MATH.4200-301 Honors Mathematical Problem Solving
MATH.5200-201 Mathematical Problem Solving

Fall 2024

Instructor: Prof. K. Levasseur -- kenneth_levasseur@uml.edu

Meetings

This class meets Tuesdays, 3:30 - 6:15 PM in (Room TBA) but if you take this course, you must also be available from 10AM to 6 PM on Saturday December 7, 2024 to compete in the William Lowell Putnam Mathematical Competition. This will be your final exam for the course.

Objectives

The main focus of the course will be to solve interesting, challeging mathematics problems. Another objective is to help you develop good habits of mathematics communication (see below).

Here is one of the problems from the 2013 competition:

Recall that a regular icosahedron is a convex polyhedron having 12 vertices and 20 faces; the faces are congruent equilateral triangles. On each face of a regular icosahedron is written a nonnegative integer such that the sum of all 20 integers is 39. Show that there are two faces that share a vertex and have the same integer written on them.

Text

The following notes serve as the main text for this course.

If you are rusty on some of the basics, The Proof Book is a free book that is available on this course's Blackboard page.

In addition, there are many resources, including free online ones. Here is a partial list.

Course Requirements, Grading

To earn a grade in this course you will need to do the following:

  1. Attend classes. Unless you have valid medical or legal excuse for missing a class, you will be considered absent. You get one free absence, and then your starting grade will be moved down the list {A, A-, B+, B, B-,...}. Your starting grade will then be the highest possible grade you can earn in the course, assuming you do "A" work for everything.
  2. Participate. I'll expect you to contribute to the best of your abilty to the discussions in each class meeting. This counts for 40% of the grade. I hope to give everyone full credit for this part, but it won't be automatic.
  3. Work independently on assignments. There will be problems assigned for work outside of class. Your work on them will represent 30% of the final grade.
  4. Compete. You must compete in the William Lowell Putnam Mathematical Competition. Competing is 20% of the grade. Competing means working on problems for at least 2.5 hours in each of the the two 3 hour sessions on the day of the competition. The scores are announced long after grades are due, so everyone who shows up gets an "A" in this part of the course. We will meet on Tuesday, December 10 to "debrief."
  5. Reflect. The final requirement for the course will be to write up a reflection on the course and the competition. In this 3-5 page paper, you can describe your efforts, preferably highlighting one of the Putnam problems. In addition, you can comment on what you've learned about mathematics and the problem solving process. This will count for 10% of the course and will be due Monday, December 16 at noon.

What will a typical class look like?

At the beginning of most classes, we can discuss updates on problems we have discussed earlier.

For each class there is a main topic (e. g., Calculus, Probability, Geometry,...). Before each class, I'll expect you to read over the notes and problems associated with the topic. You don't have to turn in anything. When the class meets, we will discuss the notes and any questions that might come up. Then we'll spend some time working on the problems.

Don't worry if you can't solve all the problems. Many of them are are difficult, but I've tried to include a few relatively easy problems in each week. I'm not telling you which problem is easy. Also, what is easy to one person isn't necessary easy to someone else. I understand that there are some topics that you might have less familiarity with than others.

After some classes I will assign a problem (or problems) for the class to turn in. You'll turn solution in using Gradescope.

LaTeX

I won't require that you use LaTeX in the course, but I'd like you to give it a try. There will be one assignment that will require using it.

Mathematical Communication Objectives

One of the objectives of this course is to help you develop your mathematical communications skills. The following are a list of the things you should keep in mind for this course. I'll be looking for you to attempt to follow these guidelines.

  1. Ask questions. Notice, identify, and clarify sources of confusion. Look for connections and relationships between ideas. Explore topics and ideas deeply.
  2. Analyze and constructively critique the reasoning of others. Actively listen and summarize key ideas to check comprehension. Test conjectures against examples and potential counterexamples. Work together to find errors and fix flaws. Assess and reconcile various approaches to the problem.
  3. Explain and justify your reasoning. Communicate and justify your conclusions to others. Indicate the general strategy or argument, and identify the key step or idea(s). Actively listen to the critiques of others. Work together to find errors and fix flaws.
  4. Attend to precision. Communicate precisely to others. Use clear definitions, and carefully state any assumptions or results used.
  5. Be clear and concise. Use the appropriate amount of generality or specificity in arguments. Avoid use of any extraneous assumptions, hypotheses, or statements. Indicate any example(s) that you have in mind.
  6. Use and develop mathematical fluency. Use standard mathematical notations and terms (as discussed in class or demonstrated in course materials). Clearly indicate and explain any use of non-standard shorthand, notation, or tools

Source: Richard Wong, UCLA, Active Learning Exchange on MAA Connect

Academic Integrity Policy

All students are advised that there is a University policy regarding academic integrity.  It is the students' responsibility to familiarize themselves with these policies. Students are responsible for the honest completion and representation of their work. Link to the Academic Integrity Policy

Student Mental Health and Well-being

We are a campus that cares about the mental health and well-being of all individuals in our campus community, particularly during this uncertain time. If you or someone you know are experiencing mental health challenges at UMass Lowell, please contact Counseling Services, who are offering remote counseling via telehealth for all enrolled, eligible UMass Lowell students who are currently residing in Massachusetts or New Hampshire. I am also available to talk with you about stresses related to your work in my class.

Disability Services Academic Accommodations

If you are registered with Disability Services and will require academic accommodations, please notify me via the Accommodate semester request process as soon as possible so that we might make appropriate arrangements. It is important that we connect to discuss the logistics of your academic accommodations; please speak to me during office hours or privately after class as we respect and want to protect your privacy. If you need further information or need to register for academic accommodations, please visit the Disability Services Website.

Diversity, Inclusion, and Classroom Community Standards

UMass Lowell and your professor value human diversity in all its forms, whether expressed through race and ethnicity, culture, political and social views, religious and spiritual beliefs, language and geographic characteristics, gender, gender identities and sexual orientations, learning and physical abilities, age, and social or economic classes. Enrich yourself by practicing respect in your interactions, and enrich one another by expressing your point of view, knowing that diversity and individual differences are respected, appreciated, and recognized as a source of strength.