# MAT 281 Discrete Mathematics

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### Course Description

The official course description in the university catalog says "Matrix algebra, graph theory, trees, combinatorics, Boolean algebra; with applications to computers and computer programming."

3 units credit.

Here is a more recent, unofficial, description reflecting the current emphasis in MAT 281: "Logic and sets, functions and relations, Boolean algebra and circuit design, mathematical induction, recursion, modular arithmetic and elementary number theory, counting techniques and combinatorics, big-O notation and complexity of algorithms, graphs and trees; with applications to computers and computer programming."

### Prerequisites

MAT 153, and CSC 121 or MAT 241 or CSC 111 or equivalent, with grades C or better.

### Text

Texts are chosen by the instructor. For example:

Discrete Structures with Contemporary Applications, by A. Stanoyevitch. Chapman & Hall (2011)

### Course Requirements, Tentative Schedule of Class Meetings and Topics, Readings, Assignments and Due dates, Exams

A schedule of class meetings, topics, assignments, due dates, exam dates, etc. will be provided by instructor. See your class syllabus.

Here is an example course, based on the above text.

Week Topics
1-2 Logic and sets.
3-4 Functions and relations, equivalence relations
5-6 Mathematical induction and recursion
7-8 Modular arithmetic and elementary number theory
9-10 Counting techniques and combinatorics
11-12 Big-O notation and the complexity of algorityms
13-14 Graphs and trees
15 Boolean algebra and circuit design

The final exam is given at the date and time announced in the Schedule of Classes.

### Learning Objectives

MAT 281 provides mathematical foundations for various topics in discrete mathematics including those necessary for core computer science courses. Upon completing MAT 281 students will

• construct and understand rigorous logical arguments and inferences
• construct and understand proofs by mathematical induction
• understand and use permutations, combinations, binomial coefficients, the pigeonhole principle, in algorithms, counting arguments, and proofs
• use "big-oh" and "big-omega" notation
• analyze the complexity of simple algorithms
• use and understand basic concepts and algorithms of graph theory
• use and understand combinatorial circuits and their properties; Boolean functions, and synthesis of circuits.

### Computers and Calculators, Computer Literacy

Most instructors encourage the use of machines, calculators computers, phones etc., for analyzing data. The use of machines may be restricted during examinations or at certain other times. Ask your instructor for the policy in your class.

Students are not expected to be programmers or to know any particular computer language before starting this class. Some instructors may expect students to be able to access information on the internet, or to use calculators, or to learn to use particular software with instruction. Basic skill in algebra and the use of mathematical symbols, order of operations etc., and the willingness to read and follow instruction manuals and help files will suffice.

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in this course. The instructor determines the relative weights of these factors and the grading scale. See the syllabus for your particular class.

### Location of Class Meetings

Classes meet on the dates and room announced in the official Schedule of Classes. This is a traditional, face-to-face class.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates, Make-Up Work, Missed Exams, and Extra-Credit Assignments

Due dates and policy regarding make-up work and missed exams are set by the instructor. Instructors may, or may not, choose to offer extra credit assignments. If extra credit assignments are offered they will be available to all students.

The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

### Accomodations for Students with Disabilities

Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how we best can help you. All disclosures of disabilities will be kept strictly confidential. Please note: you must register with DSS to arrange an no accommodation. For information call (310) 243-3660 or send an email message to dss@csudh.edu or visit the DSS website http://www4.csudh.edu/dss/contact-us/index or visit their office WH D-180

### Behavioral Expectations

We all are adults so behavior rarely is an issue. Just follow the Golden Rule: "do unto others as you would have them do unto you" then everything will be fine.

The university must maintain a classroom environment that is suitable for learning, so anyone who insists on disrupting that environment will be expelled from the class.

Revision history:

Revised spring 2011 (A. Stanoyevitch), 1/10/16 (G. Jennings).