Prerequisite: Math 111.

Hours: 3.

Text: Kenneth H. Rosen, Discrete Mathematics and Its Applications, 7th edition.

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.

Class attendance is strongly encouraged. In addition to new material, important course information will be given in class, sometimes handouts will be given. Please do not be late. The class will start on time. Pay attention. Stay on task. Please put away any phones and other distracting gadgets. Take notes. No recording or taking pictures are allowed during class. Questions addressed to the instructor are welcome at any time during class. I will sometimes ask if there are any questions, but if needed, feel free to ask for a clarification at other times as well.

Exams: There will be three 50 mins. long tests and one 2 hrs. long final comprehensive exam. All tests are given in class. See schedule for exam dates. 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. In most cases, you will be expected to take the test before it is given in class. If you are sick or have other emergency and need to take the test after the scheduled time, you will need to provide documentation.

There will be weekly homework due Wednesday at 11:59 pm. There are two ways to submit the homework.
(1) Recommended: use overleaf (LaTeX), and share your overleaf file. Use the "share" feature and give me the "edit" permissions. Then I will type my feedback in the file itself. See schedule for a basic homework template, although you may use your own if you wish.
Also recommended: you are encouraged to (but you don't have to) do the homework in a group of 2-3 people. In this case, make and share only one file. Make sure that you write the names of all group members in the file. If desired, you may change your group composition from one homework to another, and you may do some homeworks as a group and some individually.
(2) Upload to Canvas in PDF format. It is strongly recommended that you use LaTeX if you choose to type up your homework. It is not a good idea to use Word because some formulas may not look correctly. However, if you do use any other editor than LaTeX, you must save your file in PDF format (not .doc format). If you hand-write your solutions, please use a black or dark blue pen, write large, and use a scanning app (e.g. Adobe Scan) to scan your paper with good quality. Check that it is easily legible. If the paper is written in light color or photographed with bad focus/resolution and is not legible, it will not be graded. You may only submit up to 3 homeworks late, and no later than on Friday (2 days after the due date). If you are sick and unable to complete an assignment on time, please notify your instructor ASAP and ask for a longer extension. However, you will need a documentation 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 that working on your homework together is allowed and encouraged. See above for details. However, please do make sure that everyone in your homework group participates and understands all solutions. In the end, it is your responsibility to learn the material well.

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 and any instances will be reported to the appropriate office. 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. Once we return to F2F instruction, all safety protocols must be followed. In particular, masks must be worn properly at all times. Failure to comply will result in removal from class and a report on disruptive classroom behavior will be filed.

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.