# Courses for All QTM Majors

No matter what QTM major program you pursue [QSS, AMS, PPA, or BBA + QSS], the QTM coursework is identical.*

You are required to take **Calc I** [or have AP/transfer credit] plus a** minimum of 9 quantitative courses** offered through the Institute for Quantitative Theory and Methods. Each major differentiates itself by its accompanying coursework, which you may find on each of our major pages.

Please note, students must meet the minimum GPA requirement of 2.0 to graduate with any major or minor from the department.

**All classes counting toward the degree must be taken for a letter grade.**

***with one exception. **AMS majors are required to take MATH 211 & 221 instead of QTM 120; MATH 361, & 362 instead of QTM 210. **AMS majors may request permission from the QTM department to co-enroll in MATH 362 and QTM 220 in the same semester**.

## Calculus I

## QTM 110: Introduction to Scientific Methods

This course is designed to introduce students to the style of analytic thinking required for research in the sciences and the concepts and procedures used in the conduct of empirical research. In short, this course teaches a set of skills that are essential for both understanding the research you will encounter in substantive classes, and being able to produce high-quality original research of your own. Beyond simply learning how to be a more critical participant in the academic research community, you will also be better-prepared for career opportunities using statistical tools and the products thereof.

Students will be introduced to the basic toolkit of researchers which includes sampling, hypothesis testing, Bayesian inference, regression, experiments, instrumental variables, differences in differences, and regression discontinuity. More importantly, students will learn the principles of critical thinking essential for careful and credible research.

**Prerequisites: None**

**GER: None**

**Credits: 3**

**Offering schedule: Fall, Spring**

## QTM 120: Math for Quantitative Sciences

This course is a mandatory course for all Quantitative Sciences majors. It is also a prerequisite for the more advanced course offerings in the major including Regression Analysis, Maximum Likelihood Estimation, Longitudinal Data Analysis as well as the game theory sequence. The goal of the course is to provide the necessary mathematical background for students to properly derive and implement common statistical modeling techniques employed in the sciences.

In the first half of the course we will cover core concepts in linear algebra. The second half of the course focuses on multivariable calculus. This course focuses on the computation skills necessary for quantitative research.

**Prerequisites: Calculus I or equivalent**

**GER: MQR**

**Credits: 4**

**Offering schedule: Fall, Spring**

## QTM 150: Intro to Statistical Computing I

This course provides an introduction to statistical computational tools for analyzing data. The material is selected to enable you to become proficient enough to actively implement the methods and tools in your scientific research. This will require you to practice the material outside of class.

By the end of the course, students should be able to 1) deal with complex and messy real data, 2) use graphics to explore and understand data, 3) gain familiarity with basic data collections, storage, and manipulation, and 4) fluently reshape data into the most convenient form for analysis or reporting.

**Prerequisites: None**

**GER: None**

**Credits: 1**

**Offering schedule: Fall, Spring**

## QTM 151: Intro to Statistical Computing II

This course provides a practicum of skills for data science and an introduction to how to do data science with R. The material is selected to enable you to get data into the most useful structure, transform it, visualize it, and model it. This will require you to practice the material outside of class.

By the end of the course, students should be able to (1) deal with complex and messy real data (2) use graphics to explore and understand data (3) gain familiarity with basic data manipulation, (4) fluently reshape data into the most convenient form for analysis, and (5) automate cleaning and analysis.

**Prerequisites: QTM 150**

**GER: None**

**Credits: 1**

**Offering schedule: Fall, Spring**

## QTM 210: Probability & Statistics

This course covers the structure of probability theory, which is the foundation of statistics, and provides many examples of the use of probabilistic reasoning. It discusses the most commonly encountered probability distributions, both discrete and continuous. The course considers random sampling from a population, and the distributions of some sample statistics. It deals with the problem of estimation: the process of using data to learn about the value of unknown parameters of a model. Finally, it discusses hypothesis testing: the use of data to confirm or reject hypotheses formed about the relationship among variables.

