Yale requires at least two course credits in classes that involve “quantitative reasoning,” designated “QR” in the Yale College Bluebook. The mental rigor resulting from quantitative study has been celebrated since ancient times, and applications of quantitative methods have proven critical to many different disciplines. Mathematics and statistics are basic tools for the natural and social sciences, and they have become useful in many of the humanities as well. Information technology and the rigorous dissection of logical arguments in any discipline depend on algorithms and formal logical constructs. An educated person must be able to use quantitative information to make, understand, and evaluate arguments.

Many quantitative reasoning courses are taught through the departments of Mathematics, Statistics, and Computer Science. Such courses may also be found in Architecture; Astronomy; Chemistry; Economics; Engineering; Environmental Studies; Geology and Geophysics; Global Affairs; Linguistics; Molecular, Cellular, and Developmental Biology; Operations Research; Philosophy; Physics; Political Science; Psychology; and Sociology. Below is a list of popular QR courses at Yale as well as some student evaluations.

## Popular QR Courses at Yale

### AMTH 160b: The Structure of Networks

Network structures and network dynamics described through examples and applications ranging from marketing to epidemics and the world climate. Study of social and biological networks as well as networks in the humanities. Mathematical graphs provide a simple common language to describe the variety of networks and their properties.

### APHY 110b: The Technological World

An exploration of modern technologies that play a role in everyday life, including the underlying science, current applications, and future prospects. Examples include solar cells, light-emitting diodes (LEDs), computer displays, the global positioning system, fiber-optic communication systems, and the application of technological advances to medicine. For students not committed to a major in science or engineering; no college-level science or mathematics required.

### ARCH 161: Introduction to Structures

Basic principles governing the behavior of building structures. Developments in structural form combined with the study of force systems, laws of statics, and mechanics of materials and members and their application to a variety of structural systems.

*“It was a great venture into a field most of us are unfamiliar with–structural logic behind how buildings stand. It was exhilarating. I couldn’t recommend it more highly. Don’t be scared by the quantitative and scientific aspect of it, AT ALL! Every single person in my 22-person class, including those who are very shaky with math, felt good about the class. Jump in.”*

### ASTR 110: Planets and Stars

An introduction to stars and planetary systems. Topics include the solar system and extrasolar planets, planet and stellar formation, and the evolution of stars from birth to death.

### ASTR 120: Galaxies and the Universe

An introduction to stars and stellar evolution; the structure and evolution of the Milky Way galaxy and other galaxies; quasars, active galactic nuclei, and supermassive black holes; cosmology and the expanding universe.

*“It’s a great class! You learn about the universe and its evolution and about things that sound like science fiction but are actually true. It’s not completely easy, but it’s extremely enjoyable and I loved everything we learned.”*

### ASTR 160b: Frontiers and Controversies in Astrophysics

A detailed study of three fundamental areas in astrophysics that are currently subjects of intense research and debate: (1) planetary systems around stars other than the sun; (2) pulsars, black holes, and the relativistic effects associated with them; (3) the age and ultimate fate of the universe. No prerequisite other than a working knowledge of elementary algebra.

### ASTR 170a: Introduction to Cosmology

An introduction to modern cosmological theories and observations. Topics include aspects of special and general relativity; curved space-time; the Big Bang; inflation; primordial element synthesis; the cosmic microwave background; the formation of galaxies; and large-scale structure.

### ASTR 210b: Stars and Their Evolution

### ASTR 220a: Galaxies and Cosmology

### ASTR 255a: Research Methods in Astrophysics

### CHEM 112a: Chemistry with Problem Solving

### CHEM 114a or b: Comprehensive General Chemistry

### CHEM 118a: Quantitative Foundations of General Chemistry

### CPSC 101b: Great Ideas in Computer Science

### CPSC 112a or b: Introduction to Programming

### CPSC 191: Great Ideas in Computer Science

### CPSC 112 and 201: Introduction to Programming & Computer Science

Introduction to the concepts, techniques, and applications of computer science, Topics include computer systems; theoretical foundations of computing; and artificial intelligence. Examples stress the important of different problem-solving methods.

*“AMAZING AMAZING AMAZING. One of the funnest classes I’ve taken at Yale. I loved doing the problem sets. Even though they were sometimes frustrating at first, finishing one and getting everything to compile and run properly was one of the most rewarding feelings. Before taking this class I knew nothing about computers or programming. Now I can get my computer to do stuff for me!!! TOO COOL!! Great great great class.”*

### CPSC 202a: Mathematical Tools for Computer Science

Introduction to formal methods for reasoning and to mathematical techniques basic to computer science. Topics include propositional logic, discrete mathematics, and linear algebra. Emphasis on applications to computer science: recurrences, sorting, graph traversal, Gaussian elimination.

### ECON 108a or b: Quantitative Foundations of Microeconomics

Introductory microeconomics with a special emphasis on quantitative methods and examples. Intended for students with limited or no prior exposure to calculus. Preference to freshmen. Permission of Economics DUS required.

### ECON 110 and 115: Introductory Microeconomics

### ECON 251: Financial Theory

Capital asset pricing model, arbitrage pricing theory, option pricing, social security, operation of security exchanges, investment banks, securitization, mortgage derivatives, interest rate derivatives, hedge funds, financial crises, agency theory, and financial incentives.

### EENG 201b: Introduction to Computer Engineering

Introduction to the theoretical principles underlying the design and programming of simple processors that can perform algorithmic computational tasks. Topics include data representation in digital form, combinational logic design and Boolean algebra, sequential logic design and finite state machines, and basic computer architecture principles. Hands-on laboratory involving the active design, construction, and programming of a simple processor.

### ENAS 110b: The Technological World

### ENAS 120b: Introduction to Environmental Engineering

### EVST 201a: Atmosphere, Ocean, and Environmental Change

### GLBL 121a: Applied Quantitative Analysis

### G&G 140: Atmosphere, Ocean, and Environmental Change

### LING 224a: Formal Foundations of Linguistic Theories

### LING 263a: Semantics

### MATH 101: Geometry of Nature

*“One word: excellent. I highly recommend this class and Professor Frame is an incredible teacher. Help is always there when needed and this has been one of my favorite classes at Yale. I really enjoyed it!”*

### MATH 107a: Mathematics in the Real World

The use of mathematics to address real-world problems. Applications of exponential functions to population growth and radiocarbon dating; geometric series in mortgage payments, amortization of loans, future value of money; applications of basic probability theory and Bayes’s law in disease detection and drug testing; elements of logic; elements of cryptography. No knowledge of calculus required. Enrollment limited to students who have not previously taken a high school or college calculus or statistics course.

### MATH 112/115: Calculus of Functions of One Variable I & II

Applications of integration, with some formal techniques and numerical methods. Improper integrals, approximation of functions by polynomials, infinite series.

### MATH 190a: Fractal Geometry

A visual introduction to the geometry of fractals and the dynamics of chaos, accessible to students not majoring in science. Study of mathematical patterns repeating on many levels and expressions of these patterns in nature, art, music, and literature.