Prerequisite: Math 111.

Hours: 3.

Text: Kenneth H. Rosen, Discrete Mathematics and Its Applications, 5th edition (available on Amazon.com, not available in the campus bookstore).

Catalog Description: Counting techniques, matrix algebra, graphs, trees and networks, recurrence relations and generating functions, applied modern algebra.

Content: Topics to be covered include various counting techniques, permutations, combinations, binomial theorem and properties of binomial coefficients, principle of mathematical induction, pigeonhole principle, recursively defined sequences and functions, graphs, trees, and their applications. Since this course has MATH 111 as a prerequisite, the students are assumed to have some experience writing mathematical proofs. However, it is understood that many students take this course shortly after completing MATH 111. So some proof techiniques (e.g. the principle of mathematical induction) are explored at a greater depth, and thus this course prepares the students for more advanced mathematics classes.

Course goals
In addition to mastering the concepts listed in the course description, the students should:

• Master a variety of techniques for counting and enumeration.
• Recognize patterns and apply combinatorial arguments to a variety of problems.
• Improve problem solving skills.
• Practice writing mathematical proofs.
• Practice the communication and exposition of mathematical arguments.
• Apply techniques of elementary graph theory to solve a number of classical problems.

Learning Outcomes
Upon completion of this course, students should be able to:

• Use basic counting techniques to establish identities and recurrence relations.
• Use mathematical induction to establish various mathematical statements.
• Use inclusion-exclusion and the pigeonhole principle to establish various mathematical statements and formulae.
• Be familiarized with the method of abstraction and formal thinking.
• Prove elementary theorems about graphs.
• Determine the chromatic number of a given graph.

Grading policy: Your grade for the course will be based on your performance on exams and homework (more information on these below). The number of points awarded for these is as follows.

Exams: There will be three 50 mins. long tests and one 2 hrs. long final comprehensive exam. If for any reason you can not take a test at the scheduled time, please let your instructor know as soon as possible, and certainly before the test. See schedule for exam dates.

Class attendance is strongly encouraged. In addition to new material, important course information will be given in class, sometimes handouts will be given.

There will be weekly homework due Thursday at 12:30 pm (i.e. at the beginning of the class period). You may only submit up to 3 homeworks late, but not later than on Tuesday (5 days after the due date), at the beginning of class, since graded homeworks will usually be returned on Tuesday). If you are sick and unable to come to campus, please notify your instructor ASAP and ask for a longer extension.

Extra Help: It is essential not to fall behind, because each class may use the material studied previously. If you have trouble with some material, seek help in the following ways:

• Ask your instructor, either in class or privately. Don't be shy to ask questions. If you don't understand something, chances are very high that somebody else doesn't understand that either. My contact info is given on the course web page.
• Work with your classmates. Note: working on your homework together is allowed and encouraged, however, every student should write down their solutions on their own, in their own words. Also, if you have worked with someone, please indicate that on your paper.

Computers: At California State University, Fresno, computers and communications links to remote resources are recognized as being integral to the education and research experience. Every student is required to have his/her own computer or have other personal access to a workstation (including a modem and a printer) with all the recommended software. The minimum and recommended standards for the workstations and software, which may vary by academic major, are updated periodically and are available from Information Technology Services or the Universit Bookstore. In the curriculum and class assignments, students are presumed to have 24-hour access to a computer workstation and the necessary communication links to the University's information resources.

Students with disabilities: upon identifying themselves to the University, students with disabilities will receive necessary accommodation for learning and evaluation. For more information, see http://www.fresnostate.edu/studentaffairs/ssd/.

Academic honesty: cheating and plagiarism will not be tolerated in this class. For information on the University's policy, see the University Catalog (section Policies and Regulations).

Honor Code: Members of the CSU Fresno academic community adhere to principles of academic integrity and mutual respect while engaged in university work and related activities. You should:

• understand or seek clarification about expectations for academic integrity in this course (including no cheating, plagiarism and inappropriate collaboration)
• neither give nor receive unauthorized aid on examinations or other course work that is used by the instructor as the basis of grading.
• take responsibility to monitor academic dishonesty in any form and to report it to the instructor or other appropriate official for action.

Disruptive Classroom Behavior: student conduct which disrupts the learning process will not be tolerated and may lead to disciplinary action and/or removal from class.

Copyright policy: Copyright laws and fair use policies protect the rights of those who have produced the material. The copy in this course has been provided for private study, scholarship, or research. Other uses may require permission from the copyright holder. The user of this work is responsible for adhering to copyright law of the U.S. (Title 17, U.S. Code). To help you familiarize yourself with copyright and fair use policies, the University encourages you to visit its copyright web page: http://www.fresnostate.edu/home/about/copyright.html. Digital Campus course web sites contains material protected by copyrights held by the instructor, other individuals or institutions. Such material is used for educational purposes in accord with copyright law and/or with permission given by the owners of the original material. You may download one copy of the materials on any single computer for non-commercial, personal, or educational purposes only, provided that you (1) do not modify it, (2) use it only for the duration of this course, and (3) include both this notice and any copyright notice originally included with the material. Beyond this use, no material from the course web site may be copied, reproduced, re-published, uploaded, posted, transmitted, or distributed in any way without the permission of the original copyright holder. The instructor assumes no responsibility for individuals who improperly use copyrighted material placed on the web site.

Subject to Change: This syllabus and schedule are subject to change in the event of extenuating circumstances. If you are absent from class, it is your responsibility to check on announcements made while you were absent.