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.
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| Course Number |
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Course Title and Description |
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| Applied Mathematics |
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| AMTH 110a |
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Introduction to Quantitative Thinking: The Pleasures of Counting
Methods of quantitative inference and modeling are introduced via applications from a variety of different fields. Possible topics include data encryption, codes, scaling phenomena, traffic flow, warfare, and population growth. Some use of computing software such as Mathematica or MATLAB. |
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| Astronomy |
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| ASTR 110b |
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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. |
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| ASTR 120a |
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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 |
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| ASTR 160a |
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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. Further Course Information and Preparation |
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| ASTR 170a |
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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. Further Course Information and Preparation |
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| ASTR 220b |
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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 |
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| Chemistry |
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| CHEM 112a |
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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. For placement information see Chemistry pre-registration web page. |
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| CHEM 114a |
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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. For placement information see Chemistry pre-registration web page. |
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| Computer Science |
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| CPSC 112a or b |
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Introduction to Programming
Development on the computer of programming skills, problem-solving methods, and selected applications. Further Course Information and Preparation |
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| CPSC 079b |
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Digital Photorealism
Examination of the basic methods used to define shapes, materials, and lighting when creating computer-generated images. Topics include the input and behavior of different classes of mathematical models for shape, such as meshes, splines, and implicit functions; texture models, such as noise and turbulence functions and sample-based techniques; and lighting techniques such as ray tracing, radiosity, and direct lighting. Principles are applied through the use of modeling/rendering/animation software systems rather than through computer programming. No programming or previous computer graphics experience is necessary. |
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| Ecology and Evolutionary Biology |
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| E&EB 210a |
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Introduction to Statistics: Life Sciences
(see STAT 101a) |
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| Economics |
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| ECON 108a or b |
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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 |
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| ECON 110a |
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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 |
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| ECON 115a or b |
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Introductory Economics: Microeconomics
An introduction that stresses the basic tools of micro economics and the problem solving involved in policy issues. Further Course Information and Preparation |
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| Electrical Engineering |
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| EENG 001a |
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Introduction to Nanoscience
An introductory survey of the emerging discipline of nanotechnology. Topics include realistic nanosystems, methods used to fabricate and create nanostructures, the physical properties and applications of nanostructures, microelectromechanical systems (MEMS) and biological applications, and system architecture. Enrollment limited to freshmen. |
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| EENG 201b |
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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. Further Course Information and Preparation |
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| Engineering and Applied Science |
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| ENAS 060b |
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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 non-science majors with strong backgrounds in math and science.
Enrollment limited to freshmen. |
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| ENAS 110b |
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The Technological World
An exploration of modern technologies that play a role in our everyday lives, 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. Further Course Information and Preparation |
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| Environmental Studies |
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| EVST 201a |
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Atmosphere, Ocean, and Environmental Change
Physical and chemical processes that control the Earth's surface, atmosphere, ocean, and climate, and that influence human activities. Development of quantitative methods for constructing energy, water, soil, and chemical budgets. Topics include chemical composition of the Earth's crust, atmosphere, and ocean; climate and the circulation of the atmosphere and ocean; the history of the Earth's climate; global warming; energy and water resources; rivers and soil erosion; and mineral resources. Must be taken concurrently with EVST 202La. |
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| Geology and Geophysics |
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| G&G 140a |
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Atmosphere, Ocean, and Environmental Change
(see EVST 201a) |
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| Mathematics |
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| MATH 101b |
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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. In addition we shall explore the shape of the universe, ways to visualize the fourth dimension, and a brief glimpse of fractal geometry. Enrollment limited to freshmen and sophomores. Enrollment limited to students who have not previously taken a high
school or college calculus course. |
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| MATH 112a or b |
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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 |
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| MATH 190a |
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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 |
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| Philosophy |
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| PHIL 115a |
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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 |
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| Physics |
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| PHYS 101b |
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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.
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| PHYS 110b |
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Developments in Modern Physics
An introduction to modern physics and quantitative reasoning. Topics include subatomic particles, electromagnetic waves, black holes, galaxies, and the fate of the universe. Study of the stages of descriptive modeling, with examples ranging from Newtonian physics to Einstein's theory of relativity. |
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| PHYS 150a |
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General Physics
An introduction to classical physics and to selected topics in modern physics. Emphasis on fundamental principles, with examples of practical applications to medicine and other fields. PHYS 150a covers mechanics, thermodynamics, and wave motion. Further Course Information and Preparation |
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| Political Science |
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| PLSC 452a |
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Introduction to Statistics: Political Science
(see STAT 102a) |
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| PLSC 453a |
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Introduction to Statistics: Social Sciences
(see STAT 103a) |
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| Psychology |
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| PSYC 129a |
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Statistics as a Way of Knowing
An introduction to basic concepts of statistics and probability that allow us to describe, evaluate, and understand aspects of the world and make informed choices. Exploration of relationships among statistical reasoning, cognitive psychology, and philosophical theories of knowledge.
Enrollment limited to freshmen and sophomores. |
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| PSYC 200b |
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Statistics
Measures of central tendency, variability, association, and the application of probability concepts in determining the significance of research findings. |
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| Statistics |
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| STAT 100b |
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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. Further Course Information and Preparation |
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| STAT 101a |
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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 |
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| STAT 102a |
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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 |
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| STAT 103a |
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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 |
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| STAT 105a |
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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 |
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| STAT 106a |
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Introduction to Statistics: Data Analysis
An introduction to probability and statistics with emphasis on data analysis. Further Course Information and Preparation |
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| STAT 129a |
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Statistics as a Way of Knowing
(see PSYC 129a) |
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