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Phase V: Implementation
SKILLS AND CONTENTS REQUIREMENT
Quantitative and Formal Reasoning
- Definition for Bulletin:
- Williams students should be adept at understanding and communicating quantitative information. This skill demands the ability to apply a formal apparatus to the making of decisions, a comfort with numbers, and a possession of the research tools necessary to accumulate data to support or disprove hypotheses. Prior to their senior year, all students must satisfactorily complete a Quantitative and Formal Reasoning (QFR) course. Those students who receive a quantitative studies bar as incoming first-year students are required to complete MATH 100 or 101 before taking a course that fulfills 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).
- Further Explanation for Departments:
- QFR courses must have regular and substantial problem sets in which quantitative and formal reasoning skills are practiced and evaluated. Courses which require only a few illustrative problems to be solved, that involve merely plugging numbers into formulae, or that spend only a small portion of the semester on formal skills would not qualify for QFR designation.
While qualitative descriptions of scientific and mathematical topics can be worthwhile approaches to a discipline, these are not the main thrust of a QFR course. This is not to say that prose answers can play no role in a QFR course. In order to meet the QFR requirement, however, a course must clearly emphasize the skills of quantitative and formal reasoning. Translating real world phenomena into a mathematical description, computing quantitative results, and relating those results in words are the sorts of skills we would like to develop in a QFR course.
Although many courses in the department of Mathematics and Statistics would fulfill the requirement, by no means should QFR courses be limited to this department. A diverse set of offerings from a variety of departments emphasize the use of multistep mathematical, statistical, or logical inference. These include courses such as:Computer Science 134 - Introduction to Computer Science
among many others.
Economics 255 - Econometrics
Philosophy 103 - Logic and Language
Physics 141 - Particles and Waves - Enriched
Psychology 201 - Experimentation and Statistics
Courses to be designated as QFR must be approved by the CEP.