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 2002-2003:

Astronomy 111(F) Introduction to Astrophysics (Q)

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

Biology 202(F) Genetics (Q)

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

Biology 305(F) Evolution (Q)

Biology 306(F) Advanced Molecular Genetics (Q)

Biology 322(S) Biochemistry II-Metabolism (Same as Chemistry 322 and Biochemistry and Molecular Biology 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 and Biochemistry and Molecular Biology 322) (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(F) Understanding the Web: Technologies and Techniques (Q)

Computer Science 108(S) Artificial Intelligence: Image and Reality (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 334(S) Principles of Programming Languages (Q)

Computer Science 336T(S) Computer Networks (Q)

Computer Science 338(S) Parallel Processing (Q)

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

Computer Science 371(F) Computer Graphics (Q)

Computer Science 432(F) Operating Systems (Q)

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

Economics 120(F,S) Principles of Macroeconomics (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 353(S) Decision-making and Judgment (Q)

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

Economics 372(F) Public Choice (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)

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)

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

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

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

Mathematics 143(F) Elementary Statistics and Data Analysis (See Statistics 101) (Q)

Mathematics 170(S) Mathematics of Finance (Q)

Mathematics 209(S)(formerly Mathematics 210) 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 251(F,S) Discrete Mathematics (Q)

Mathematics 301(F) Real Analysis (Q)

Mathematics 302(S) Complex Analysis (Q)

Mathematics 305(S) Applied Real Analysis (Q)

Mathematics 312(S) Abstract Algebra (Q)

Mathematics 315(F) Groups and Characters (Q)

Mathematics 316(F) Protecting Information: Applications of Abstract Algebra and Quantum Physics (Same as Physics 316) (Q)

Mathematics 321(S) Knot Theory (Q)

Mathematics 326(F) Counterexamples in Topology (Q)

Mathematics 360(S) Mathematical Logic (Q)

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

Mathematics 375(S) Game Theory (Q)

Mathematics 402(S) Measure Theory and Probability (Q)

Mathematics 415(F) Geometric Group Theory (Q)

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

Philosophy 103(S) Logic and Language (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) Foundation 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 316(F) Protecting Information: Applications of Abstract Algebra and Quantum Physics (Same as Mathematics 316) (Q)

Physics 402T(S) Applications of Quantum Mechanics (Q)

Physics 411T(F) Classical Mechanics (Q)

Physics 454(S) Elementary Particle Physics (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) (formerly Mathematics 143) Elementary Statistics and Data Analysis (Q)

Statistics 201(S) (formerly Mathematics 243) Statistics and Data Analysis (Q)

Statistics 231(F) (formerly 244) Statistical Design of Experiments (Q)