrete and/or differential dynamical systems. Along the way, we will find real world applications of the above subjects.

Learning objectives

Two things:

  • I hope this course will help you have fun and nerdy conversations with friends (or strangers on the bus), whether they’re math people or not. At the least, if you don’t like the awkward silence, strike a conversation about $\infty$!
  • I hope you will find beauty in mathematics by knowing that mathematics is all about ideas, not computations (although computations play a big part in the usefulness of mathematics).

Tentative Syllabus (subject to change)

  • Unit 1: pigeonhole principle and numbers
  • Unit 2: core concepts (logic, set, functions, relations)
  • Unit 3: proof techniques and infinity
  • Unit 4: graph
  • Unit 5: probability
  • Unit 7 (if time permits): game

Class Policies (subject to change)


  • Lectures will be recorded and livestreamed but the recordings will not be readily available (see attendance section for more details).
  • If you must sleep, please don’t snore. (Thanks Gautam Iyer for this amazing policy!)
  • Please be respectful to your classmates.


  • Attendance is strongly encouraged, either in person or on a live Zoom meeting. If you have to be absent for any reason, please submit a Course Absence Report. Only those students who submit the reports will have access to lecture recordings in case then want to catch up.


  • Homework must be turned in by 23:59 p.m. ET on the due date.
  • All homework must be scanned and submitted electronically (I will NOT take homework slipped under my door).
  • Collaboration for homework is strongly encouraged but you MUST write up your own work. Word-to-word copying is plagiarism.
  • Generously credit all of the people who you collaborate with at the beginning of your work.
  • If you use outside sources (internet, books, friends, etc.) for a particular problem, acknowledge them at the beginning of the problem. You will NOT be penalized for consulting outside sources as long as you credit them.
  • Late homework policy:
    • Late homework wll NOT be accpeted. However, the three worst homeworks will be dropped.
  • Advice:
    • Eat well and get enough sleep.
    • Start early. One problem per day is more pleasant than seven problems in one night.
    • Try to understand the materials rather than rote memorization. This will show in exams.
    • Try to write clearly and demonstrate clarity of thoughts.


There are 2 midterms and 1 final. They are at the same length and level of difficulty.

Please make sure to adhere to the following points:

  • NO collaboration
  • NO calculator

Grading (subject to change)

  • 2 Midterms + Final: 30%
  • Homework: 70%
  • 3 worst homeworks will be dropped.
  • Worst exam (either midterm or final) will be dropped.


In general, take good care of your health. You’re a human being first, before a student. Your academinc performance will be affected if you are not in good health. If you experience mental health issues, please consider counseling at Penn’s Counseling & Psychological services. It is NOT a weakness to seek help. I do that from time to time.

  • 24/7 mental health hotline (CAPS): 215-898-7021.

Accomodations for Students with Disabilities

If you have a disability and have a letter from the Student Disabilities Services office, please meet and discuss with me as early as possible so I can make appropriate accomodations for you.

Academic Integrity

Please read the Code of Academic Integrity carefully.

Cheating will NOT be tolerated and will be reported to the Office of Student Conduct. In the worst case, it can result in expulsion.

That said, make sure you keep the following points:

  • Discussing homework is not cheating and strongly encouraged.
  • You need to write up your own solutions after discussions. Word-by-word copying is cheating.