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SMC|Academic Programs|Mathematics|Math 10 - Discrete Structures

Math 10 - Discrete Structures

Course Details

Description

This course is intended for computer science, engineering and mathematics majors. Topics include sets and relations, permutations and combinations, graphs and trees, induction and Boolean algebras.

Prerequisites

Math 8

How It Transfers

UC, CSU IGETC AREA 2 (Mathematical Concepts)

Textbook

Roman, Steven, An Introduction to Discrete Mathematics, Harcourt Brace Javanovich, Inc., 1989

Mathematics Skills Associated With This Course

 

Entry Level Skills

 

Skills the instructor assumes you know prior to enrollment in this course

  • Differentiate and integrate exponential, logarithmic, hyperbolic functions.
  • Use various techniques of integrations and applications.
  • Analyze infinite series (congruence and divergence).
  • Use Power and Taylor series to express an infinite series. 
  • Recognize indeterminant forms and improper integral (using polar coordinates or parametric equations). 
  • Use analytical geometry (rotation of axes) to differentiate and integrate. 
  • Know the binomial theorem.

 

 

Course Objectives

Skills to be learned during this course

  • Prove propositions using techniques including mathematical induction, contradiction and contrapositive.
  • Prove logical equivalence of compound statements using truth tables and properties of conjunction, disjunction and negation.
  • Translate an English argument into symbolic form using logical connectives, and determine whether or not an argument is valid, both with and without using truth tables
  • Find a disjunctive normal form for a Boolean function.
  • Demonstrate the application of Boolean functions to logic circuits.
  • Refine logic circuits using Karnaugh maps.
  • Determine whether a relation is reflexive, symmetric, antisymmetric or transitive.
  • Prove and use theorems about equivalence relations and orderings.
  • Use permutations, combinations and multinomial coefficients to solve basic combinatorial problems.
  • Solve combinatorial problems using the pigeonhole principle, distribution, and the principle of inclusion-exclusion.
  • Verify binomial coefficient identities by combinatorial arguments.
  • Solve first and second order recurrence relations
  • Prove theorems and use algorithms from graph theory related to connectedness, Eulerian graphs, and rees.
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