Princeton Sociology Summer Methods Camp 2020

The Princeton Sociology Summer Methods Camp gives incoming Sociology PhD students a running start at the beginning of their PhD program. The computational and statistical training provides necessary foundation for statistics and methods classes. We understand that participants come into the program with different backgrounds and experiences, and the Summer Methods Camp will be helpful for everyone, regardless of background.

This 2020 Summer Methods Camp will take place in several parts due to the COVID-19 pandemic. Math lessons will begin virtually August 3rd. Coding lessons will be either virtual or in-person (TBD) and will take place August 24th-25th and 28th. Liv Mann and Joe Sageman are this year’s graduate student instructors and Professor Brandon Stewart is faculty advisor.

Learning objectives

The Methods Camp is designed to give you training in both math and computing. In math, you will receive training in three main areas: calculus, probability, and matrix algebra. In computing, you will receive training in three main areas: data wrangling, iteration, and visualization.

At the end of the Methods Camp, students will be able to:

  • Start the semester excited and ready to learn new methods
  • Explain in words and pictures what is a derivative, what is an integral, and how derivatives are useful for optimization.
  • Define probabilities in sets, perform basic set operations, calculate conditional probabilities, and use Bayes rule.
  • Perform matrix addition, subtraction, multiplication, and inversion.
  • Combine the 5 dplyr verbs, join data sets, and convert between long and wide formats
  • Use loops, purrr, and functions to avoid repeating yourself
  • Make simple graphs in ggplot2, write RMarkdown documents, and write basic equation in LaTeX

Pre-arrival

Reading Assignment

The textbook we will use for Methods Camp is Essential Mathematics for Political and Social Research by Jeff Gill. You are not expected to master the topics covered in the readings by the time you arrive at camp! These readings and the summer assignments are meant as a first introduction to what we’ll be covering during the camp itself. If you find yourself struggling with a topic, reach out to us!

Chapter 1: The Basics

This chapter introduces you to some of the basic notation you will see used during camp and in classes. It also reviews the concepts of indexing, functions, polynomial functions, exponents, and logs. Reviewing the notation will be helpful to all students. If you are comfortable with the other concepts, this chapter shouldn’t take too much of your time.

Chapter 3: Linear Algebra & Chapter 4: Linear Algebra Continued

These chapters cover vector and matrix math.

Chapter 3 reviews math with vectors (addition, subtraction, different forms of multiplication), vector norms, types of matrices, math with matrices, and other matrix manipulation. The examples in this chapter are helpful for understanding the usefulness of certain concepts. Section 3.6: Advanced Topics, is challenging. Read it at least once, but don’t spend too much time on it.

Chapter 4 is about the theoretical and abstract properties of vectors and matrices. If you find these topics challenging, take your time and really read the material line by line. Don’t devote too much time to sections 4.5, 4.8, and 4.9, but make sure to take your time with section 4.6: Matrix Inversion.

Chapter 5: Elementary Scalar Calculus & Chapter 6: Additional Topics in Scalar and Vector Calculus

These chapters cover calculus concepts.

Chapter 5 introduces basic calculus concepts. If you are comfortable with the concepts of limits, derivatives and rates of change, taking derivatives, L’Hospital’s Rule, Rolle’s Theorem and the Mean Value Theorem, definite and indefinite integrals, and finding indefinite integrals, you may be able to skim this chapter. However, understanding these basics will be important for your stats courses.

Chapter 6 covers partial derivatives, maxima and minima, root-finding, multi-dimensional integrals, finite and infinite series, and calculus with vectors and matrices. Sections 6.2, 6.3, 6.4, and 6.6 are particularly important. Sections 6.5, 6.7, and 6.8 may be more challenging.

Chapter 7: Probability Theory

This chapter covers probability theory, which will be a major focus of the early part of your fall statistics course. Pay special attention to sections 7.5, 7.6, 7.7, and 7.8. Overall this section might not be challenging, but I recommend taking your time with it. The more comfortable you are with probability theory, the better!

