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Natural and Social Sciences

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Earth Sciences
Date: 
Monday, April 1, 2013
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Social networks pervade our social and economic lives.   They play a central role in the transmission of information about job opportunities and are critical to the trade of many goods and services. They are important in determining which products we buy, which languages we speak, how we vote, as well as whether or not we decide to become criminals, how much education we obtain, and our likelihood of succeeding professionally.   The countless ways in which network structures affect our well-being make it critical to understand how social network structures impact behavior, which network structures are likely to emerge in a society, and why we organize ourselves as we do.  This course provides an overview and synthesis of research on social and economic networks, drawing on studies by sociologists, economists, computer scientists, physicists, and mathematicians.
 
The course begins with some empirical background on social and economic networks, and an overview of concepts used to describe and measure networks.   Next, we will cover a set of models of how networks form, including random network models as well as strategic formation models, and some hybrids.   We will then discuss a series of models of how networks impact behavior, including contagion, diffusion, learning, and peer influences.

Course Syllabus

  • Week 1: Introduction, Empirical Background and Definitions
Examples of Social Networks and their Impact, Definitions, Measures and Properties: Degrees, Diameters, Small Worlds, Weak and Strong Ties, Degree Distributions

  • Week 2: Background, Definitions, and Measures Continued
Homophily, Dynamics,  Centrality Measures: Degree, Betweenness, Closeness, Eigenvector, and Katz-Bonacich. Erdos and Renyi Random Networks: Thresholds and Phase Transitions,

  • Week 3: Random Networks 
Poisson Random Networks, Exponential Random Graph Models, Growing Random Networks, Preferential Attachment and Power Laws, Hybrid models of Network Formation

  • Week 4:   Strategic Network Formation 
Game Theoretic Modeling of Network Formation, The Connections Model, The Conflict between Incentives and Efficiency, Dynamics, Directed Networks, Hybrid Models of Choice and Chance
 
  • Week 5:  Diffusion on Networks. 
Empirical Background, The Bass Model, Random Network Models of Contagion, The SIS model, Fitting a Simulated Model to Data

  • Week 6:  Learning on Networks. 
Bayesian Learning on Networks, The DeGroot Model of Learning on a Network, Convergence of Beliefs, The Wisdom of Crowds, How Influence depends on Network Position.

  • Week 7: Games on Networks. 
Network Games, Peer Influences:  Strategic Complements and Substitutes, the Relation between Network Structure and Behavior, A Linear Quadratic Game, Repeated Interactions and Network Structures.

Recommended Background

The course has some basic prerequisites in mathematics and statistics.  For example, it will be assumed that students are comfortable with basic concepts from linear algebra (e.g., matrix multiplication), probability theory (e.g., probability distributions, expected values, Bayes' rule), and statistics (e.g., hypothesis testing), and some light calculus (e.g., differentiation and integration).  Beyond those concepts, the course will be self-contained.

Suggested Readings

The course is self-contained, so that all the definitions and concepts you need to solve the problem sets and final are contained in the video lectures.  Much of the material for the course is covered in a text: Matthew O. Jackson  Social and Economic Networks, Princeton University Press (Here are Princeton University Press and Amazon pages for the book).  The text is optional and not required for the course.  Additional background readings, including research articles and several surveys on some of the topics covered in the course can be found on my web page.

Course Format

The course will run for eight weeks.  Each week there will be video lectures available, as well as a standalone problem set and some occasional data exercises, and there will be a final exam at the end of the course for those who wish to earn a course certificate.  

 

FAQ: 

Will I get a Statement of Accomplishment after completing this class?

Yes. Students who successfully complete the class will receive a Statement of Accomplishment signed by the instructor.

Economic Networks diagram

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Date: 
Monday, April 8, 2013
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In this course we will seek to “understand Einstein,” especially focusing on the special theory of relativity that Albert Einstein, as a 26-year-old patent clerk, introduced in his so-called “miracle year” of 1905. Our goal will be to go behind the myth-making and beyond the popularized presentations of relativity in order to gain a deeper understanding of both Einstein the person and the concepts, predictions, and strange paradoxes of his theory. Some of the questions we will address include: How did Einstein come up with his ideas? What was the nature of his genius? What is the meaning of relativity? What’s “special” about the special theory of relativity? Why did the theory initially seem to be dead on arrival? What does it mean to say that time is the “fourth dimension”? Can time actually run more slowly for one person than another, and the size of things change depending on their velocity? Is time travel possible, and if so, how? Why can’t things travel faster than the speed of light? Is it possible to travel to the center of the galaxy and return in one lifetime? Is there any evidence that definitively confirms the theory, or is it mainly speculation? Why didn’t Einstein win the Nobel Prize for the theory of relativity? 

