**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 2008-2009:

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 202(F) Genetics (Q)

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

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

BIOL 305(S) 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 321(F) Biochemistry I-Structure and Function of Biological Molecules (Same as Biochemistry and Molecular Biology 321 and Chemistry 321) (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 321(F) Biochemistry I-Structure and Function of Biological Molecules (Same as Biochemistry and Molecular Biology 321 and Biology 321) (Q)

CHEM 322(S) Biochemistry II-Metabolism (Same as BIMO 322 and Biology 322) (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) Introduction to Computer Science (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 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 356T(S) Advanced Algorithms (Q)

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

CSCI 371(F) Computer Graphics (Q)

CSCI 432(S) Operating Systems (Q)

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

ECON 111(S) Introduction to Economics and Its Applications (Q)

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

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

ECON 252(F,S) Macroeconomics (Q)

ECON 253(F) Empirical Methods in Political Economy (Same as Political Economy 253) (Q)

ECON 255(F,S) Econometrics (Q)

ECON 353(F) Decision Theory (Q)

ECON 379(F) Economics of the Environment (Same as Environmental Studies 379) (Q)

ECON 385(S) Games and Information (Q)

ECON 386(S) Environmental Policy and Natural Resource Management (Same as Economics 515 and Environmental Studies 386) (Q)

ECON 392(F) Finance and Capital Markets (Q)

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

ECON 468(S) Microfinance (Same as Economics 508) (D) (Q)

ECON 475(F) Advanced Microeconomic Theory (Q)

ECON 508(S) Microfinance (Same as Economics 468) (D) (Q)

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

ECON 515(S) Environmental Policy and Natural Resource Management (Same as Economics 386 and Environmental Studies 386) (Q)

ENVI 108(S) Energy Science and Technology (Same as Physics 108) (Q)

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

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

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

ENVI 379(F) Economics of the Environment (Same as Economics 379) (Q)

ENVI 386(S) Environmental Policy and Natural Resource Management (Same as Economics 386 and Economics 515) (Q)

GEOS 215(S) 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)

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

MATH 305(S) Applied Real Analysis (Q)

MATH 312(F,S) Abstract Algebra (Q)

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

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

MATH 327(S) Computational Geometry (Q)

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

MATH 370T(F) Mathematics and Politics: Social Choice and Fair Division (Q)

MATH 404(S) Ergodic Theory (Q)

MATH 406(S) Analysis and Number Theory (Q)

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

MATH 481(F) The Big Questions (Q)

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

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

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

STAT 346(S) Regression and Forecasting (Q)

STAT 440(S) Categorical Data Analysis (Q)

PHIL 103(S) Logic and Language (Q)

PHYS 107(F) Newton, Einstein, and Beyond (Q)

PHYS 108(S) Energy Science and Technology (Same as Environmental Studies 108) (Q)

PHYS 109(S) 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)

POEC 253(F) Empirical Methods in Political Economy (Same as Economics 253) (Q)

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