Math 479 Syllabus – Fall 2022

Office Hours:  T-Th 5:15-6:00pm, 7:40-8:10pm and beyond (or following the end of Math 479, whichever comes last) and by appointment.

[Note: Office hours may be held in LSC 316, LSC 125, or LLSC 311C. Check all three locations.]

Required Textbooks: P. Zeitz, The Art and Craft of Problem Solving, Wiley, 2nd edition, ISBN: 0-471-78901-1

Course Prerequisites: intense love of mathematics.  Oh, and also MATH 221 and either MATH 142 or MATH 299, or else permission of the instructor.

Course Description: An introduction to the creative, inspirational, and playful side of mathematics exemplified in high quality middle school, high school, and undergraduate mathematics competitions and mathematical research. Emphasis is placed on building a repertoire of mathematical strategies and tactics, then applying these methods in unfamiliar situations.

Course Objective: To provide the student with an introduction to the joys of mathematical problem solving by actually solving problems. Students should strive to improve their ability to solve mathematical problems through hands-on practice and obtain an understanding of the strategies, tactics, and tools of the problem solver as illustrated by the textbook and the instructor.

Course Format: This course will not be a traditional lecture-style mathematics course, but rather is a training session in problem solving mathematics.

Consider the difference between taking a course on the theory of running (where you learn about the nutrition, form, training programs, types of sneakers, various events, strategies, and history of the sport) vs. taking a training program in running (where you actually run and run and run lots of miles to get in shape even if you hardly know what you are doing).

Or consider the difference between taking a course in music and piano theory (where you learn how to interpret sheet music and learn the parts of the piano and listen to famous piano compositions on CD) vs. taking piano lessons where you actually practice and practice and practice playing the piano yourself.

Similarly our course is not a course about the theory of problem solving (where you learn about what others say about problem solving or the history of famous solutions to problems) but rather it is hands-on training in problem solving that will be primarily focused on having you solve problems yourself, no matter how good or bad at it you may be.

Just as any runner, no matter how fit or talented, benefits from lots of running in training, so shall you benefit from lots of problem solving. Rather than interacting with you in the role of instructor, I will interact with you in the role of coach.

Thus, rather than learn material related to problem solving, and then working exercises related to that material, we will do things the other way around.  You will be given problems to solve, and if a particular problem requires that you learn a particular topic in mathematics, then we will learn that topic at that point.  So the course will be problem-driven, rather than topic-driven. The problems will motivate the topics rather than the other way around.

Because of the unusual nature of the course, you should think of this class as you might think of a physics lab or chemistry lab course, where most of what you do is in the class itself, and often an experiment will require extensive amount of time beyond the end of the scheduled class period.  While attendance beyond 7:40pm is optional, in the past most classes ended between 8:30-10:00pm and the students stayed voluntarily (yes, because it’s THAT much fun!).  You may find yourself caught up in saving gnomes or solving a mathematical mystery.  So clear your schedule for Tuesday and Thursday nights.

Course requirements: There are no traditional homework assignments or exams in the course. The following are mandatory however.

• Must-know Facts: As various mathematical topics (“tools” as Zeitz calls them) come up in the course as required by particular problems I will tell you “must know” facts.  Those facts should be written in a special notebook, and should be memorized permanently before the next class meeting.  At any point in the course we will have unannounced quizzes to determine if you know what you must know. These may be oral or written or online.
• Synchronous in-class problem sets: We will have some timed problem sets that are to be worked in class. Some will be done individually and some as a group.
• Asynchronous outside-of-class problem sets: We will also have more extensive problems and problem sets that are to be done outside of class and answered and written up or submitted on AiM to hand in. Some will be done individually and some as a group.
• Synchronous in-class Problem Discussions All students will be required to discuss solutions to problems with other students both individually and in groups in class. The quality and frequency of your participation in these discussions are an important required aspect of the course.
• Contests! You are all now officially part of the University of Scranton Mathletic Team! All students will be required to participate in the high school (unofficially) and undergraduate (officially) mathematics competitions that are assigned during the semester. Whether participating officially or unofficially, your solutions to those contests will be evaluated by me as an important term project in the course. At minimum we will participate in the Putnam and as many USAMTS rounds as are available. VTRMC may also be required if it is available this year.

