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Size: 770 KB

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Categories:

1. Home Study
2. Visualization
3. Class or Laboratory
4. Math and Computers
5. Course

Subjects:

1. Logic
2. Permutations
3. Counting
4. Iteration and Recursion
5. Probability

Title: Discrete Mathematics 2: Counting, Recursion, and Logic: Next Steps

Book Description: While the first half of the course works with finite sets from a universe of 46 animals, in the second half, we work with two types of sets:

Finite sets of numbers, and
Products of finite sets of numbers.

We examine three ways to define sets. The first is by recursive definition, the second is by propositions, and the third is by algebra, that is, through the use of Boolean Operations, Products, and the construction of images and preimages of functions and relations.
The second half of the course (7-8 weeks) could cover the topics in the sequence of lectures:

1. Iteration and Recursion
2. The Art of Searching
3. Sets defined by Propositions
4. Critical Path Analysis
5. The Art of Counting
6. Automatic Problem Solving
7. Relations and Functions
8. Graphs and Logic
9. Digraphs as Relations

The following lab activities accompany these lectures:

1. Recursion Lab
2. Path Finder Lab
3. Number Set Constructor
4. Rule-Based System Lab
5. Relations/Functions Lab
6. Workshop
7. Graph Constructor
8. Fly-by-Night Airline

Author: James White

Contained in Discrete Mathematics Course.

Suggested Use: Second half of a 14-week course in Discrete Mathematics. The above list reproduces the titles of lectures and laboratories (Readings) and the Laboratory Instructions for the second half of a two part 14-week course in Discrete Mathematics. The Readings are reproduced first. These guide the student through the sequence of topics in the course.
The lectures and laboratories reproduced here also appear in the WorkBook (online) and in the accompanying documentation, and may be printed individually. After the readings, we have reproduced the Laboratory Instructions. These are meant to be read separately from the Readings.
These instructions also appear in the WorkBook in the various laboratory environments under the buttons labeled: Instructions.
The documentation for the first part of this course appears in Discrete Mathematics 1.

The course is an experiment in interactive mathematics, and it follows the Text: Discrete Mathematics, by Norman Biggs, Oxford University Press. It contains a Set/Graph Theory Language that supports many of the explorations, and it makes MathScript available to readers so that they may design their own programs to explore various aspects of the subject. Teachers may create their own online lectures, and follow different texts. The documentation is intended to be a guide for the teacher into the interactive explorations. It is hoped that in any case the laboratory environments will be useful for them in the design of their interactive courses. To help fix ideas, the above was the syllabus for the course offered by James White at California State University, at Monterey Bay, Fall, 1997.

Topics: set theory, logic, propositional calculus, boolean algebra, relations, iteration, recursion, counting, critical paths, prolog, automatic theorem proving, ruleset, inference engine function composition, permutations, demorgans laws, order, cardinality, digraphs

Number of Pages: 20

Animation: Yes

Grade Level: