Yale University

**MATH 255:**Analysis I (Spring 2023)

Textbook: Rudin, Principles of Mathematical Analysis, ch. 1-7.

Introduction to Analysis. Properties of real numbers, limits, convergence of sequences and series. Power series, Taylor series, and the classical functions. Differentiation and Integration. Metric spaces. The course focuses on conceptual understanding. Familiarity with writing mathematical proofs is assumed, and is further developed in the course.

**MATH 30.04:**Evolutionary Game Theory and Applications (Spring 2022)**MATH 22:**Linear Algebra with Applications (Spring 2020)

Pioneered by John Maynard Smith and others, evolutionary game theory has become an important approach to studying a wide range of biological and social problems, such as microbial interactions and animal behavior. In evolutionary game dynamics, the fitness of individuals depends on the relative abundance of all individual types in the population, and higher-fitness individual types tend to increase in abundance. This course introduces basic concepts in evolutionary game theory, including evolutionarily stable strategies, replicator dynamics, finite populations, and games on networks, along with applications to social evolution, particularly to understanding human cooperation.

Textbook: Lay, Lay and McDonald, Linear Algebra and Its Applications.

This course presents the fundamental concepts and applications of linear algebra with emphasis on Euclidean space. Significant goals of the course are that the student develop the ability to perform meaningful computations and to write accurate proofs. Topics include bases, subspaces, dimension, determinants, characteristic polynomials, eigenvalues, eigenvectors, and especially matrix representations of linear transformations and change of basis. Applications may be drawn from areas such as optimization, statistics, biology, physics, and signal processing.

**S&DS 542**: Theory of Statistics (Spring 2024)**S&DS 612**: Linear Models (Fall 2023)**S&DS 538:**Probability and Statistics (Fall 2022)

Textbook: Rice, Mathematical Statistics and Data Analysis.

Principles of statistical analysis: maximum likelihood, sampling distributions, estimation, confidence intervals, tests of significance, regression, analysis of variance, and the method of least squares.

Textbook: Christensen, Plane Answers to Complex Questions.

The geometry of least squares; distribution theory for normal errors; regression, analysis of variance, and designed experiments; numerical algorithms (with particular reference to the R statistical language); alternatives to least squares.

Textbook: Chang, own course notes. Also Blitzstein and Hwang, Introduction to Probability.

Fundamental principles and techniques of probabilistic thinking, statistical modeling, and data analysis. Essentials of probability, including conditional probability, random variables, distributions, law of large numbers, central limit theorem, and Markov chains. Statistical inference with emphasis on the Bayesian approach: parameter estimation, likelihood, prior and posterior distributions, Bayesian inference using Markov chain Monte Carlo. Introduction to regression and linear models. Computers are used for calculations, simulations, and analysis of data.

**GOVT 19.01:**Applied Multivariate Data Analysis (Winter 2019)

This course introduces mathematical and statistical models in the social sciences beyond the level of bivariate regression. Topics to be covered include multivariate regression, selection bias, discrete choice, maximum likelihood models, multi-level modeling, and experiments. We will use use these models to study voter turnout, elections, bargaining in legislatures, public opinion, political tolerance, the causes and duration of wars, gender bias in employment, educational testing, poverty and income, and a host of other topics. Students will write a paper of original research using some of the methods covered in class.

**COSC 72/LING 48:**Accelerated Computational Linguistics [Python] (Winter 2022)**GEOG 50.03:**GIS Programming and Databases [SQL, Python, QGIS] (Summer 2021)**GOVT 83.21/QSS 30.03:**Experiments in Politics (Fall 2020)**QSS 17:**Data Visualization [R] (Spring 2020)**QSS 30.01:**Sports Analytics [R] (Fall 2019)**COSC 01:**Introduction to Programming and Computation [Python] (Fall 2018)

The study of human language from a computational perspective. This accelerated course has programming background equivalent to that provided by COSC 1 as a prerequisite. This course will survey formal models for representing linguistic objects, and statistical approaches to learning from natural language data. We will pay attention to the use of computational techniques to understand the structure of language, as well as practical engineering applications like speech recognition and machine translation. Students will implement simple algorithms for several key tasks in language processing and learning.

This course is an introduction to Python programming and database (SQL) programming and design for intermediate Geographic Information Systems (GIS) users. This course teaches students to design and write clearly structured programs in Python in the ArcGIS environment. Students will develop programs to manage geospatial data, perform geoprocessing analysis to solve spatial problems, and automate mapping and visualization tasks. This course emphasizes the challenges and uniqueness of spatial data organization from specific database models to national spatial data infrastructures. Students gain theoretical and practical experience in designing, implementing, and managing geo-relational and object-relational databases.

This class is a lab-style seminar in which we will design, field, and analyze an experimental study. Our goal is to publish a scholarly article about our findings in a peer-reviewed journal of political science - an ambitious project that will require a substantial commitment from each student. Flexibility will also be essential since the course will evolve during the semester based on the needs of the project.

Big data are everywhere – in government, academic research, media, business, and everyday life. To tell the stories hidden behind blizzards of data, effective visualization is critical. This course primarily teaches R, a free software environment for statistical computing and graphics, which is widely regarded as one of the most versatile and flexible tools for data visualization and, more broadly, data science. Students completing the course will know how to “wrangle” and visualize data critical to their scientific endeavors.

Sports organizations are becoming increasingly aware that analytics are an important component of team success. This course will introduce students to various statistical techniques used in modern sports analysis and in particular will teach participants how statistical methods can be used to analyze game outcomes and evaluate players and strategies. The course will include lectures, in-class exercises using the R statistical computing environment, and guest speakers from the sports industry.

This course introduces computational concepts that are fundamental to computer science and are useful for the sciences, social sciences, engineering, and digital arts. Students will write their own interactive programs to analyze data, process text, draw graphics, manipulate images, and simulate physical systems. Problem decomposition, program efficiency, and good programming style are emphasized throughout the course. No prior programming experience is assumed.

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