Prerequisites: Math 111; EHD 50 (may be enrolled concurrently; or permission of instructor).

Hours: 3.

Content: Topics to be covered include: brief review of logic, types of proofs, and principle of mathematical induction; Dirichlet's box principle (also called pigeonhole principle), number theory, case study, invariants, coloring proofs, working backwards, geometry, mathematical games and algorithms, non-routine calculus problems, problems from math olympiads and journals. More topics may and probably will be added later. Students will be asked to present their solutions on the board. Working in groups is encouraged. The purpose of this class is to learn to solve non-standard problems, and also to practice writing proofs in a complete and correct way.

See also the Catalog Description.

Course goals
Introduce students to a variety of problem solving techniques as well as challenging ("non-routine") problems accessible to 7-12 graders; practice writing rigorous proofs in the problem solving setting.

Learning objectives
Upon completion of this course, students should know/understand:

• Importance of a formal (rigorous) proof
• Meaning of logical operations (and, or, negation, implication) and quantifiers (universality and existence)
• Difference between different types of proof (direct, by contradiction, by contrapositive, by example/counterexample, etc.)
• Principle of Mathematical Induction
• Dirichlet's Box Principle
• Divisibility properties of integer numbers; congruences
• The concept of invariant
• Basic graph theory terminology (vertex, edge, degree of a vertex, etc.)

Primary learning outcomes
Upon completion of this course, students will be able to do:

• Translate word problems into mathematical equations and relations
• Recognize problems which can be solved using one of the following techniques:
  • Dirichlet's Box Principle
  • Mathematical Induction
  • Divisibility and/or Congruences
  • Case Study
  • Patterns
  • Invariants
  • Coloring
  • Symmetry
  • Graphs
  • Working backwards
• Set up and solve appropriate equations for solving calculus problems involving slopes and areas.

Grading policy: Your grade for the course will be based mostly on your performance on exams and homework (more information on these below). You will also receive points for submitting solutions of problems to jounals, class presentations, and reporting mistakes in the book. The number of points awarded for these are shown below.

Exams: There will be three 1-hour tests and one final comprehensive exam. Tests will be given in class. The final exam will be given during the final exam week. If for any reason you can not take a test at the scheduled time, please let me know as soon as possible, and certainly before the test. See schedule for exam dates. No books, notes, or calculators are allowed on any of the tests.
Solutions to past exams will be posted on the schedule page.

Class attendance is required. One or two "problem(s) of the day" will be assigned for each class period. Students will be randomly called to present their ideas/solutions. These presentations are part of your grade. If you are called and you are absent, you will receive zero points for your presentation. (If you are sick or have another serious reason to miss a class, notify your instructor before the class to be missed; if you are unable to notify the instructor before class, please provide doctor's note, etc.) In addition to these presentations and new material/problems discussions, important course information will be given in class, sometimes handouts will be distributed.

There will be weekly homework due Friday at 1 pm, usually on the topic(s) of the preceding week. There will be 13 written homework assignments. Each homework will consist of 3-5 problems and will be worth 15 points total. Three lowest homework scores will be dropped. Homework problems will be new problems, sometimes somewhat similar to the problems discussed in class and sometimes quite different. You may have to spend a few hours on each homework (remember, the main pupose of this class is to learn to solve unfamiliar, non-routing problems). If you have any questions, or need someone to listen to and possibly comment on your ideas, please do not hesitate to ask your instructor (this is what her office hours are for!). Also, you are encouraged to work with your classmates. Please bring your homework to class. We will often discuss homework in class, so no late papers will be accepted unless you are sick or have another serious reason to miss the class.

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

• Ask me, either in class or privately. My contact info is given on the course web page. 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. In particular, you are more than welcome to ask questions about solutions in the book. But I will not help you with the homework problems. Those are for you to solve. Remember, the purpose of this class is for you to learn to solve non-routine problems. However, if you'd like to know a solution to a homework problem after it's due, let me know, and I'll be very glad to discuss the problem.
• Work with your classmates. Note: working on your homework together is allowed and even encouraged, however, every student should write down their solutions on their own. The best thing to do, after you have worked with other people, is to put aside all the notes you made, and write a complete solution from scratch, in your 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). 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.