**Prerequisites: QTM 120**

**GER: MQR**

**Credits: 4**

**Offering schedule: Fall, Spring**

## QTM 220: Regression Analysis

This course covers basic techniques in quantitative research. It introduces students to widely used procedures for regression analysis for descriptive and causal inference, and provides intuitive, applied, and formal foundations for regression and more advanced methods treated later in the major course sequence. The first half of the course addresses the foundations of statistical hypothesis testing via linear regression models. This module of the course will provide the formal derivation of the ordinary least squares regression model as well as an overview of its practical implementation and the underlying modeling assumptions. The second module shifts focus to the implications of violating the assumptions of the OLS model including issues of omitted variable bias, multicollinearity, and heteroskedasticity. While the course will emphasize the mathematical foundations of these concepts, each topic will also cover the implementation of the relevant methods in the statistical computing program R.

**Prerequisites: QTM 150, QTM 210*, (starting Fall 2019, QTM 110)**

**GER: MQR**

**Credits: 4**

**Offering schedule: Fall, Spring**

***Students taking the alternative sequence for QTM 210 (MATH 361 & 362) may co-enroll in MATH 362 & QTM 220 with permission from the QTM department.**

## QTM Upper-Level Electives

**Prerequisites vary, ** but more than 50% of QTM's upper-level electives require QTM 220.

Refer to Course Atlas for this semester's upper-level elective offerings. QTM electives include 300- and 400-level lecture and seminar style courses (excluding QTM 398R, QTM 496, QTM 497, and QTM 499).

# QTM Upper-Level Electives

**Prerequisite(s):** QTM 110 or QTM 100

This course introduces the methods of rhetorical analysis and user experience design as a means of developing complex information for a variety of audiences, ranging from professional peers to the general public. Communication via prose, speech, visuals, and gestures springs from work in a variety of genres, which may include short research reports, informative and persuasive infographics, technical instructions, translations, and student-generated data sets. We will attend carefully to document design and explore especially the possibilities for developing narratives using quantitative data.

You will develop your work with an eye toward publishing it in an electronic portfolio (ePortfolio) using readily available, easy-to-use tools as part of the Domain of One's Own initiative. No prior technical knowledge or media-making experience is required.

**Prerequisite(s):** None

From the study of legislatures and courts to the design of electoral systems and regulation, game theory applications are far-ranging and have become one of the predominant means of modeling and evaluating social interaction in fields as diverse as economics, law, and biology. Game theory insights have also profoundly changed and expanded the use of auctions across industries; auctions and related mechanisms are used to sell online advertising, to allocate resources in the “sharing economy,” to assign contractors to suppliers, and to apportion spectrum to telecommunication companies. Game theorists working on market design have transformed the medical resident matching market, improved school choice procedures, and started novel markets for kidney exchange. Increasingly, firms are adopting game theory tools to improve not only their competitive position via their external relations with customers, competitors, and suppliers, but also their internal markets for resources and talent. This course provides a technical introduction to the non-cooperative theory of games and its various tools that analyze strategic interactions. Selected topics include normal and dynamic games, games of incomplete information and repeated games. Applications are drawn from a wide range of disciplines including business, economics, political science, biology, and sociology.

**Prerequisite(s):** QTM 220

This course introduces the workhorse of data analysis: multiple regression. Violations of conditions for valid inference of multiple regressions are demonstrated in the observational data and typical treatments are introduced accordingly. Specifically, the course devotes to endogeneity and heterogeneity problems in social science. We deal with endogeneity problem with instrumental variable methods and simultaneous system. For heterogeneity, we bring in the additional time dimension for panel data models. For all methods, finite sample and large sample properties are studied.

**Prerequisite(s):** QTM 220 or department permission

This course exposes students to popular languages for data analysis, important programming and computing concepts, and emphasizes good workflows for reproducible research. It teaches basic Python concepts and syntax. Students primarily write code in Jupyter/IPython notebooks. The class starts with essential computer literacy and shell commands, and finishes with topics such as Numpy for scientific computing, Pandas for data science, and cloud computing using notebooks on Amazon Web Services and Google Cloud Platform.

**Prerequisite(s):** QTM 220

This course provides students with a theoretical and practical basis for analyzing complex data sets that depend on time. Concepts introduced include detrending, autoregressive models, time series forecasting, hetereoscedastic models, multivariate time series analysis, causality, spectral analysis, and dimensionality reduction. Interspersed with explorations of the mathematical underpinnings of these concepts are data analysis practicums using R, providing context to the theoretical ideas that are introduced, as well as a final project that allows students to study a particular problem in depth. Students emerge from this class knowing how to approach noisy real-world data of this type, possessing a broadly-generalizable toolkit that spans disciplines from economics to astronomy to geology to medicine to ecology.

