# Math 210 - Spring 2020

### Instructor: Ted Chinburg

Lectures TTh 1:30-3:00 , room 4C6 in DRL labs

Office: DRL 4E4, Ext. 8-8340.
Office hours: These will be on Skype, at times to be decided in class, and by appointment
E-mail: ted@math.upenn.edu

Math. Dept. Office: DRL 4W1, Ext. 8-8178.

## Homework

• Homework assignment 1 (due Jan. 30).
• Homework assignment 2 (due Feb. 13).
• Homework assignment 3 (due March 3).
• Homework assignment 4 (due April 2).
• Homework assignment 5 (due April 14).
• Homework assignment 6 (due April 28).
• Optional Extra Credit for Homework assignment 6 (due May 7).
• Homework assignment 7 (due May 7).

## Course Guide

### Course Goals:

This course will initially focus on mathematics related to the media. We will study media behavior using game theory, information theory, probability theory, the theory of networks and differential equations. The latter part of the course will be about applying probability theory and differential equations to understanding various questions arising from the covid-19 epidemic. Here are some particular questions we will study:
1. If one knows the outcome of a medical test, what is the probability the answer is actually correct?
2. How can we correctly update our prior estimates on the probabilities of various events based on new information?
3. What degree of social distancing is needed from different parts of the population is needed in order to change the extinguish a pandemic? How can people gauge their own success in achieving this?
4. How do mathematical models of an epidemic actually work?
5. What is the physics behind person-to-person transmission of various kinds of diseases? What does this say about how to avoid such transmission?

### Texts:

1. On Bullshit by Harry Frankfurt, Princeton University Press, 2005. ISBN 0-691-12294-6. This book is available from Amazon.

This book gives a careful philosophical analysis of bullshit. The main distinction Frankfurt draws between lying and bullshit is that liars know the truth and are concerned that their listeners believe something false. Bullshitters are much less concerned with the truth value of what they are saying, or that their listeners literally believe them. They are instead focused on bringing about some other reaction in their listeners, e.g. that the listener will support them in some way. This book has many useful insights, and a good college education should include developing the ability to recognize and classify bullshit. Developing a mathematical theory to go along with Frankfurt's philosophical approach is a main goal of this course. In particular, mathematical game theory will help answer Frankfurt's question about why there is so much bullshit in our culture.

2. How math can save your life by James Stein, John Wiley and Sons, 2010. ISBN 978-0-470-43775-9. This book is available from Amazon.

Stein's book gives a better introduction to game theory than many textbooks, and it is written in a far more interesting way. The book includes many amusing topics, and is an excellent example of how with a little imagination one can view many real life situations in a mathematical way.

3. For All Practical Purposes W. H. Freeman, U.S.A.. ISBN: 1-4292-0900-3 ISBN-13: 978-1-429-20900-7.

This book is available: from Amazon It's not necessary to obtain access to the online materials connected with this book. As far as I can tell, the later editions of the book do not really add value, and cost much more.

4. Probability and Statistics 4th Edition Addison Wesley, U.S.A., ISBN: 978-0-321-50046-5. Authors: Morris H. DeGroot and Mark J. Schervish

This book gives an exceptionally clear description of basic probability theory and statistics. I recommend googling "deGroot statistics" in order to find various options for obtaining this book.

### Syllabus:

In the first part of the course we will study half-truths using mathematical, philosophical and empirical perspectives. The mathematics needed involves the connection between game theory and linear programming as well as methods for solving linear programming problems. The course will involve developing and analyzing mathematical models and constructing rigorous mathematical proofs. Because the course will involve the use of vectors in three dimensional space and some linear algebra, math 114 is a prerequisite.

The second part of the course will concerns probability theory and differential equations relating to the covid-19 epidemic.

### Electronic and web resources:

We will be using several different kinds of software to talk about course material, especially in view of the fact that the course will have to go entirely online after spring break.
1. Before class, please look a the video that will be posted for the lecture that day on the Course Schedule page. It will be very helpful if you note down any questions you have about the video before we meet online to discuss it.
2. The main tool we will be using for online classes is Zoom. You can obtain a free copy of this by clicking on this link and downloading the appropriate version for your browser and-or phone. We will be meeting in two groups on Tuesdays and Thursdays. The first group consists of all people in class whose last names begin with Aa through Ol. I will send an e-mail invitation to the first group a little before 1:30 p.m., and we will discuss the day's topics till a little before 2:15. I will then send an e-mail to the second group consisting of people whose last names begin with Or through Zz. I will send an invitation to the second group a little before 2:15 p.m. and we will continue through 3:00 p.m..
3. A backup application we will use is Skype in the event that there are problems with Zoom.

### Office hours:

By appointment and by Zoom and Skype in the evenings.

### How to make attending lectures efficient:

Before each lecture, check the current homework and lecture schedule. This will contain readings for each day as well as videos about the content to be discussed in class. There will also be links to homework problems.

### Homework:

Each homework will have a due date. You will need to send your homework directly to the grader for the course, Hao Zhang (zhangphy@sas.upenn.edu). You can do this by either typing your homework, writing it out on paper and sending a picture, or scanning it and sending a scan. Hao will send your homework back to you by e-mail. We will discuss the homework during our online sessions, and I would encourage you to discuss it with other students as long as you write up your work yourself. A good procedure is to try the work first on your own and then go over it with others.

### Exams:

Because of covid-19, the mid-term exam given on March 3 will be the only exam given in the course. I'd originally planned to have a writing project take the place of a final exam. Because of the difficulty of groups of people getting together to work on such projects, we will instead move to having the rest of the course based on homework assignments.

### Getting help:

You are very welcome to arrange a time to meet with me online to discuss the course.