Basic Idea: Combine continuous and discrete mathematics in a highly
integrated sequence (perhaps including some probability and statistics)
Reorganize calculus, linear algebra, and differential equations
Add some topics from discrete mathematics early
Example: Core Mathematics Curriculum Reform at Harvey Mudd
College covers linear algebra and discrete dynamical systems in the
first semester of the first year (Math 12), probability and statistics in the third
semester (Math 62), and more linear algebra in the four semester (Math
63). (The core sequence still emphasizes continuous mathematics, but it
contains more discrete mathematics earlier than than a traditional calculus sequence.)
Example: West Point apparently trying a similar approach
Advantages:
The common 2-year sequence works well for many disciplines
Topics can be introduced "just-in-time" for many disciplines
Since all students take the same sequence, advising is relatively easy
Disadvantages:
At both Harvey Mudd and West Point, computer science majors still must take
a fifth course in discrete mathematics (and maybe a sixth) to get the
proper background
Details of the Harvey Mudd core assume high school students will have
completed a full year of calculus before college
Variation: Add some discrete mathematics topics to
existing courses
In precalculus, provide a different context for existing topics (in much
the same way as a slow-paced calculus course)
(suggested by Shelly Gordon, SUNY at Farmingdale)
In calculus, provide modest coverage of a few topics (e.g., difference
equations)
Advantages:
Difference equations can help motivate differential equations
Experience with proofs may seem more natural when considering relatively
simple examples from discrete mathematics
Disadvantages:
All evidence suggests that this approach cannot cover enough discrete
mathematics to meet the needs of computer science, so CS students still
must take another course
If discrete mathematics covered in precalculus, then well prepared CS
students might have to take precalculus for the discrete mathematics --
even though they are ready for a more rigorous course
