The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proofs" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.
Discrete Mathematics (Quick Study Academic) download.zip
Course ObjectiveThe course objective is to provide students with an overview of discrete mathematics. Students will learn about topics such as logic and proofs, sets and functions, probability, recursion, graph theory, matrices, Boolean algebra and other important discrete math concepts.
Course Topics Category Objectives Introduction to Logic & Proofs Explain the applications of logic and propositions in mathematics; recognize problems with logical propositions. Sets & Functions in Discrete Math Discuss the functions of mathematical sets; explain the concept of cardinality; use sets to define functions. Counting Rules, Combinations & Permutations Define permutations and combinations; explain the pigeonhole principle; use induction to prove mathematical properties. Discrete Probability Find expected values using theoretical and empirical probability distributions. Binomial Probability Find binomial probabilities; determine a binomial random variable's mean and standard deviation. Recursion & Advanced Counting Explain recursive functions; recognize and solve recurrence relations problems; generate functions and explain inclusion/exclusion in mathematical sets. Principles of Graphs & Graph Theory Recognize the components of numeric graphs; distinguish between Euler and Hamilton paths; find the most efficient path in a graph. Trees in Discrete Mathematics Evaluate trees and their discrete math applications; explain the functions of binary search trees. Matrices in Discrete Math Recognize the elements of matrices and explain their mathematical applications and uses; perform addition, subtraction, multiplication, translation and rotation on matrices. Boolean Algebra & Logic Gates Explain Boolean logic; read truth tables and Karnaugh maps; evaluate logic that's used in various gates.
Description: Basic concepts of discrete mathematics: logic and set theory, proof techniques, relations, functions, combinations, recurrence relations, introduction to analysis of algorithms, and graph theory. Laboratory fee applies.SUNY GEN ED-n/a; NCC GEN ED-MATH Offered: Fall, Winterim, Spring, Summer
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