Courses
Students are required to take a minimum of seven to nine* quantitative courses as a part of the major in Quantitative Sciences, all of which are offered through the Institute for Quantitative Theory and Methods. Each student will complete the four core QSS courses described below. After the four core courses are completed, the student will then complete three QTM 385 special topics courses or upper-level electives to fulfill the quantitative side of the QSS major. Additional elective courses may need to be taken to fulfill 50 credit hours for the QSS degree. QSS or substantive field courses can constitute additional electives.
***Any student who declares QSS Fall 2017 and after is required to take QTM 150 and QTM 151***
*If you declared before Fall 2017, you will take a minimum of seven quantitative courses. If you declared Fall 2017 and after, you will take a minimum of nine quantitative courses (core coursework + QTM 150/151 + QSS electives)
Course Atlas
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, SP18
NOTE: This course is not QTM 100, nor is it a sequence course related to QTM 100. QTM 100 is a basic statistics course unrelated to the QSS major.
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 and 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
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: 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 and 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 120, QTM 210
GER: MQR
Credits: 4
Offering schedule: Fall, SP18
Electives
Electives |
Prerequisites |
Description |
QSS Electives |
Prerequisites: Varies, but typicall all four core courses (QTM 110, QTM 120, QTM 210, QTM 220), unless otherwise denoted | Refer to Course Atlas for current upper-level elective listings. QSS major electives include 300- and 400-level courses (excluding QTM 390, QTM 398R, QTM 496, and QTM 497) |
QTM 302W: Technical Writing |
QTM 100 or core sequence |
This course introduces the methods of rhetorical analysis and user experience design as 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. |
QTM 315: Game Theory |
QTM 120 |
Want to a better Poker Player, Parent, General, or CEO? Game theory is the study of individual behavior and social outcomes in strategic situation. What’s a “strategic situation”? Any setting where decisions maker must take into account the incentives of other actors when making a choice? For example, Samsung’s to invest in a new feature for a phone depends on how likely they think Apple would be to introduce a similar set of features. Similarly, politicians deciding on an electoral platform must anticipate the platform choices of opponents. Even parenting involves strategic considerations: a parent’s decision on how strict to be depends on how they believe they child will respond and a child’s response to a parent’s rules depends on their punishments they anticipate for breaking the rules. Insights from the class have broad implications for questions as diverse as building brands and reputations to social norms to evolution. Game theory is used by economists, political scientists, engineers, sociologists, psychologist, computer scientists, and biologists, among others. The business models of companies such as Google, Uber, Airbnb, EBay, and Apple all borrow heavily and directly from insights from game theory. Public policy is guided by strategic concerns, and game theorist have won many Nobel Prizes (15+). |
QTM 345: Advanced Statistics |
QTM 220 |
This is an elective course for advanced statistics on non-experimental data. The majority of data in the empirical studies are non-experiemental data that contain several drawbacks to be taken care of. The course will cover the methodology to handle the one of the most important non-experimental data feature: endogeneity issue. Further, we will touch on techniques for the panel data that prevails in the available datasets. |
QTM 355: Time Series Analysis |
QTM 220 | This course covers the fundamentals of time series analysis in both the natural and social sciences, utilizing analytical, statistical, and numerical approaches. We will focus on the application of these methods to complex, real world data from medicine, economics, geology, and other fields. |
QTM 385: Data Science Computing |
QTM 285, QTM 150/151, or the core sequence |
This course emphasizes practical techniques and tools for producing open, reproducible, computational answers to scientific questions. Students will use the Python programming language and R, along with a standard set of numerical and data visualization tools. No Python knowledge is assumed. Software tools may include Git, Python, R, LaTeX, and KnitR. Additional topics include version control, collaborative programming, visualization, and workflow portability. |
QTM 385: Generalized Linear Model |
QTM 220 |
• Why a student might want to take the elective 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. • Anything else that might attract students to their classes 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. |
QTM 385: Intro to Applied Multivariate Statistics |
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. |
QTM 385: Intro to Statistical & Machine Learning |
QTM 220 |
• 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. |
QTM 385: Mathematics of Voting |
QTM 120 |
In this class we look at models of voting and related topics. We begin with a fundamental question: What is the best way to conduct an election, or more precisely, what is the fairest way to combine individual preferences into a single group preference? Another question we consider is how can indivisible resources, such as representatives in a legislative body, be divided fairly among members of a group? Surprisingly, mathematics can give insight into these questions. The mathematical skills used in this class include mathematical modeling, symbolic representation, and deductive reasoning. These skills are useful in a wide variety of fields outside of Mathematics, particularly in Economics and Political Science. In addition to mathematical skills, students who take this course will have a better understanding of problems with election methods and the difficulties of insuring fairness when a group wants to divide resources or make a choice based on the preferences of the individuals in the group. |
QTM 385: Text Analysis |
QTM 220 | TBD |
QTM 446W: Big/Small Data & Visualization |
None |
The course deals with the new tools of data analysis and visualization developed to deal with big data. It is the huge amounts of (mostly textual) web-based data that offer both humanities and social sciences new avenues of research in the form of digital humanities. What used to be the esoteric domain of computer scientists in data mining, artificial intelligence, natural language processing, is rapidly becoming accessible to the average web user. That is the goal of the course: pull together a wide range of tools, from natural language processing (NLP) to data visualization of networks and geographic maps, with no prerequisite of specialized knowledge, beyond basic computer literary. We will focus on freeware software, from Stanford CoreNLP, topic modeling in Mallet, KWIC (Key Words in Context), Word2Vec (vectors representations of words, shown to capture many linguistic regularities of a corpus), Gephi, Cytoscape, Palladio, Google Earth, QGIS, CartoDB, TimeMapper, Google Fusion Tables. We will also use word cloud software to represent a “bag of words”: Tagcrowd, Tagul, Tagxedo, Wordclouds, Wordle, Voyant. |
QTM 491: Design and Analysis of Experiments |
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 QSS major electives.
ENVS 250: Fundamentals of Cartography and GIS |
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. |
PHYS/BIOL 212: Computational Modeling |
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.
As was said by the great Leonardo, "He who loves practice without theory is like the sailor who boards 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.
Essentially any academic field that does mathematical modeling uses methods and skills developed by this elective course.
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 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). |
BIOL 463: Population Biology and Evolution of Disease |
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. |
Substantive courses of interest
- Are you pursuing one of the unstructured tracks in QSS? Are you unsure of what substantive courses to choose?
- Are you pursuing a structured track in QSS and have an open elective or two to complete? Are you unsure of what elective to choose?
We compiled a list of substantive courses that may be of interest to you! This list includes track eligible courses that contain a quantitative component.