Students may choose one of three approaches to the course: a more quantitative approach, a more qualitative approach, or an auditing approach. The more quantitative approach will include weekly problem sets, while the more qualitative approach will include a creative project relating to the young Einstein and/or the special theory of relativity.
 

Course Syllabus

Week One (Einstein in Context): Einstein quotes of the week; a thought experiment involving relativity; physics and Einstein circa 1900.

Week Two (Events, Clocks, and Reference Frames): Einstein quotes of the week; synchronizing clocks; the famous June 1905 paper; thinking more deeply about events and observers; understanding inertial frames of reference; spacetime diagrams; the Galilean transformation; Einstein's starting point: the two postulates.

Week Three (Ethereal Problems and Solutions): Einstein quotes of the week; a few words about waves; the luminiferous ether; the Michelson-Morley experiment vs. stellar aberration; how do you solve a problem like the ether?; the solutions of Fitzgerald, Lorentz, Poincare, and Einstein.

Week Four (The Weirdness Begins): Einstein quotes of the week; the light constancy principle; time and length are suspect; what isn't suspect; exploring the Lorentz factor; the miracle of the muon.

Week Five (Spacetime Switching): Einstein quotes of the week; the Lorentz transformation; leading clocks lag; the ultimate speed limit.

Week Six (Breaking the Spacetime Speed Limit?): Einstein quotes of the week; spacetime diagrams revisited; regions of spacetime; cause and effect, or vice versa?; faster than light paradoxes.

Week Seven (Paradoxes to Ponder): Einstein quotes of the week; the pole-in-the-barn paradox; the spaceships-on-a-rope paradox; how length contraction actually works; the twin paradox.

Week Eight (To the Center of the Galaxy and Back): Einstein quotes of the week; traveling the galaxy in one lifetime; the reception of relativity; Einstein's Nobel Prize and the nature of genius; relativity beyond science.

Recommended Background

No prior knowledge is required. Anyone who is willing to engage with the material is welcome. (For students choosing the more quantitative approach, a familiarity with basic algebra will be helpful. But a brief math review will be provided.)

Suggested Readings

Although the course is designed to be self-contained, it is recommended (but not required) that you read the following profile: "Young Einstein: From the Doxerl Affair to the Miracle Year," by L. Randles Lagerstrom, available for US$2.99 from Amazon Direct Publishing (http://www.amazon.com/dp/B00BKKHS4U). You may also download the free software for viewing it here:http://www.amazon.com/gp/feature.html?ie=UTF8&docId=1000493771. (Versions are available for PCs, Macs, tablets, and smart phones.)

Course Format

Students may choose one of three approaches to the course: a more quantitative approach, a more qualitative approach, or an auditing approach. The more quantitative approach will include weekly problem sets, while the more qualitative approach will include a creative project relating to the young Einstein and/or the special theory of relativity. (Students who choose the quantitative approach may also do a creative project if they wish.)

The more quantitative approach is designed for those students who desire the deepest understanding of the special theory of relativity (within the introductory context of this course). Although one can gain a good understanding of the theory via a qualitative approach, the theory is ultimately a mathematical theory. The mathematics required, however, is not advanced. A familiarity with basic algebra will suffice. (For those whose knowledge is rusty, a review of the math needed is provided in a video clip.) The primary assignments for students who take this approach will be to watch lecture videos each week, take an assessment quiz for each video, take a weekly review quiz, and work on weekly problem sets.

The more qualitative approach is designed for those students who desire a deeper understanding of Einstein and the special theory of relativity, focusing on the concepts and results. The primary assignments for students who take this approach will be to watch lecture videos each week, take an assessment quiz for each video, and take a weekly review quiz. (Though the videos will cover quantitative aspects of the theory, the quizzes will focus on the concepts and results.) Students will also complete a creative project relating to the young Einstein and/or the special theory of relativity (e.g., a video, poem, musical piece, artwork, animation, etc.). The creative project may be instructional, humorous, serious, or dramatic, or some combination thereof. Further guidelines will be given in a later handout.

The auditing approach is designed for those students who want to learn more about Einstein and the special theory of relativity, but may not want to complete all the assignments in one of the other approaches.

 

FAQ: 
  • Will I get a Statement of Accomplishment after completing this class?

