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 2007-2008:

ASTR 111(F) Introduction to Astrophysics (Q)

ASTR 211(F) Astronomical Observing, Image Processing, and Analysis (Q)

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

BIOL 203(F) Ecology (Same as Environmental Studies 203) (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 322(S) Biochemistry II-Metabolism (Same as BIMO 322 and Biology 322) (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 315(S) Computational Biology (Same as INTR 315 and Physics 315) (Q)

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

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

CSCI 373(F) Artificial Intelligence (Q)

CSCI 374T(S) Machine Learning (Q)

CSCI 434T(F) Compiler Design (Q)

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

ECON 255(F,S) Econometrics (Q)

ECON 353(S) Decision Theory (Q)

ECON 379(F) The Economics of Sustainability (Same as Environmental Studies 379) (Q)

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

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

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

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

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

ENVI 379(F) The Economics of Sustainability (Same as Economics 379) (Q)

GEOS 301(F) Structural Geology (Q)

INTR 315(S) Computational Biology (Same as Computer Science 315 and Physics 315) (Q)

LING 230(F) Introduction to Logic and Sematics (Same as Philosophy 131) (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 305(S) Applied Real Analysis (Q)

MATH 306(F) Chaos and Fractals (Q)

MATH 312(S) Abstract Algebra (Q)

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

MATH 315(F) Groups and Characters (Q)

MATH 322(F) Differential Geometry (Q)

MATH 323(S) Applied Topology (Q)

MATH 355(F) The Art of Creating Mathematics (Q)

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

MATH 373(S) Investment Mathematics (Q)

MATH 415(S) Geometric Group Theory (Q)

MATH 416T(F) Diophantine Analysis (Q)

MATH 419(S) Algebraic Number 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 341(F) Bayesian Statistics (Q)

STAT 346(S) Regression and Forecasting (Q)

STAT 442T(S) Computational Statistics and Data Mining (Q)

PHIL 131(F) Introduction to Logic and Sematics (Same as Linguistics 230) (Q)

PHYS 107(F) Newton, Einstein, and Beyond (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 315(S) Computational Biology (Same as Computer Science 315 and INTR 315) (Q)