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Math 2305: Discrete Mathematics

This course is designed to prepare math, computer science, and engineering majors for a
background in abstraction, notation, and critical thinking for the mathematics most directly
related to computer science. Topics include: logic, relations, functions, basic set theory,
countability and counting arguments, proof techniques, mathematical induction, combinatorics,
discrete probability, recursion, sequence and recurrence, elementary number theory, graph
theory, and mathematical proof techniques.

Prerequisite: MATH 2313 or 2413 Calculus I

Learning Outcomes
Upon successful completion of this course, students will:

  1. Construct mathematical arguments using logical connectives and quantifiers.
  2. Verify the correctness of an argument using propositional and predicate logic and truth
  3. Demonstrate the ability to solve problems using counting techniques and combinatorics in
    the context of discrete probability. 4. Solve problems involving recurrence relations and
    generating functions.
  4. Use graphs and trees as tools to visualize and simplify situations.
  5. Perform operations on discrete structures such as sets, functions, relations, and sequences.
  6. Construct proofs using direct proof, proof by contraposition, proof by contradiction, proof by
    cases, and mathematical induction.
  7. Apply algorithms and use definitions to solve problems to prove statements in elementary
    number theory.

Required Reading
“Discrete Mathematics and Its Applications” by Kenneth Rosen, McGraw Hill, 8th edition

Recommended Reading
1. Schaum’s Outline of Discrete Mathematics, Third Edition (Schaum’s Outlines) 3rd Edition by
Seymour Lipschutz (Author)
2. Discrete Mathematics: An Open Introduction
By Oscar Levin (Author)

3. Introductory Discrete Mathematics by V. K. Balakrishnan

4. Mathematical Maturity via Discrete Mathematics (Dover Books on Mathematics)
by Vadim Ponomarenko (Author)

List of discussion/lecture topics

1: The Foundations: Logic and Proofs
2: Basic Structures: Sets, Functions, Sequences, Sums, Matrices
3: Algorithms
4: Number Theory and Cryptography
5: Induction and Recursion
6: Counting
7: Discrete Probability
8: Advanced Counting Techniques
9: Relations
10: Graphs
11: Trees
12: Boolean Algebra
13: Modeling Computation

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