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## Master Syllabus

 Administrative Unit: Computer and Mathematical Sciences Department Course Prefix and Number: MATH 225 Course Title: Discrete Mathematics I
Number of:
 Credit Hours 3
 Lecture Hours 3
 Lab Hours 0
 Catalog Description: This course provides a foundation in formal mathematics and theorem-proving. Topics include functions, relations, sets, simple proof techniques, propositional logic, elementary number theory, the fundamentals of counting, recursion, and an introduction to algorithms. Prerequisite: Grade of C or higher in MATH 201. Prerequisite(s) / Corequisite(s): Grade of C or higher in MATH 201. Course Rotation for Day Program: Offered Fall & Spring. Text(s): Most current editions of the following:Discrete Mathematics and its ApplicationsBy Rosen ( Science Engineering & Math) Recommended Course Learning Outcomes Apply the fundamental laws of logic and rules of inference to form logical arguments. Write mathematical proofs including proofs by contrapositive, contradiction and induction. Demonstrate understanding of the concept of a function including the concepts: range, domain, one-to-one, onto and inverse. Describe and explain basic set theory definitions and operations. Determine the complexity of an algorithm and the growth rates of functions. Employ the basic properties of integers such as divisibility, primes and congruencies to solve basic number theory problems. Calculate numbers of possible outcomes of elementary combinatorial processes using the sum and product rules, permutations and combinations. Major Topics/Skills to be Covered: Calculate numbers of possible outcomes of elementary combinatorial processes using the sum and product rules, permutations and combinations. Illustrate the use of quantifiers to form mathematical statements and arguments. Apply the fundamental laws of logic and rules of inference to analyze arguments and to form logical arguments. Describe and explain basic set theory definitions and use the set theoretic operations. Describe and explain the well-ordering principles and use in the method of proof by induction. Employ the basic properties of integers such as divisibility, primes and congruencies to solve basic number theory problems. Demonstrate a thorough knowledge of the concept of a function including the concepts: range, domain, one-to-one, into, onto, and inverse. Describe and explain the recursive definition of sequences and functions. Use equivalence relations to partition sets. Determine the complexity of an algorithm. Recommended maximum class size for this course: 20 Library Resources: Online databases are available at the Columbia College Stafford Library.  You may access them using your CougarTrack login and password when prompted.
Prepared by: Suzanne Tourville Date: April 1, 2015
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this course for Columbia College are expected to facilitate learning pursuant to the course learning outcomes and cover the subjects listed in the Major Topics/Skills to be Covered section. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.

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