Math 210 - Spring 2017

Instructor: Ted Chinburg

Lectures MWF 12-1, 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.

Math. Dept. Undergraduate Program Information

Announcements as of 1/11/17

Current homework and lecture schedule

Some Possible Term Projects

Homework

  • Homework assignment 1 (due Jan. 25).
  • Homework assignment 2 (due Feb. 8).
  • Homework assignment 3 (due Feb. 24).
  • Homework assignment 4 (due March 17).
  • Homework assignment 5 (due April 7).

    Extra Credit Problems (See also the regular homework assignments)

    Course Guide

    Course Goals:

    This course will 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.

    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.

    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 next part of the course will have to do with information theory, thermodynamics and the media. Information theory was originally developed to optimize digital communication. Shannon entropy, for instance, measures the expected number of binary bits needed to communicate per unit of time, given the probabilities of the different messages which might be sent. This has become a new tool in understanding thermodynamics and processes which increase entropy, e.g. in the theory of evolution. We will explore some consequences of this to the media, politics, tweets and alternative news sources.

    A final topic we hope to be able to cover in the course concerns dynamical systems and zombie epidemic models. Using the stability theory of differential equations we will build some models of how populations with different views interact over time. We will apply this theory to study zombie ideas, these being notions which persist over time despite being repeatedly debunked.

    Electronic and web resources:

    We will be using several different kinds of software to talk about course material. If you have time, it would be a good idea to try out some of the software below before we use it in class, if you don't already use it on a regular basis. In some cases, I would appreciate it if you could send me the information I will need to contact you, as described below.
    1. We'll use Skype during online office hours as well as during course podcasts. It's possible to carry on a conference call with 24 people on Skype, and we have 22 class members at the moment. So we can in fact have a conference call which includes everyone in class. Please send an e-mail to me at ted@math.upenn.edu with your Skype name so that I can put you on conference calls. If you think there may be times when it would be more convenient to reach you by phone, please also send a phone number I can use.
    2. From time to time, I will put both streaming and downloading video on the web. For example, if I have to be out of town for a particular class, I will put a video on the web and I will run a simultaneous Skype conference at our regular class time for a discussion of the video as people watch this. We can experiment with the chat function on Skype, as well as with periodic pauses of the video for discussions.

    Office hours:

    By appointment and by Skype in the evenings.

    How to make attending lectures efficient:

    Before each lecture, check the current homework and lecture schedule, and read the appropriate parts of the text. After each lecture, you should review your lecture notes, reread the corresponding sections of the book and solve related homework problems.

    Homework:

    Each homework will have a due date on which it will be collected. It will then be graded and returned. I will try to have a lead time of at least a week between the time homework is assigned and the time it is due. You are encouraged to get help with the homework, and work together on it. Just copying someone else's work of course does little good to anyone, but cooperative effort and discussion of problems can be very effective in learning mathematics. A good procedure is to try the work first on your own and then go over it with others. Each student must hand in their own homework.

    Exams:

    There will two exams in the course. The first will be on Friday, February10. This is a week before the official drop date (Feb. 17), so you will have feedback from the exam before the drop date. The second exam exam will be on Monday, April 3.
    A final writing project will take the place of a final exam.

    Writing project:

    During the semester, I will be posting suggestions about articles and mathematical papers you might find interesting. You'll eventually work with a group of other students on a project based on one of these papers or a topic you find yourself. Your group will make a presentation to the class about your project and also write a paper about this. This is a great opportunity for you to study a subject in more depth, and to try doing some research on your own!

    Getting help:

    You are very welcome to arrange a time to meet with me either in math department or online.

    Approximate Grading Weights:

  • 45% -- Homework
  • 15% -- Midterm exam Friday, Feb. 10, in class.
  • 15% - Midterm exam, Monday, April 3, in class.
  • 25% -- Writing project

    Here are some number theory links:

    A terrific link about the Golden Ratio and Fibonacci numbers!
    Euclid's Elements
    The Prime Page
    Survey article by Peter Shor on quantum computing
    Last updated: 1/8/17
    Send e-mail comments to: ted@math.upenn.edu