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Summer Session Course List

Summer 2018

Course Numbers:
        0001 - 0099: undergraduate credit only
        0100 - 0199: undergraduate or graduate
        0200 & Up: strictly graduate

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Title:   Mathematics of Poverty & Inequality (Online)      

Course Number:      MATH 0010A   
Room: Online

Course Description:

In 2010, there were 388 billionaires in the world whose combined wealth exceeded that of half the earth's population. Today, that number is 62, and all indications are that it continues to decrease.  The enormous concentration of wealth and the unchecked growth of inequality have emerged as crucial social issues of our time. To what extent can mathematics help shed light on this problem? We will begin with definitions of money, wealth and income (concepts that are often confused in the popular literature) so that we can speak precisely about this subject. We will briefly survey historical thought on this subject from mathematical, economic and philosophical perspectives. We will then discuss how wealth distributions are quantified, and how inequality is measured. This will lead us to study the theory of distributions and density functions, histograms and kernel estimation. In turn, this will enable us to understand the history of empirical studies of wealth distribution, including the important observations of Pareto, Lorenz, Gini, Gibrat and others. Along the way, we will learn about the Lorenz-Pareto, Gini, Atkinson, and Foster-Greer-Thorbecke indices, and upward mobility measures.
Next we turn our attention to various ways of understanding wealth concentration. This will lead us to a study of random walks, the Gambler's Ruin problem, an introduction to Markov processes, and the concept of stochastic dominance. From this viewpoint, we will study pyramid and Ponzi schemes, both from a mathematical and an ethical perspective.
The centerpiece of this course will be an introduction to dynamical models, especially agent- based models, with particular emphasis on asset-exchange models, especially the Yard-Sale Model.  We will show how such simple models of agent transactions at the microeconomic level can be used to derive dynamical equations for the wealth distribution. Along the way, we will learn about strong and weak forms of conservation laws, multi-agent distributions and density functions, the random-agent approximation leading to the Boltzmann equation, and the small-transaction approximation leading to the Fokker-Planck equation for the wealth distribution. We will study the phenomenology exhibited by these equations, including a phase transition discovered by Bouchaud and Mezard in 2000 called wealth condensation, which is thought to explain the origin of oligarchy.
The course will finish with a litany of state-of-the-art results and outstanding problems, with particular emphasis on that of reconciling asset-exchange models with neoclassical microeconomics.  Toward this end, we will review the latter subject, beginning with the notion of utility as understood by Bentham and Walras, introducing the notion of Pareto efficiency, and leading up to a mathematical description of General Equilibrium theory. We will review some of the assumptions built into this line of thinking, and some of the known problems with those assumptions, including asymmetric information, irrational expectations, behavioral economic effects, and stochasticity. In particular, we will highlight some of Akerlof's recent work on asymmetric information.
Some description will be given of available databases for the study of wealth distribution, including that maintained by the Federal Reserve and the U.S. Census Bureau, as well as international data available, for example from the World's Top Incomes Database
This is an online course that will not meet on campus. Most course activities and interactions will occur asynchronously and online through TRUNK, Tufts' learning management system. You can take this course from anywhere as long as you have a reliable internet connection (broadband highly recommended). Online courses are held to the same academic standards as campus-based courses and students can expect high levels of interaction with faculty and classmates.
Online courses at Tufts are not self-paced, however they typically offer much more flexibility for students. Typically, course content is organized in a weekly structure, so students will be expected to login and participate regularly. However students can generally set their own schedule within each week as long as assignments and activities are completed on time.
All online courses will have regular instructor office hours where students have an opportunity to speak to their teacher, via telephone or web conferencing. Some courses may require a live session or two where students are expected to login to a web conferencing site at a certain date and time.
Some online courses require proctored exams. Students in the area can come to the Medford campus to take these exams at a specific date and time. Students taking the course truly from a distance will need to identify an acceptable proctor and go through Summer Session's proctor verification process.

Instructor: Bruce Boghosian           Instructor Website

Offered in: First session
Class Dates: Wednesday, May 23, 2018 to Friday, Jun 29, 2018
Day(s): Online           Online Session Times: Online
Credit Value: 3          Call Number:      50094

Audit Enroll Option: No                     
Status: Open


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