Coding Assignment

In order to prepare you for the coding portion of the summer assignment and work we will be doing during the camp, we are asking you to complete the following RStudio Primers.

  • The Basics - compete all sub-modules.

  • Work With data - complete all sub-modules.

  • Visualize Data - complete Exploratory Data Analysis and Scatterplots sub-modules, browse others.

  • Tidy Your Data - browse these; we will cover this material in the camp so it would be good to be familiar with it, but you won’t need it for the summer assignment.

  • Iterate - complete Introduction to Iteration.

  • Write Functions - complete Function Basics and How to Write a Function, browse others.

Additional Resources

Math Resources

Coding Resources

Camp

Camp this year will consist of two components: online math lessons and coding lessons (either online or in person, TBD).

Math Lessons

Math lessons will begin on August 3rd 2020 and last for three weeks. The weekly schedule will be:

Monday: live lecture, to be recorded and posted to Slack for asynchronous access.

Wednesday: lecture worksheet due

Sunday: homework assignment due

We will release more detailed information about math lessons in July.

Coding Lessons

Coding lessons will be held August 24th-25th and August 28th. At this time we do not know if lessons will be held virtually or in-person. We will update you as we receive more information. Coding lesson schedule to be released in August.

Logistics

This section contains information on important dates and other logistical concerns.

Important Dates:

June 26th: Assignment 1 due

July 24th: Assignment 2 due

August 3rd: Math lessons begin

August 24th-25th, 28th: Coding lessons

Individual Check-ins:

Liv and Joe will be setting up individual Zoom check-ins at the end of June and in mid-July. We can accommodate time zone differences as needed.

Slack:

Our primary means of communication and your primary resource for answering questions will be the camp Slack. Please post questions publicly whenever possible, but you can also direct message Liv and Joe.

FAQs

  • Should I participate in the camp if I have no plans to do quantitative work beyond what’s required? Yes! The aim of the camp is to make all students feel comfortable approaching the statistics training in the first year of the program, which in turn, is a crucial foundation for the second year empirical paper and future work. Both of us are available over email over the summer and will be holding daily office hours during the camp itself, and we’re both happy to spend extra time working with anyone more nervous about the quantitative requirements in the program to make sure you feel comfortable about the pace of the camp and related assignments.

  • Should I participate in the camp if I am highly confident about everything math and programming-related? Yes! Quantitative training means different things at different places, and the department wants to make sure everyone is on the same page going into the statistics sequence so that time isn’t spent during the course reviewing foundational concepts. In addition, the camp will feature lunchtime workshops highlighting qualitative methodology in the department, which is a good chance to meet professors you may not know already and get a sense of the range of the department’s work.

  • How does this camp fit into the first-year statistics sequence? The purpose of the camp is so that you can hit the ground running in whatever statistics sequence you opt to take your first year– both in terms of foundational math concepts and computing in R.

About

The Sociology Summer Methods Camp began in 2016, and the materials that we currently use include contributions from many of the people who have taught and participated in the program. Here is a list of all the instructors:

  • 2016: Rebecca Johnson, Janet Xu (graduate students instructors) and Brandon Stewart (faculty advisor).
  • 2017: Janet Xu, Xinyi Duan (graduate student instructors) and Matthew Salganik (faculty adviser).
  • 2018: Xinyi Duan, Katie Donnelly (graduate student instructors) and Brandon Stewart (faculty adviser).
  • 2019: Katie Donnelly, Liv Mann (graduate student instructors) and Matthew Salganik (faculty adviser).
  • 2020: Liv Mann, Joe Sageman (graduate student instructors) and Brandon Stewart (faculty adviser).

We would also like to acknowledge the many other people who have shaped the material including: the instructional staff of the Math Camp for the Department of Politics at Princeton and the instructional staff of the Math Camp for the Department of Government at Harvard.

All of the teaching materials that we created are available under a Creative Commons-By license. You can find them on GitHub. Please feel free to use and improve them.