**Prerequisite(s):**

•* Why take this class?*

In many of the real data problems, the dependent variable may be count or categorical responses, such as the number of traffic accidents per day in a city, the number of trades in a time interval for a certain stock, whether a respondent has a depression symptom (“yes/ no”), how severe is their symptom (“none/ low/ moderate/ high”). For such data, the linear regression model is not appropriate. The generalized linear models are natural extensions of the linear regression model, designed to analyze count or categorical dependent variables.

•* What academic fields use the methods / skills in the elective?*

Generalized linear models are widely used in both academic field, such as biology, psychology, political science, finance, marketing, and many others.

•* Concrete examples of how to apply learned skills outside the classroom:*

These models are also standard quantitative tools in the industry, such as insurance, banking, marketing, information technology, and many others.

•* Any other perks?*

In addition, the students will be trained to implement the models in a popular statistical software R, solve real data problems, and write a statistical report.

**Prerequisite(s):** QTM 220

• *Why a student might want to take the elective*

This course provides you with a practical introduction to statistical methods for analyzing multivariate data that involve multiple response variables. The techniques covered have been routinely applied to the investigation of problems in the physical, social, and medical sciences. Specifically, you will learn the basics of and how to apply:

a) Data visualization techniques, b) Principal component analysis, c) Multidimensional scaling, d) Exploratory factor analysis, e) Confirmatory factor analysis, f) Cluster analysis, g) Confirmatory factor analysis, h) Structural equation modeling, i) Linear mixed-effects models

• *What academic fields use the methods / skills in the elective*

Many academic fields use the methods and skills studied in the course. Some examples are applied statistics, medicine and health, business and economics, psychology, biology, environmental studies, meteorology, sociology, education, geology, and sports.

• *Concrete examples of how to apply learned skills outside the classroom*

Students will be able to interpret 2D and 3D graphics and to prepare and use them in data mining and analysis. Students will be able to read and understand research literature and reports that employ the statistical techniques described above. Students will be able to formulate research questions and perform a data analysis to address them using the techniques described above.

• *Anything else that might attract students to their classes*

Students have the option to choose research articles and a data set of interests to them for reviews and data analysis. Students will develop practical data analysis and report writing skills. Students will explore and learn more about their research interests as well as those of their peers.

**Prerequisite(s):**

• *Why a student might want to take the elective*

Statistical learning refers to a set of tools for modeling and understanding complex datasets and making predictions. This subject is within an interdisciplinary field at the intersection of statistics and computer science, which develops statistical models and interweaves them with computational algorithms. The course will provide a first introduction to statistical learning and its core models and algorithms that are becoming increasingly popular in academic fields and industry.

• *What academic fields use the methods / skills in the elective*

In academic fields, such as genetics, neuroscience, political science, etc., statistical learning methods help to answer fundamental questions that previously would have been impossible, by extracting meaningful information from big data.

• *Concrete examples of how to apply learned skills outside the classroom*

In industry, they are the engines of new technologies, such as Internet search, speech recognition, computer vision, artificial intelligence, and advanced risk management methods in finance.

• *Anything else that might attract students to their classes*

In addition, students will be trained to implement the statistical learning methods using a popular statistical software R and gain experience on real data analysis.

**Prerequisite(s):** QTM 120, some knowledge of probability & statistics (e.g., AP Stats, QTM 210, MATH 362)

We will explore three topics in mathematics related to fairness. In the first part of the course, we will study that Apportionment Problem: how to fairly allocate N equally valuable resources to M entities of varying sizes, specifically in the context of assigning seats in a legislative body fairly among states or other political entities. Our second topic is Fair Division: the problem of dividing resources of varying worth among several equally deserving people so that each person believes they receive a fair share. Our third topic concerns Gerrymandering: the drawing up of political boundaries in order to give an unfair advantage in an election to one party or group. We will look at mathematical and statistical methods for detecting gerrymandering and methods for fairly drawing congressional districts

