QR Courses without Prerequisite

The following introductory-level courses without prerequisites enable students to fulfill the skills requirement in quantitative reasoning (QR) through study in a wide range of quantitative disciplines. In addition, there are a multitude of QR courses with prerequisites (such as single-variable calculus, introductory computer programming, or introductory work in a natural or social science) that can be fulfilled through introductory-level course work or advanced placement. Students may view the complete list of QR courses or search for QR courses in specific departments using the OCI (Online Course Information) Web site.

Each student will wish to select courses that match his or her interests and level of preparation. Information about expected preparation is available through links following each course’s brief description.

Course Number Course Title and Description

Applied Mathematics

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.

Applied Physics

APHY 110b

The Technological World
See ENAS 110b


ASTR 110a

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. No prerequisite other than a working knowledge of elementary algebra.

ASTR 120b

Galaxies and the Universe
An introduction to stellar populations and the structure and evolution of the Milky Way galaxy; external galaxies, radio galaxies, and quasars; cosmology and the expanding universe. 

Further Course Information and Preparation

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 210b

Stars and Their Evolution
An intensive introduction to stars. Nuclear processes and element production, stellar evolution, stellar deaths and supernova explosions, and stellar remnants including white dwarfs, neutron stars, and black holes.  A close look at our nearest star, the sun. Prerequisite: a strong background in high school mathematics and physics.

ASTR 220a

Galaxies and Cosmology
An intensive introduction to extragalactic astronomy. The structure and contents of galaxies, evolution of galaxies, observational cosmology, and the history of the universe. 

Further Course Information and Preparation


CHEM 112a

Chemistry with Problem Solving
For beginning students in chemistry or for those whose exposure to the subject has been moderate. Special emphasis on scientific problem-solving skills through an additional discussion section devoted to quantitative reasoning. Enrollment by placement only and limited to freshmen.

CHEM 114a or b

Comprehensive General Chemistry
A comprehensive survey of modern descriptive, inorganic, and physical chemistry for students with a good secondary school exposure to general chemistry. Enrollment by placement only.

Computer Science

CPSC 112a or b

Introduction to Programming
Development on the computer of programming skills, problem-solving methods, and selected applications. 

Further Course Information and Preparation

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. 

Further Course Information and Preparation

ECON 110a

Introduction to Economic Analysis: Microeconomics

An introduction to microeconomics, taught as a lecture discussion, that is an alternative to ECON 115a or b.
Limited to freshmen. Preregistration for ECON 110a is required by signing the preregistration sheet posted on the bulletin board at 28 Hillhouse Avenue on the first Monday before classes. 

Further Course Information and Preparation

ECON 115a or b

Introductory Economics: Microeconomics
An introduction that stresses the basic tools of micro economics and the problem solving involved in economic policy analysis. 

Further Course Information and Preparation

Electrical Engineering

EENG 222 Nanotechnology: The New Science of Small
An introduction to the emerging discipline of nanotechnology. Topics include the physical effects of nanoscale systems, the synthesis and fabrication of nanostructures, and their applications ranging from micromachines to electronics to biology. Societal and economic impacts, as well as ethical issues created by nanotechnologies, will be discussed.

Engineering and Applied Science

ENAS 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.

ENAS 120b

Introduction to Environmental Engineering
Introduction to engineering principles related to the environment, with emphasis on causes of problems and technologies for abatement. Topics include air and water pollution, global climate change, hazardous chemical and emerging environmental technologies. Prerequisites: high school calculus and chemistry or CHEM 114, 115 (may be taken concurrently) or permission of instructor.

Environmental Studies

EVST 201a

Atmosphere, Ocean, and Environmental Change
Physical processes that control Earth’s atmosphere, ocean, and climate. Quantitative methods for constructing energy and water budgets. Topics include clouds, rain, severe storms, regional climate, the ozone layer, air pollution, ocean currents and productivity, the seasons, El Niño, the history of Earth’s climate, global warming, energy, and water resources. Must be taken concurrently with EVST 202La.

Global Affairs

GLBL 121a

Applied Quantitative Analysis
Mathematical fundamentals that underlie analytical approaches in public policy and the social sciences. Development of mathematical skills in areas such as linear functions, single and multiple variable differentiation, exponential functions, and optimization. Statistical approaches include descriptive statistics, principles of sampling, hypothesis tests, simple linear regression, multiple regression, and models for analyzing categorical outcomes.

