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Math 145. Problem solving. Fall 2022.

Prerequisite: Math 111.

Hours: 3.

Textbook: M. Nogin, Strategies of Problem Solving, Third Edition (PDF is posted in Files on Canvas and on the schedule page).

Content: Topics to be covered include: Principle of Mathematical Induction, Dirichlet's box principle (also called Pigeonhole principle), number theory, case analysis, working backwards, mathematical games and algorithms, invariants, coloring proofs, graphs, combinatorics, calculus. Other topics may also be discussed. Some problems will be from math competitions and journals. Students will be asked to present their solutions on the board. Working in groups is encouraged. The purpose of this class is to develop/improve problem solving skills, communicate your mathematical ideas, and to practice writing proofs in a correct and complete way.

Catalog description: A study of formulation of problems into mathematical form; analysis of methods of attack such as specialization, generalization, analogy, induction, recursion, etc. applied to a variety of non-routine problems. Topics will be handled through student presentation.

Course goals
Introduce students to a variety of problem solving techniques as well as challenging ("non-routine") problems accessible to 7-12 graders; practice communicating mathematical ideas verbally and symbolically in the problem solving setting.

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

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

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 class presentations, submitting solutions of problems to jounals, and participating in Math Department's problem solving activities outside (more information below). The number of points awarded for these are shown below.

Test 1 60 points
Test 2 60 points
Test 3 60 points
Final exam 90 points
Problem of the day presentations 40 points
Written Homework 150 points
Participation in departmental problem solving activities 40 points
Total 500 points

Points earned grade
437.5-500 (87.5-100%) A
375-437 (75-87.4%) B
312.5-374.5 (62.5-74.9%) C
250-312 (50-62.4%) D
0-249.5 (0-49.9%) F

Exams: There will be three tests (50 minutes long each) and one final comprehensive exam (2 hours long). 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.

Class attendance is required. One "problem 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. Up to three absences during the semester for undocumented reasons are allowed. If you are unable to notify the instructor before class or exceed three absences, 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 may be distributed.

There will be weekly homework due Friday night at 11:59 pm (with some exceptions due to holidays at the end of the semester when two homeworks will be due Wednesday night), usually on the topic(s) covered recently (roughly during the preceding week). There will be 11 written homework assignments. Each homework will consist of 3 problems and will be worth 15 points total. The lowest homework score 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 purpose of this class is to learn to solve unfamiliar, non-routine problems). You should do homework in groups of 2-4 people. If you do not have a group, contact your instructor. The groups do not have to be the same for all homeworks: you may do one homework with one person/group and another homework with another. However, if you decide to change your group, you should notify your group members well in advance (2 weeks notice is recommended.) Write the names of all group members on the first page clearly. Please make sure that everyone in the group understands and agrees with all solutions. If a member of your group did not participate, do not include their name on the homework. Remember that the primary goal of homework is to learn, so if someone else does a problem and you do not participate, you don't learn anything. You need to actively participate to make sure you learn well. The whole group will receive the same grade. 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 any of your classmates even if they are not in your group. However, your group has to write all solutions by yourself, in your own words. Any copying will be considered cheating and will not be tolerated. Homework has to be typed in LaTeX and submitted through overleaf. Please share your homework file before the deadline, and give your instructor "can edit" permissions. No late submissions will be accepted unless you are sick or have another serious reason to delay homework (notify your instructor in advance, or provide doctor's note, etc.) Tip: share your overleaf file with your instructor as soon as you start working on your homework. It will not be checked or graded before the deadline, but that way you will be sure that you turned it in on time. Continue working on your homework at any time before the deadline, however, you may not make any changes after the deadline. If any edits are made after the deadline, this will be considered cheating, and your homework will not be accepted.

Participation in departmental problem solving activities is expected and counts toward your grade in the course. Below are the activities supported by the Mathematics Department. You are welcome to participate in any of these. Choose anything that interests you and fits your schedule. Your instructor will be present and take attendance at the Journal Problem Solving Group meetings and Math Circle, grades 7-8. For all other sessions, report your attendance via this Google form.

Another opportunity for extra credit: to encourage you to read the book carefully (and to reward you for doing so) 1 point of extra credit will be given for reporting a new mistake/typo in the textbook. The list of reported but not yet fixed mistakes is here.

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:

If you are having any difficulties, seek help immediately - don't wait until it is too late to recover from falling behind, or failing to understand a concept!

Students with disabilities: upon identifying themselves to the University, students with disabilities will receive necessary accommodation for learning and evaluation. For more information, see

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:

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.

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 University 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.

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.

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Last major revision: 20 August 2022.