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 2005-2006:

ASTR 111(F) Introduction to Astrophysics (Q)

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

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

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

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

CSCI 223(F) Software Development (Q)

CSCI 237(F) Computer Organization (Q)

CSCI 256(S) Algorithm Design and Analysis (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 338T(S) Parallel Processing (Q)

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

CSCI 374T(F) Machine Learning (Q)

CSCI 434(S) Compiler Design (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 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 351(F) Tax Policy (Q) (W)

ECON 353(F) Decision Theory (Q)

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

ECON 384(F) Corporate Finance (Q)

ECON 385(S) Games and Information (Q)

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

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

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

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

LING 131(F) Introduction to Logic and Semantics (Same as Philosophy 131) (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 180(F) 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 211T(F) Mathematical Reasoning and Linear Algebra (Q)

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

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

MATH 285T(F) Teaching Mathematics (Q)

MATH 301(F) Real Analysis (Q)

MATH 305(S) Applied Real Analysis (Q)

MATH 306(F) Chaos and Fractals (Q)

MATH 307(S) Methods in Mathematical Modeling and Operations Research (Q)

MATH 312(S) Abstract Algebra (Q)

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

MATH 313T(S) Explorations in Number Theory and Geometry (Q)

MATH 317(F) Applied Abstract Algebra (Q)

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

MATH 324T(F) Topology (Q)

MATH 327T(S) Tiling Theory (Q)

MATH 352(S) Combinatorics (Q)

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

MATH 373(F) Investment Mathematics (Q)

MATH 401(F) Functional Analysis with Applications to Mathematical Physics (Q)

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

MATH 411(S) Commutative Algebra (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 346(S) Regression and Forecasting (Q)

STAT 358T(F) Introduction to Biostatistics (Q)

STAT 441(F) Bayesian Statistics (Q)

PHIL 131(F) Introduction to Logic and Semantics (Same as Linguistics 131) (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 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 319(F) Integrative Bioinformatics, Genomics, and Proteomics Lab (Same as Biology 319, Chemistry 319, Computer Science 319 and Mathematics 319) (Q)

PHYS 405T(F) Electromagnetic Theory (Q)

PHYS 418(S) Gravity (Q)

PHYS 451(S) 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 Philosophy 222) (Q)