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 100/101/102, 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 2004-2005:

ASTR 111(F) Introduction to Astrophysics (Q)

BIOL 106(S) Life as an Algorithm (Same as Computer Science 106) (Q)

BIOL 202(F) Genetics (Q)

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

BIOL 302(S) Communities and Ecosystems (Same as Environmental Studies 312) (Q)

BIOL 305(F) Evolution (Q)

BIOL 306(F) Cellular Regulatory Mechanisms (Q)

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

CHEM 151(F) Concepts of Chemistry (Q)

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

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

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

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

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

CSCI 105(F,S) Understanding the Web: Technologies and Techniques (Q)

CSCI 106(S) Life as an Algorithm (Same as Biology 106) (Q)

CSCI 108(F) Artificial Intelligence: Image and Reality (Q)

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

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

CSCI 223(S) Software Development (Q)

CSCI 237(F) Computer Organization (Q)

CSCI 256(S) Algorithm Design and Analysis (Q)

CSCI 315(S) Computational Biology (Same as INTR 315) (Q)

CSCI 334(S) Principles of Programming Languages (Q)

CSCI 336T(F) Computer Networks (Q)

CSCI 338(F) Parallel Processing (Q)

CSCI 361(F) Theory of Computation (Same as Mathematics 361) (Q)

CSCI 432(S) Operating Systems (Q)

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

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

ECON 208(F) Modern Corporate Industry(Q)

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

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

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

ECON 252(F,S) Macroeconomics (Q)

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

ECON 255(S) Econometrics (Q)

ECON 353(S) Decision-making and Judgment (Q)

ECON 384(S) Corporate Finance (Q)

ECON 385(S) Games and Information (Q)

ENVI 203(F) Ecology (Same as Biology 203)(Q)

ENVI 215(F) Climate Changes (Same as Geosciences 215) (Q)

ENVI 221(S) Economics of the Environment (Same as Economics 221)

ENVI 312(S) Communities and Ecosystems (Same as Biology 302) (Q)

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

GEOS 301(F) Structural Geology (Q)

INTR 160(F) Mathematical Politics: Voting, Power, and Conflict (Same as Mathematics 175) (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(S) Computational Biology (Same as Computer Science 315) (Q)

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

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

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

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

MATH 106(F) Multivariable Calculus (Q)

MATH 170(F) Mathematics of Finance (Q)

MATH 175(F) Mathematical Politics: Voting, Power, and Conflict (Same as INTR 160) (Q)

MATH 180(S) The Art of Mathematical Thinking: An Introduction to the Beauty and Power of Mathematical Ideas (Q)

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

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

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

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

MATH 251T(S) Introduction to Mathematical Proof and Argumentation (Q)

MATH 301(F) Real Analysis (Q)

MATH 302(S) Complex Analysis (Q)

MATH 305(S) Applied Real Analysis (Q)

MATH 312(S) Abstract Algebra (Q)

MATH 315(F) Groups and Characters (Q)

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

MATH 321(F) Knot Theory (Q)

MATH 324(S) Topology (Q)

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

MATH 375(F) Game Theory (Q)

MATH 403(F) Irrationality and Transcendence (Q)

MATH 404T(S) Ergodic Theory (Q)

MATH 414(S) Galois Theory (Q)

MATH 419(F) An Introduction to Fuchsian Groups (Q)

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

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

STAT 231T(F) Statistical Design of Experiments (Q)

STAT 346(S) Regression and Forecasting (Q)

STAT 421(F) Introduction to Categorical Data Analysis (Q)

PHIL 103(S) Logic and Language (Q)

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

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

PHYS 131(F) Particles and Waves (Q)

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

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

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

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

PHYS 201(F) Electricity and Magnetism (Q)

PHYS 202(S) Waves and Optics (Q)

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

PHYS 301(F) Quantum Physics (Q)

PHYS 302(S) Statistical Physics (Q)

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

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

PHYS 411T(F) Classical Mechanics (Q)

PHYS 451(F) Solid State Physics (Q)

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

PSYC 222(S) Minds, Brains, and Intelligent Behavior An Introduction to Cognitive Science (Same as Cognitive Science 222, INTR 222 and Philoso