QUANTITATIVE / FORMAL REASONING COURSES

Williams students should be adept at reasoning mathematically and abstractly. The ability to apply a formal method to reach conclusions, to use numbers comfortably, and to employ the research tools necessary to analyze data lessen barriers to carrying out professional and economic roles. Prior to their senior year, all students must satisfactorily complete a Quantitative/Formal Reasoning (QFR) course-those marked with a "(Q)." Students requiring extra assistance (as assessed during First Days) are normally placed into Mathematics 100/101, which is to be taken before fulfilling the QFR requirement.

The hallmarks of a QFR course are the representation of facts in a language of mathematical symbols and the use of formal rules to obtain a determinate answer. Primary evaluation in these courses is based on multistep mathematical, statistical, or logical inference (as opposed to descriptive answers).

Courses that may be used to meet the requirement in 2003-2004:

Astronomy 111 (F) Introduction to Astrophysics (Q)

Astronomy 211(F) Observations and Data Reduction Techniques in Astronomy (Q)

Biology 202(F) Genetics (Q)

Biology 203(F) Ecology (Same as Environmental Studies 203) (Q)

Biology 235T(F) Biological Modeling with Differential Equations (Same as Mathematics 335T) (Q)

Biology 305(F) Evolution (Q)

Biology 322(S) Biochemistry II-Metabolism (Same as Chemistry 322) (Q)

Chemistry 151(F) Concepts of Chemistry (Q)

Chemistry 153(F) Concepts of Chemistry: Advanced Section (Q)

Chemistry 155(F) Current Topics in Chemistry (Q)

Chemistry 156(S) Organic Chemistry: Introductory Level (Q)

Chemistry 322(S) Biochemistry II-Metabolism (Same as Biology 322) (Q)

Chemistry 332(S) Materials Science: The Chemistry and Physics of Materials (Same as Physics 332) (Q)

Cognitive Science 222(S) Minds, Brains, and Intelligent Behavior: An Introduction to Cognitive Science (Same as INTR 222, Philosophy 222 and Psychology 222) (Q)

Computer Science 105(S) Understanding the Web: Technologies and Techniques (Q)

Computer Science 134(F,S) Introduction to Computer Science (Q)

Computer Science 136(F,S) Data Structures and Advanced Programming (Q)

Computer Science 237(F) Computer Organization (Q)

Computer Science 256(S) Algorithm Design and Analysis (Q)

Computer Science 315(F) Computational Biology (Same as Physics 315 and INTR 315) (Q)

Computer Science 323(F) Software Engineering (Q)

Computer Science 334(S) Principles of Programming Languages (Q)

Computer Science 337T(S) Digital Design and Modern Architecture (Q)

Computer Science 361(F) Theory of Computation (Same as Mathematics 361) (Q)

Computer Science 373(S) Artificial Intelligence (Q)

Computer Science 434(F) Compiler Design (Q)

Economics 110(F,S) Principles of Microeconomics (Q)

Economics 120(F,S) Principles of Macroeconomics (Q)

Economics 208(F) Modern Corporate Industry (Q)

Economics 221(F) Economics of the Environment (Same as Environmental Studies 221) (Q)

Economics 251(F,S) Price and Allocation Theory (Q)

Economics 251M(F,S) Price and Allocation Theory (Q)

Economics 252(F,S) Macroeconomics (Q)

Economics 253(F,S) Empirical Economic Methods (Q)

Economics 255(S) Econometrics (Q)

Economics 351(S) Tax Policy (Q)

Economics 364(F) Incentives and Information (Q)

Economics 367(S) Empirical Methods in Macroeconomics (Same as Economics 514) (Q)

Economics 384(S) Corporate Finance (Q)

Economics 385(F) Games and Information (Q)

Economics 395(S) Development Finance (Same as Economics 508) (Q)

Economics 508(S) Development Finance (Same as Economics 395) (Q)

Economics 514(S) Empirical Methods in Macroeconomics (Same as Economics 367) (Q)

Environmental Studies 203(F) Ecology (Same as Biology 203) (Q)

Environmental Studies 215(F) Climate Changes (Same as Geosciences 215) (Q)

Environmental Studies 221(F) Economics of the Environment (Same as Economics 221) (Q)

Geosciences 215(F) Climate Changes (Same as Environmental Studies 215) (Q)