    Yes. Students who successfully complete the class will receive a Statement of Accomplishment signed by the instructor.

  • What resources will I need for this class?

    For this course, all you need is an Internet connection and the willingness to think.

  • What is the coolest thing I'll learn if I take this class? Learning how an unknown patent clerk came up with the special theory of relativity is certainly a fascinating story. And there are many cool things we will learn that come out of the theory itself, such as that one person can age significantly more slowly than another, that it's possible to travel to the center of the galaxy and back in one lifetime, and that time travel into the future is possible. But perhaps the coolest thing is simply to learn more about, in Einstein's words, "the mystery ... of the marvelous structure of reality."
Instructor(s): 
Larry Randles Lagerstrom
Space-like background

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Date: 
Monday, March 4, 2013
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The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years.
 
Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.
 
The primary audience is first-year students at college or university who are thinking of majoring in mathematics or a mathematically-dependent subject, or high school seniors who have such a college career in mind. They will need mathematical thinking to succeed in their major. Because mathematical thinking is a valuable life skill, however, anyone over the age of 17 could benefit from taking the course. 

Course Syllabus

Instructor’s welcome and introduction
 1.  Introductory material
 2.  Analysis of language – the logical combinators
 3.  Analysis of language – implication
 4.  Analysis of language – equivalence
 5.  Analysis of language – quantifiers
 6.  Working with quantifiers
 7.  Proofs
 8.  Proofs involving quantifiers
 9.  Elements of number theory
10.  Beginning real analysis

Recommended Background

High school mathematics.

Suggested Readings

There is one reading assignment at the start, providing some motivational background.
 
There is a supplemental reading unit describing elementary set theory for students who are not familiar with the material.
 
There is a course textbook, Introduction to Mathematical Thinking, by Keith Devlin, available at low cost from Amazon’s Print on Demand service (CreateSpace), but it is not required in order to complete the course.

Course Format

The course starts on Monday September 17 and lasts for seven weeks, five weeks of lectures (two a week) followed by two weeks of monitored discussion and group work, including an open book final exam to be completed in week 6 and graded by a calibrated peer review system in week 7. In each of weeks 2 through 6, there will be a separate tutorial session where the instructor will demonstrate solutions to some of the assignment problems from the previous week.

 

 

FAQ: 
  • Will I get a certificate after completing this class?

    The course does not carry Stanford credit. If you finish the course, you will get a Certificate of Completion, and for those who do well on the coursework and the final exam the certificate will indicate Completion with Distinction.

  • What are the assignments for this class?

    At the end of each lecture, you will be given an assignment (as a downloadable PDF file, released at the same time as the lecture) that is intended to guide understanding of what you have learned. Worked solutions to problems from the two weekly assignments will be described the following Wednesday (so in weeks 2 through 6) in a video tutorial session given by the instructor.

    Using the worked solutions as guidance, together with input from other students, you will self-grade your assignment work for correctness. The assignments are for understanding and development, not for grade points. You are strongly encouraged to discuss your work with others before, during, and after the self-grading process. These assignments (and the self-grading) are the real heart of the course. The only way to learn how to think mathematically is to keep trying to do so, comparing your performance to that of an expert and discussing the issues with fellow students and – as far as possible – with “course tutors” who will self-identify themselves as such in the questionnaire at the start of the course.

  • Who is a tutor for this course?

    A designation of “tutor” will be assigned to individuals who indicate (in the questionnaire at the start of the course) that they are familiar with the course contents or else have direct access to someone who is (such as being a current students in a similar class at a physical college or university). Tutors will be so designated in their on-line identity, so others will recognize them. We will also ask them if they are willing to monitor the online forum discussions and jump in if they see an individual or group who has got something wrong or otherwise needs help.

  • Is there a final exam for this course?

    At the start of week 6, you will be given an open-book exam to be completed by the end of the week. Completed exams will have to be uploaded as either images (or scanned PDFs) though if you are sufficiently familiar with TeX you have an option of keyboard entry on the site. The exam will be graded during week 7 by a calibrated peer review system. The exam will be based on material covered in the first 8 lectures, but completion of lectures 9 and 10 and their associated assignments (which look at some examples of the notions developed in the earlier lectures) will likely improve your performance on the exam.

  • How is this course graded?

    There are two final grades: “completion” and “completion with distinction”. Completion requires viewing all the lectures and completing all the quizzes (both in-lecture “progress quizzes” and weekly “credit quizzes”). Distinction depends on the scores in the weekly credit quizzes and the result of the final exam.


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