Syllabus

Description:

A comprehensive survey of mathematics. Students will solve problems from across the Gonzaga mathematics curriculum and present their solutions to each other. At the end of the semester students will take the Educational Testing Service's Major Field Test (MFT) in Mathematics. The course is mostly intended as a review/summary and does not aim to teach new material, though some introduction of unfamiliar topics may be provided.

Outcomes:

Students will solve problems using sound mathematical techniques, present their solutions clearly, and analyze and improve the work/presentations of others.

Math Major Learning Outcomes:

• Critically Analyze: students should be able to determine the validity of a mathematical argument and suggest improvements to that argument.
• Communicate Mathematically: students should be able to communicate mathematical ideas precisely and clearly through written, oral, visual, and/or symbolic forms of expression.
• Abstraction: students should appreciate mathematics in its own right and as a tool for abstraction. They should be able to solve problems using the abstract language and tools of mathematics.
• Mechanical and Computational Skills: students should demonstrate mechanical and computational proficiency in problem-solving using mathematical tools and processes.

Grades:

Grades will be based on your participation in class, including the practice tests and the final presentation, and your score on the Major Field Test (MFT). All parts of the class other than the the MFT will be graded for completion only. The MFT will count for 34% of your grade. Your percentile rank on the MFT will be used to determine what proportion of that 34% you earn. There will, however, be a curve: if x is your percentile then the proportion of the 34% you earn will be 1-(1-x)^4(1+4x).

You will also receive feedback on your work throughout the semester. Presentations will be evaluated using this rubric (link) and practice exams will receive numerical scores. These scores won't factor into your grade, but you should use them to help identify your strengths and weaknesses in the class.

Presentations

Before each class you will solve problems from the GRE Subject Test in Mathematics and prepare them for presentation. This means making sure you understand the solution and have a clear notes to work from if you are asked to present. The order of presentations will be randomly determined (and the number of presentations per class will also vary). Students in the audience should ask questions and suggest improvements where possible. When possible, problems should be solved as if they aren't multiple choice. If there is a faster/better method that uses the choices provided, please present both methods.

Other suggestions for presentations: Make sure the problem is shown on the projector. For all but the simplest problems you should explain the problem to the class: what do you actually need to do in order to solve the problem? Next briefly explain how you will accomplish this. Then present your complete solution, being sure that each step is clearly connected to the problem and/or earlier steps. Too little and too much detail can both be bad. It may be helpful to plan stopping points when you can check to make sure that everyone is still following you. It may also be helpful to plan out how you will use the dry-erase boards.

Written work

You will have two writing assignments this semester: a mathematical cover letter/personal statement/autobiography and a final reflection. These essays are partly a way for me to get to know you better and hear about your Gonzaga experience. They're also an opportunity for you to articulate who you are as a mathematician and how that connects to the rest of your life. I'll admit that these are exactly the kind of assignment that I liked least when I was a student. So why am I making you write these essays? I never liked writing/talking about myself, but I've had to do more and more of that after graduating from college. First there was a personal statement for my grad school applications, then similar things for scholarships, more versions of a personal statement in job applications and in interviews, then annual reports to my bosses in which I justified my existence, etc. The point is that these things actually turned out to be important, and this is a chance for you to practice in a low-stakes situation. I encourage you to find a way to enjoy these things as much as possible: write a pastiche of your favorite novel, write in verse, write as if you're reviewing yourself on Amazon... Details on actual requirements for the assignments are here (link). If you are applying for graduate school and need to write a personal statement, then you are welcome to submit that personal statement for one (or both) essays (depending on the details of the personal statement; talk to me to figure out the details).

Links and Resources

• 2021 edition of the class
• 2017 edition of the class
• 2014 edition of the class
• Presentation rubric (.tex)
• Schedule
• Writing assignments

Office hours (in person by default, virtual by request)

• Monday 10-11
• Tuesday 12-1 in the Math Learning Center
• Wednesday 10-11
• Thursday 2-3
• Or by appointment

Logan Axon
Department of Mathematics
AD Box 51
Gonzaga University
Spokane, WA 99258
Office: Herak 227A
Phone: 509.313.3897
Email: axon@gonzaga.edu

Last updated 8/26/2024