Attendance Policy: Since the course is intended to provide hands-on problem solving training as opposed to a traditional lecture format, class attendance is a necessary component of the course. Should you miss a class for any reason, you are still responsible for all announcements made and all material discussed during that class, including must-know facts. You should not come to class sick, however, under any circumstances. I will find a way for you to make up the enjoyment without infecting others.

Masks Policy: You should always bring a high quality mask with you to class, and will be required to wear it when working in small, close-quarter, problem solving groups. This policy may be revised throughout the semester as recommendations and campus covid numbers change.

Email and the Web: All students in this course are required to have a university email account and are expected to check their email frequently for announcements and other information I may send to you. I will use email and our website quite extensively in the course. If you prefer to check your home email instead of your university email you can forward your university email to you home account. Each student is also expected to be able to access any information that I post on the web which is related to your course. You may access this information from the mathematics department computer lab. Contact the Help Desk if you need assistance.

Cheating: Cheating is repugnant to the very nature of problem solving. Please drop the course immediately if you feel the urge to cheat for you have clearly failed miserably as a problem solver and nobody in the class will like you. Plus, you will also fail the course.

Grading and Student Learning Outcomes

There will be no exams, no homework, and no grades in the course.  There will just be LOTS of problems, some of which will be worked in class, some as group projects that will be written up and handed in, some worked for your own enjoyment and benefit and training.  Grades and exams and deadlines and time limits on class meetings are antithetical to the spirit and nature of the art of problem solving. If you are concerned about what grade you are getting in the course, then you are definitely not doing well.  On the other hand if all you care about is solving the current batch of problems with no concern for your grade in the course, then you are doing fine.  Problem solving must be motivated by love and curiosity and passion and desire and pride and the need to overcome a challenge and experience new vistas by climbing to great heights, not by mundane paranoid concerns over grades and gpa.

Still, the university does require that each student receive a grade in the course when the course is completed. So here is roughly how it will be determined.

Coach Picks the Teams: The grade you receive will be completely determined by me based on my subjective professional judgment of your performance taking into account your written and oral presentations, your interaction with the other students, your class attendance, peer evaluations, the quality and quantity of the problems you attempt and hand in, the uniqueness of your approach to particular problems, and other such criteria. This mechanism for determining course grades is consistent with the spirit of problem solving and training in general where the coach of the activity selects the team members who will constitute his “A” team, “B” team, etc. Note that you will not be judged on your level of skill as a problem solver but rather on how much you improve, how much you learn, and how much effort you put into the course.

Attendance Required: Also, since attendance and class participation is a major component of the course we will have the following grading policy.

There are approximately 28 classes in this course. In order for a class to count towards your attendance you should be present throughout the entire class, and participate in the day’s activities (e.g. participate in group activities, no sleeping, etc). You may miss up to two classes due to sickness or conflicts without penalty, but will be penalized one letter grade (A to A-. A- to B+, etc) for each class you miss after that. Absence due to documented illness, especially covid, will not count as a missed class toward this penalty.

Mandatory Competitions: Finally, you will be required to participate in several actual mathematics competitions throughout the semester. These will be weighed heavily when determining your final course grade. While we are not limited to the following list, you will participate (either unofficially or officially as necessary) in the following competitions.

1. USAMTS Round 1: This is a take-home high school level mathematics competition where the competitors have up to a month to work on five proof based problems.  Round 1 is usually available in September and due sometime in October.  I will give you more details as they become available.
2. VTRMC: The Virginia Tech Regional Mathematics Contest is an undergraduate mathematics competition that is taken on campus (usually on a Saturday in October).  Due to the pandemic it has not yet been announced if, when, and how the contest will take place this year.
3. USAMTS Round 2: The second round is usually available some time in October and due near the end of November. Your write ups and effort on both of these USAMTS rounds will count heavily toward your course grade.
4. Putnam Exam: The most important contest is the Putnam Exam, which is usually held on the first Saturday of December. This has traditionally been Part I of our Final Exam in the course. So we will continue that tradition. s members of the Scranton Matheletics Team you all must take it and will be given feedback us (Coach Leong and myself). High school students and anyone with an undergraduate degree must also take it, but must participate unofficially.
5. Other Contests: Given that our usual contests like VTRMC and the Putnam have not yet been officially announced, we may require participation in other contests to replace their role in the course once we know more details.

You are required to participate in all of these contests if and when they become available.

Adaptability: I retain the right to modify or change any of the policies stated in this syllabus during the term if I feel it is in the best interests of the students and the course.