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Math 2150 DISCRETE STRUCTURES (4) 2005
Catalog Description
Topics in discrete mathematics. Elementary logic, set theory and relations; induction, enumeration techniques, recurrence relations, trees and graphs. Boolean algebra, algorithm analysis. Prerequisite: Math 1304.
Note to the instructor: This course covers a variety of topics, intro- ducing students to some interesting and useful areas of mathematics. This class, together with linear algebra, serve to show lower- division students what more there is to math than calculus. Also, a key goal of the course is better problem-solving and proof techniques by all of the students. The course should also show students how discrete mathematics is used.
Topics covered:
Sets, operations on sets
Relations and functions: binary relations, orders, equivalence relations and partitions Logic and propositional calculus Boolean algebra
Methods of proof: what is a proof? how does one do a proof? Induction proof techniques
Recursive definitions and algorithms: mathematical view
Combinatorics: permutations, combinations
Graphs: connectivity, trees, spanning trees, paths, etc.
Algorithms: integers and alogithms, number theory, complexity
Requirements and suggestions for the course:
- Emphasize problem-solving techniques. Try to help students understand how to approach challenging problems.
- Emphasize proofs. Students should be able to identify a good proof, and should be able to construct proofs of their own. They should understand proof by contradiction, induction, etc.
- Cover applications of fields where possible, especially to areas of Computer Science.
- Good communication skills are required on all written work.
- Group discussions and problem-solving sessions are encouraged.
- Various mathematical systems are covered in the course. Students should be exposed to the basic ideas and encouraged to take further courses.
Texts:
Rosen : Discrete Mathematics and its Applications
Ross and Wright: Discrete Mathematics
Mott, Kandel, Baker: Discrete Mathematics for Computer Scientists and Mathematicians