Approach 1: Tony Ralston et al in early 1980s

• Proposal, largely from Conference on Discrete Mathematics in the Mathematics Curriculum, Williams College, June 1982
• 1 semester: calculus with discrete mathematics
  1 semester: discrete mathematics
  2 semesters: calculus and linear algebra
• early treatment of discrete mathematics added breadth and emphasis on proofs
• reaction to perceived dismal state of calculus (before calculus reform)
• historically, calculus reform took a different approach
• Observation: early coverage of discrete mathematics delayed calculus and differential equations needed by physics, engineering, etc.
• Result: this approach in wide disuse today

Approach 2: Currently in Use at Grinnell

Grinnell's current curriculum moves discrete mathematics to the second semester of the sophomore year, with a calculus/linear algebra prerequisite.

• Advantages:
  • Incoming students have a common mathematics track, regardless of potential major
  • Discrete mathematics covered at a relatively sophisticated level
  • Students need not choose continuous or discrete math until their interests have matured (at least somewhat)
  • Physics and CS majors can follow different tracks after linear algebra
  • Both differential equations and combinatorics satisfy some prerequisites for various upper-level mathematics courses.
• Disadvantages:
  • CS students study discrete mathematics relatively late
  • CS students must take 3 semesters of mathematics before getting to the topics most relevant to their interests
  • The lengthy prerequisite chain makes the addition of a second semester of discrete mathematics difficult.
  • Students starting mathematics late have a difficult time catching up.

created May 30, 2003 last revised May 30, 2003

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