**Prerequisite(s):** QTM 120, some knowledge of probability & statistics (e.g., AP Stats, QTM 210, MATH 362)

This class is about the mathematics of Social Choice Theory, which is the theory of group decision-making. We will study voting methods mainly in the context of political elections and look at the properties of various methods. It also covers the problem of apportionment (dividing up resources fairly) in the context of apportionment of seats in the U.S. House of Representatives; and possibly other topics such as yes-no voting systems. The mathematics in this course is mainly logical deduction and general quantitative reasoning. We may use some probability, but note that there will be no use of statistics in this class. Using social choice theory as a framework, students learn approaches to modeling voting behavior based on winner selection and fair division.

**Prerequisite(s):** QTM 220

This course teaches theories and techniques commonly used in the practice of data science. The primary focus is on text analysis covering text parsing, language models, sequence estimation, vector space models and distributional semantics, as well as statistical approaches including cluster analysis and supervised learning. Modern topics such as cloud computing, big data analysis, and data visualization are also discussed.

Introductory courses on computer programming and probabilities & statistics are recommended asprerequisites for this course. All exercises assume Python programming. Students are expected to present their work on the final project in groups towards the end of the term.

**Prerequisite(s):** None

This course provides students with a rigorous introduction to the field of social choice theory. Social choice concerns the study of preference aggregation: most commonly, taking a collection of individuals with heterogeneous preferences as an input and then examining potential ways in which a collective, or social, preference is constructed. Our goal is to mathematically formalize and axiomatize the properties of different aggregation rules and to characterize rules that yield desirable outcomes. Students master various proof techniques as they work through the major results in this field (Arrow’s theorem, the Gibbard-Satterthwaite theorem, and the revelation principle, among many others), and learn how these results can be applied to a variety of fields in the social sciences. The course concludes with an introduction to mechanism design, which lies at the intersection of social choice and game theory.

**Prerequisite(s):** QTM 220

Interest in social network analysis has exploded in the past few years, partly due to the latest advancements in statistical modeling and the rapid availability of network data and partly due to the recognition that many analytical problems can be re-cast as a network problem. Aiming to examine social connections and interactions from structural perspectives, network analysis has become an essential method and tool for studying a variety of issues in social and natural sciences, such as friendship formation, peer influence, social inequality, career mobility, social marketing, organizational competition, economic development, political alliance, diffusion of innovations, contagion of health outcomes, and even protein interactions, to name only a few. This course covers the major methods to collect, represent, and analyze network data. Selected topics include centrality analysis, positional analysis, clustering analysis, the exponential random graph model for modeling network formations, the stochastic actor-oriented model for dynamic network analysis, meta network analysis, weighted network analysis, text network analysis, causal analysis of network effects, and social network-based predictions and interventions. Examples are drawn from a wide range of disciplines including business, economics, education, political science, public health, and sociology. Students learn hands-on skills to conduct their own research by using popular network packages in R such as “statnet” and “RSiena”.

**Prerequisite(s):** None

The course deals with new tools of data analysis and visualization, especially for text data (Natural Language Processing, NLP).

The course relies on the Stanford parser CoreNLP as the main NLP engine, but a number of other NLP tools will also be used (topic modeling with Mallet and Stanford Topic Modeling Toolbox, Word2Vec, vectors representations of words, shown to capture many linguistic regularities of a corpus, N-gram, and word co-occurrences). Through these tools, the course will show how to analyze large corpora of text. All NLP tools can be downloaded from the PC-ACE website (Program for Computer-Assisted Coding of Events, www.pc-ace.com).

The course will also show how to use different tools of data visualization, especially network graphs dealing with relationships between objects (social actors, concepts, or just words), both static and dynamic (changing with time), and spatial maps dealing with objects in space (and time, dynamic maps) through Geographic Information System (GIS) tools. We will focus on freeware software, from Gephi to Cytoscape, Palladio, Google Earth Pro, QGIS, Carto, TimeMapper, Google Fusion Tables.

