Computer Science 203, Discrete Structures, is a required course for Computer Science Majors. The class covers proof techniques, counting methods, calculation, and problem-solving strategies through topics such as logic, sets, numbers, functions, relations, graphs, combinatorics, discrete probability, modular arithmetic, summations, and recurrences. Discrete mathematics is the mathematics of the integers {..., -2, -1, 0, 1, 2, ...}, which underlies all conventional discrete computers.

Students in this course will learn how to:

• Prove theorems
• Calculate, including solving summations and recurrences--both by hand and using Maple
• Count values
• Solve problems
• Communicate effectively using the language, vocabulary, and concepts of discrete mathematics.
Proof techniques including direct/indirect, contradiction, contrapositive, counterexample, epsilon-delta, counting arguments (e.g. Pigeon-hole Principle), diagonalization, and strong and weak mathematical induction will be covered. Counting methods include the fundamental principles of counting (addition and product rules), permutations, combinations, k-permutations, permutations with repeated elements, D'Alembert's method, urn model, principle of inclusion/exclusion, setting up and solving recurrences, partition and sum, and seat-of-the-pants approximations. Calculation topics include summations, recurrences (first- and second-order homogeneous and nonhomogeneous linear difference equations with constant coefficients), simplification, approximation by bounding, change of coordinates, and the symbolic and numerical math package Maple.

In fall 2002, some sections will use the textbook by Susanna S. Epp, and others will try the text by Kenneth H. Rosen. In December 2002, the instructors will decide which text to use in the future.

Chapters in Epp textbook covered (in order):

• Part I: Proofs (Chapters 5, 1, 2, 3, 4)
• Part II: Calculation (7, 8, 10--excluding 7.4, 7.6, 8.1)
• Part III: Counting (6, 7.4, 7.6, 8.1).

Chapters in Rosen textbbok covered (in order):

• Part I: Proofs (Chapters 1-3)
• Part II: Calculation (Chapters 5.1-5.4, 6-7)
• Part III: Counting (Chapters 4, 5.5-5.6))

All instructors are strongly urged to ensure common minimum standards as described in the semester schedule and lecture descriptions followed by course coorinator Dr. Alan T. Sherman.

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