Geosciences 301(F) Structural Geology (Q)

INTR 222(S) Minds, Brains, and Intelligent Behavior: An Introduction to Cognitive Science (Same as Cognitive Science 222, Philosophy 222 and Psychology 222) (Q)

INTR 315(F) Computational Biology (Same as Physics 315 and Computer Science 315)(Q)

Linguistics 111(S) Articulatory and Acoustic Phonetics (Q)

Linguistics 131(F) Introduction to Logic and Semantics (Same as Philosophy 131) (Q)

Mathematics 103(F,S) Calculus I (Q)

Mathematics 104(F,S) Calculus II (Q)

Mathematics 105(F,S) Multivariable Calculus (Q)

Mathematics 106(F) Multivariable Calculus (Q)

Mathematics 170(F,S) Mathematics of Finance (Q)

Mathematics 209(S) Differential Equations and Vector Calculus (Q)

Mathematics 210(S) Mathematical Methods for Scientists (Same as Physics 210) (Q)

Mathematics 211(F,S) Linear Algebra (Q)

Mathematics 211T(S) Mathematical Reasoning and Linear Algebra (Q)

Mathematics 251(F,S) Discrete Mathematics (Q)

Mathematics 251T(F) Introduction to Mathematical Proof and Argumentation (Q)

Mathematics 285(S) Teaching Mathematics (Q)

Mathematics 301(F) Real Analysis (Q)

Mathematics 305(S) Applied Real Analysis (Q)

Mathematics 312(S) Abstract Algebra (Q)

Mathematics 313(F) Introduction to Number Theory (Q)

Mathematics 314(S) Polynomial Arithmetic (Q)

Mathematics 315(F) Groups and Characters (Q)

Mathematics 323(F) Applied Topology (Q)

Mathematics 327(S) Geodetic Surfaces (Q)

Mathematics 335T(F) Biological Modeling with Differential Equations (Same as Biology 235T) (Q)

Mathematics 341(S) Probability (Q)

Mathematics 361(F) Theory of Computation (Same as Computer Science 361) (Q)

Mathematics 381(S) History of Mathematics (Q)

Mathematics 425(F) Geometry (Q)

Mathematics 426(S) Hyperbolic 3-Manifolds (Q)

Mathematics 428(F) Matrix Groups (Q)

Mathematics 433(S) Mathematical Modeling and Control Theory (Q)

Philosophy 131(F) Introduction to Logic and Semantics (Same as Linguistics 131) (Q)

Philosophy 222(S) Minds, Brains, and Intelligent Behavior: An Introduction to Cognitive Science (Same as Cognitive Science 222, INTR 222 and Psychology 222) (Q)

Physics 100(S) Physics of Everyday Life (Q)

Physics 109(F) Sound, Light, and Perception (Q)

Physics 131(F) Particles and Waves (Q)

Physics 132(S) Electromagnetism and the Physics of Matter (Q)

Physics 141(F) Particles and Waves-Enriched (Q)

Physics 142(S) Foundations of Modern Physics (Q)

Physics 151(F) Seminar in Modern Physics (Q)

Physics 201(F) Electricity and Magnetism (Q)

Physics 202(S) Waves and Optics (Q)

Physics 210(S) Mathematical Methods for Scientists (Same as Mathematics 210) (Q)

Physics 301(F) Quantum Physics (Q)

Physics 302(S) Statistical Physics (Q)

Physics 315(F) Computational Biology (Same as Computer Science 315 and INTR 315) (Q)

Physics 332(S) (formerly 318) Materials Science: The Chemistry and Physics of Materials (Same as Chemistry 332) (Q)

Physics 405T(F) Electromagnetic Theory (Q)

Physics 418(S) Gravity (Q)

Psychology 201(F,S) Experimentation and Statistics (Q)

Psychology 222(S) Minds, Brains, and Intelligent Behavior: An Introduction to Cognitive Science (Same as Cognitive Science 222, INTR 222 and Philosophy 222) (Q)

Statistics 101(F,S) Elementary Statistics and Data Analysis (Q)

Statistics 201(F,S) Statistics and Data Analysis (Q)

Statistics 231(F) Statistical Design of Experiments (Q)

Statistics 346(S) Regression and Forecasting (Q)