Geology and Geophysics

G&G 140a

Atmosphere, Ocean, and Environmental Change
(see EVST 201a)


LING 224a

Formal Foundations of Linguistic Theories

Study of formal systems that play an important role in the scientific study of language. Exploration of a range of mathematical structures and techniques; demonstrations of their application in theories of grammatical competence and performance including set theory, graphs and discrete structures, algebras, formal language and automata theory. Evaluation of strengths and weaknesses of existing formal theories of linguistic knowledge.

LING 263b

Introduction to truth-conditional compositional semantics. Set theory, first- and higher-order logic, and the lambda calculus as they relate to the study of natural language meaning. Some attention to analyzing the meanings of tense/aspect markers, adverbs, and modals.


MATH 101b

Geometry of Nature
Geometric patterns in nature, including classical models of spirals in seashells and sunflowers, symmetry of honeycombs and snowflakes, and the curvature of soap films; the shape of the universe; ways to visualize the fourth dimension; and a brief introduction to fractal geometry. Enrollment limited to freshmen and sophomores who have not previously taken a high school or college calculus course.

MATH 112a or b

Calculus of Functions of One Variable I
Limits and their properties. Definitions and some techniques of differentiation and the evaluation of definite integrals, with applications. Graphical, symbolic, and numerical methods use the mathematical software package Mathematica. 

Further Course Information and Preparation

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. 

Further Course Information and Preparation


PHIL 115a

First Order Logic
An introduction to formal logic. Study of the formal deductive systems and semantics for both propositional and predicate logic. Some discussion of metatheory. 

Further Course Information and Preparation


PHYS 100a

Energy Technology and Society
The technology and use of energy. Impacts on the environment, climate, security, and economy. Application of scientific reasoning and quantitative analysis. Intended for students not committed to a major in science or engineering; no college-level science or mathematics required. 

PHYS 101b

Movie Physics
A critical evaluation of Hollywood action movies using the laws of physics and back of the envelope estimates to distinguish between fictional and real movie physics. Enrollment limited to freshmen and sophomores. Intended for students with little or no prior exposure to calculus and statistics.

Political Science

PLSC 452a

Introduction to Statistics: Political Science
(see STAT 102a)

PLSC 453a

Introduction to Statistics: Social Sciences
(see STAT 103a)


PSYC 200b

Measures of central tendency, variability, association, and the application of probability concepts in determining the significance of research findings.


SOCY 162a

Methods in Quantitative Sociology 
Introduction to methods for reading and conducting quantitative sociological research. Data description and graphical approaches to data analysis; elementary probability theory; assumptions and properties of bivariate and multivariate linear regression; regression diagnostics. 

Further Course Information and Preparation


STAT 100b

Introductory Statistics
An introduction to statistical reasoning. Topics include numerical and graphical summaries of data, data acquisition and experimental design, probability, hypothesis testing, confidence intervals, correlation and regression. Application of statistical concepts to data; analysis of real-world problems.

STAT 101a

Introduction to Statistics: Life Sciences
Statistical and probabilistic analysis of biological problems presented with a unified foundation in basic statistical theory. Problems are drawn from genetics, ecology, epidemiology, and bioinformatics. 

Further Course Information and Preparation

STAT 102a

Introduction to Statistics: Political Science
Statistical analysis of politics, elections, and political psychology. Problems presented with reference to a wide array of examples: public opinion, campaign finance, racially motivated crime, and public policy.

Further Course Information and Preparation

STAT 103a

Introduction to Statistics: Social Sciences
Descriptive and inferential statistics applied to analysis of data from the social sciences. Introduction of concepts and skills for understanding and conducting quantitative research. 

Further Course Information and Preparation

STAT 105a

Introduction to Statistics: Medicine
Statistical methods relied upon in medicine and medical research. Practice in reading medical literature competently and critically, as well as practical experience performing statistical analysis of medical data.

Further Course Information and Preparation

STAT 230b

Introductory Data Analysis 
Survey of statistical methods: plots, transformations, regression, analysis of variance, clustering, principal components, contingency tables, and time series analysis. The R computing language and Web data sources are used.