**Prerequisite(s):** QTM 220

This course provides students with a rigorous introduction to the field of social choice theory. Social choice concerns the study of preference aggregation: most commonly, taking a collection of individuals with heterogeneous preferences as an input and then examining potential ways in which a collective, or social, preference is constructed. Our goal is to mathematically formalize and axiomatize the properties of different aggregation rules and to characterize rules that yield desirable outcomes. Students master various proof techniques as they work through the major results in this field (Arrow’s theorem, the Gibbard-Satterthwaite theorem, and the revelation principle, among many others), and learn how these results can be applied to a variety of fields in the social sciences. The course concludes with an introduction to mechanism design, which lies at the intersection of social choice and game theory.

**Prerequisite(s):** QTM 220

Experiments are a prominent instrument of inquiry in the natural and the social sciences. The first part of the course introduces the logic of experimentation and discusses various methodological issues in the design and analysis of experiments. Topics include randomization inference, blocking, non-compliance, attrition, interference, and heterogeneous treatment effects. The second part of the course builds on this foundation to discuss some practical issues and ethical considerations in designing and implementing experiments.

# Equivalent Elective Courses

These courses are not formally cross-listed as "QTM" courses, but they count as QTM electives**Prerequisite(s):** None

This course provides an introduction to the study and design of maps and the use of geographic information systems (GIS) as a problem-solving tool for geographic and spatial analysis. Course lectures will focus on fundamental concepts and the applications of GIS, data collection and processing, cartographic design techniques, and trends in geospatial technologies.

The Bureau of Labor Statistics has reported that GIS and geospatial skills are in high demand among employers. These skills are particularly important for students interested in pursuing careers in academia, in the government, or in the private sector. Many local and federal governmental agencies, such as the Department of Defense, hire employees with GIS skills. Some large consulting firms also require employees to have mapping and GIS skills. Universities tend to be one of the larger employers of those with GIS skills, as a variety of research projects require employees who can use the program. In addition, many private firms also look to hire people with these skills, including real estate, surveying, oil, and electric companies. Exposure to GIS and cartography programs can be helpful career training for interested students.

**Prerequisite(s):** PHYS 151*

Computation is one of the pillars of modern science, in addition to experiment and theory. In this course, various computational modeling methods will be introduced to study specific examples derived from physical, biological, chemical, and social systems. We study how one makes a model, implements it in computer code, and learns from it. We focus on modeling deterministic dynamics, dynamics with randomness, on the comparison of mathematical models to data, and, at the end, on high performance computing.

· *Why a student might want to take the class*

As was said by the great Leonardo, "He who loves practice without theory is like the sailor who boards a ship without a rudder and compass and never knows where he may cast.” Theory nowadays is often equivalent to mathematical models, which one solves using computers. This course will teach you how to formulate mathematical models and how to solve them using computers. Along the way, you will learn Python — a flexible computer language that you will be able to use in other applications as well.

· *What academic fields use the methods / skills taught in this class*

Essentially any academic field that does mathematical modeling uses methods and skills developed by this elective course.

· E*xamples of how to apply learned skills outside the classroom*

We will study examples in epidemiological modeling (relevant to a lot of CDC work), in chemical physics (will be of relevance to those developing new materials in chemistry and physics), or physiology (of relevance to those of you who will become doctors or biomedical researchers).

You cannot be an effective researcher nowadays without knowing how to solve problems on a computer — and this class will give you these skills.

***PHYS 151 requirement may be waived if the student has taken QTM 120, 210, 220, and one class that exposes him/her to how mathematics is used to represent natural phenomena (like Game Theory).**

**Prerequisite(s):** BIOL 141/142L; Math 112 or 116 (or equivalent)

Application of basic principles of population genetics and population biology to the study of infectious diseases, aging, and cancer.

Infectious diseases as well as aging and cancer will be treated as population dynamic and evolutionary phenomena. Primary consideration will be given to the following topics: (1) the within-host population and evolutionary dynamics of microparasite (viruses, bacteria,and protozoa) infections, the immune defenses, and the treatment of these infections with antibiotics and other chemotherapeutic agents; (2) the epidemiology of infectious diseases and their control by vaccination, prophylaxis, and chemotherapy; (3) the evolution of parasites and their virulence (why do parasites harm their hosts?); (4) the population biology and evolution of cancers and the evolution of senescence.

The course will include lectures, discussion, and group project work which will involve hands-on computer simulations and modeling.