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Mathematics 142

MATH 142
Discrete Mathematics

Catalog Entry

MATH 142. Discrete Mathematics
Three lecture hours (3).

Prerequisites: Mathematics major or permission of the instructor.

Introduces the student to discrete structures and mathematical tools which are used to represent, analyze, and manipulate discrete objects. These include sets, functions, relations, graphs, combinatorics, discrete probability, recurrence relations, mathematical induction, symbolic logic, and graphs and trees.

 

Detailed Description of Course

Course content includes:

  • Combinatorics
  • Critical Path Analysis
  • Matching Problems
  • Algorithms for Solving Problems
  • Permutations and Combinations
  • Basic Probability
  • Pigeonhole Principle
  • Multiplication Principle
  • Addition Principle
  • Sets
  • Set Operations
  • Equivalence relations
  • Division Algorithm
  • Congruence
  • Functions
  • Logic
  • Mathematical Induction
  • Symbolic Logic and truth tables
  • Methods of Proof
  • Graphs
  • Representations
  • Di-graphs
  • Paths and Circuits (including but not limited to Euler and Hamiltonian circuits and paths)
  • Trees
  • Spanning Trees
  • Minimal/Maximal Spanning Trees
  • Depth-First Search
  • Binary Trees
  • Recurrence relations
  • Sequences
  • Linear Functions
  • Pascal’s Triangle
  • Binomial Theorem

 

Detailed Description of Conduct of Course

In addition to lecture, students will work collaboratively on assignments created to help students understand the application of discrete mathematics concepts used in problem solving. Calculators and computers will be used to present and work the material in and outside class.

 

Student Goals and Objectives of the Course 

In accordance with the NCATE standards for discrete mathematics, students will be able to demonstrate knowledge of the concepts of discrete mathematics such as (but not limited to): Perform operations on sets, prove logical statements using truth tables, prove problems by mathematical induction, use counting properties to solve combinatorics problems, understand basic principles of Graph Theory such as: path, cycle, connected graphs, subgraphs, etc., determine the shortest path in weighted graphs as it occurs in practical problems, and understand and apply trees and (minimal) spanning trees. To problem solve discrete mathematics problems; students will understand the application of an algorithm by applying them to problem situations such as those involving search and optimization. Students will develop the ability to communicate mathematically.

 

Assessment Measures

Students will demonstrate content understanding via written (and/or oral) exams, written homework problems, collaborative work in class, and class discussion. Students may be required to complete a project.

 

Other Course Information

 

Review and Approval Date