Syllabus

Description:

A comprehensive survey of mathematics. Students will gain experience with both written and oral communication of mathematics while reviewing a breadth of mathematical topics. Students will be required to take the Educational Testing Service’s Major Field Test in Mathematics. Required of all Mathematics majors in their final year.

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 participation in class (weekly presentations, a practice test, 3 writing assignments, topic guides, and the final presentation) as well as a score on the Major Field Test (MFT). All parts of the class other than the the MFT will be graded for completion only. A total of 70% of the final grade will come from satisfactory completion of the following:

• weekly presentations (20%);
• 3 writing assignments and participation in making topic guides (20%);
• a final presentation to the faculty (20%).
• a practice test (10%);

The MFT percentile will count for the remaining 30% of the final grade. There will be a curve: a percentile rank of x will earn 1-(1-x)^4(1+4x) of the 30%.

Students will also receive feedback on their work during the semester. Presentations will be evaluated using this rubric (link). Practice exams will receive numerical scores. These scores won't factor into grades, but should be used to help identify areas needing further study.

Presentations

Before each class students will solve problems from the GRE Subject Test in Mathematics and prepare them for presentation. In general this requires:

• solving the problem;
• writing a clear solution;
• adding any additional annotations that will help with a presentation of the solution (e.g. statements of less-common theorems or definitions, or references to background material).

The order of presentations will be randomly determined if there aren't volunteers (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, students should present both methods.

Other suggestions for presentations: Make sure the problem is shown on the projector. For all but the simplest problems explain the problem to the class: what is actually required to solve the problem? Next briefly explain how to accomplish this. Then present the complete solution, being sure that each step is clearly connected to the problem and/or earlier steps. Both too little and too much detail can be bad. For long solutions, plan to check to make sure that everyone is still following. It may also be helpful to plan out how to use the dry-erase boards (is there a graph or sketch, are the computations long, etc.).

Writing assignments

There will be 3 writing assignments: (1) a mathematical cover letter/personal statement/autobiography, (2) a CV, and (3) a final reflection. Details on actual requirements for the assignments are here (link). If a students is writing a personal statement for a grad school application (or other application), they may submit that personal statement for one of the writing assignments (depending on the details of the personal statement; talk to Dr. Axon to figure out how this will work).

Topic Guides

Students will work in small groups (2 or 3) or individualy to make brief guides to selected topics. Topic guides will be coordinated with MATH 496 and shared between all sections of both courses. Students must participate in producing at least one topic guide.

Using AI

Students are allowed to use AI but should be carefult to use it in a responsible way. AI can help solve problems or clarify concenpts; students should make sure to use it to help them learn, not to avoid learning. Students who use AI will need to get good at evaluating its answers, which may be harder than just doing some things without AI. Students who cannot work without AI will have a hard time participating in the class and their grades may suffer.

Course Links

• Back to the schedule
• Writing assignments

Office hours (Herak 233 unless otherwise specified)

• Tuesday
  • 1:25-2:25 in the Math Learning Center (Bollier 218)
  • 2:30-3:30
• Wednesday
  • 9:30-10:30
  • 3:30-4:30
• Or by appointment

Logan Axon
Department of Mathematics
AD Box 51
Gonzaga University
Spokane, WA 99258
Office: Herak 233
Phone: 509.313.3897
Email: axon@gonzaga.edu

Last updated 9/2/2026