**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 2006-2007:

ASTR 111(F) Introduction to Astrophysics (Q)

BIMO 321(F) Biochemistry I-Structure and Function of Biological Molecules (Same as Biology 321 and Chemistry 321) (Q)

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

BIOL 106(F) 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 235T(F) Biological Modeling with Differential Equations (Same as Environmental Studies 235T and Mathematics 335T) (Q)

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

BIOL 305(S) Evolution (Q)

BIOL 306(S) Cellular Regulatory Mechanisms (Q)

BIOL 319(F) Integrative Bioinformatics, Genomics, and Proteomics Lab (Same as Chemistry 319, Computer Science 319, Mathematics 319 and Physics 319) (Q)

BIOL 321(F) Biochemistry I-Structure and Function of Biological Molecules (Same as Chemistry 321 and Biochemistry and Molecular Biology 321)

BIOL 322(S) Biochemistry II-Metabolism (Same as BIMO 322 and 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 319(F) Integrative Bioinformatics, Genomics, and Proteomics Lab (Same as Biology 319, Computer Science 319, Mathematics 319 and Physics 319) (Q)

CHEM 321(F) Biochemistry I-Structure and Function of Biological Molecules (Same as Biochemistry and Molecular Biology 321 and Biology 321)

CHEM 322(S) Biochemistry II-Metabolism (Same as BIMO 322 and 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 106(F) Life as an Algorithm (Same as Biology 106) (Q)

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

CSCI 109(S) The Art and Science of Computer Graphics (Q)

CSCI 134(F,S) Digital Computation and Communication (Q)

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

CSCI 237(F) Computer Organization (Q)

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

CSCI 318T(F) Numerical Problem Solving (Same as Mathematics 318T) (Q)

CSCI 319(F) Integrative Bioinformatics, Genomics, and Proteomics Lab (Same as Biology 319, Chemistry 319, Mathematics 319 and Physics 319) (Q)

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

CSCI 336T(F) Computer Networks (Q)

CSCI 337T(S) Digital Design and Modern Architecture (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 221(S) Economics of the Environment (Same as Environmental Studies 221) (Q)

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

ECON 252(F,S) Macroeconomics (Q)

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

ECON 255(F,S) Econometrics (Q)

ECON 351(F) Tax Policy (Q) (W)

ECON 353(F) Decision Theory (Q)

ECON 372(F) Public Choice (Q)

ECON 384(F) Corporate Finance (Q)

ECON 385(F) Games and Information (Q)

ECON 464(S) *(formerly 367)* Empirical Methods in Macroeconomics (Same as Economics 514) (Q)

ECON 514(S) Empirical Methods in Macroeconomics (Same as Economics 464) (Q)

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

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

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

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

GEOS 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)

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 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 301(F) Real Analysis (Q)

MATH 302(S) Complex Analysis (Q)

MATH 303(F) Analytic Number Theory (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 318T(F) Numerical Problem Solving (Same as Computer Science 318T) (Q)

MATH 319(F) Integrative Bioinformatics, Genomics, and Proteomics Lab (Same as Biology 319, Chemistry 319, Computer Science 319 and Physics 319) (Q)

MATH 321(S) Knot Theory (Q)

MATH 327(S) Geodetic Surfaces (Q)

MATH 335T(F) Biological Modeling with Differential Equations (Same as Biology 235T and Environmental Studies 235T) (Q)

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

MATH 404T(F) Ergodic Theory (Q)

MATH 405(S) Geometric Ordinary Differential Equations (Q)

MATH 414(S) Galois Theory (Q)

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

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

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

STAT 313T(F) Advanced Mathematical Methods in Statistical Inference (Q)

STAT 346(S) Regression and Forecasting (Q)

STAT 440T(S) 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 109(F) Sound, Light, and Perception (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 319(F) Integrative Bioinformatics, Genomics, and Proteomics Lab (Same as Biology 319, Chemistry 319, Computer Science 319 and Mathematics 319) (Q)

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

PHYS 411T(F) Classical Mechanics (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 Philosophy 222) (Q)