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:

	1.  Emphasize problem-solving techniques.  Try to help students
	    understand how to approach challenging problems.

	2.  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.
	
	3.  Cover applications of fields where possible, especially to
	    areas of Computer Science.

	4.  Good communication skills are required on all written work.

	5.  Group discussions and problem-solving sessions are encouraged.

	6.  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