20804265Introduction to Discrete Mathematics
Course Information
Description
This course introduces students to discrete mathematical techniques and structures, such as logic, integers, recursion, sets, counting, probability, graphs, trees, and algorithms. The course also develops students' ability to think mathematically and write proofs. Many applications are drawn from computer science, and the course prepares computer science students for future study, but programming experience is not required. The course is also suitable for majors in mathematics, math education, and engineering, as well as anyone interested in the beauty of numbers, patterns, and logical reasoning.
Total Credits
3
Course Competencies
  1. Use symbolic logic to express and apply formal reasoning
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
    through active participation in class discussions and activities
    Criteria
    translate English sentences into logical statements, including compound and conditional statements, and statements using predicates and quantifiers
    construct truth tables for the above types of statements
    identify logically equivalent statements
    identify valid and invalid arguments

  2. Write formal proofs
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
    through active participation in class discussions and activities
    Criteria
    construct clear, concise, and valid arguments using direct proof
    construct clear, concise, and valid arguments using counter examples
    construct clear, concise, and valid arguments using contradiction
    you construct clear, concise, and valid arguments using contraposition
    you construct clear, concise, and valid arguments using proof by induction

  3. Explore sequences and recursion
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
    through active participation in class discussions and activities
    Criteria
    understand and construct formulas for sequences
    use isummation and product notation
    understand and construct recursively defined sequences
    solve recurrence relations by iteration
    prove propositions about sequences and recursion

  4. Explore sets, functions, and relations
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
    through active participation in class discussions and activities
    Criteria
    know and apply the definitions of sets, subsets, partitions, the empty set, power sets, and Cartesian products
    know and apply the definitions of functions defined on general sets
    determine whether a function is one-to-one and/or onto
    know and apply the definitions of a relation and its inverse
    determine whether relations are reflexive, symmetric, and/or transitive
    know and apply the definitions of equivalence relations and equivalence classes
    prove propositions about sets, functions, and relations

  5. Apply the fundamental techniques of counting
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
    through active participation in class discussions and activities
    Criteria
    use possibility trees and the multiplication rule to count events
    use formulas to count permutations
    use formulas to count combinations
    count elements of disjoint sets using the addition rule
    apply the Pigeonhole Principle
    prove propositions involving counting

  6. Explore graphs and trees
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
    through active participation in class discussions and activities
    Criteria
    know and apply the basic terminology of a graph
    translate relations into directed graphs
    apply the concept of degree
    determine whether a graph is a tree
    prove propositions about graphs and trees

  7. Apply the concepts of elementary number theory
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
    through active participation in class discussions and activities
    Criteria
    prove properties of divisibility
    use the Unique Factorization of Integers Theorem
    use the Quotient-Remainder Theorem
    use the Triangle Inequality
    know and apply the definitions of div and mod