MAT 108: Introduction to Abstract Mathematics (Fall 2026) (CRN 36156 (D1), 36157 (D2))
     MWF 11:00-11:50AM, 26 Wellman

http://www.math.ucdavis.edu/~gravner/MAT108/

INSTRUCTOR:
TA:
Grader:

PREREQUISITES: A good working knowledge of calculus (courses MAT 21AB). You are responsible for satisfying the prerequisites!

TEXTBOOK: A Transition to Advanced Mathematics, 8th Edition, by D. Smith. M. Eggen. R. St. Andre (Brooks-Cole, 2014). Chapters 1-5 will be covered, with some additional material depending on time. Earlier editions of the book are also fine. Homework problems will be scanned from the 7th edition and available on the Homework assignments page to prevent confusion.

GRADE: Course grade will be based on the following:

I will follow this grading curve:

ADDITIONAL POLICIES:

I will make everything as predictable as I can, which I think is necessary more than ever. In particular, course policies will not change (either for the class in general or for particular students) due to world events, unless otherwise ordered by the university administration.

Thursday meeting (D1 meets Tue., 7:10-8pm, 217 Olson; D2 meets Tue., 6:10-7pm, 217 Olson) is a discussion session, lead by the TA, and devoted to homework, and further elaboration on lecture material. Attendance of discussion sessions is mandatory.

Please bear in mind that talking, texting, etc. disrupt the lectures. Use of computers, cellphones, recorders, or any other electronic devices during lectures is prohibited, except for the purpose of taking notes.

If you have any problem at all that requires special accommodation, please let me know well in advance!

Sample exams (with solutions) are available on the materials page. However, material presented in the lectures will be the basis for the exams. Solutions for the midterms will also be posted on the materials page.

Use of books, notes, electronic devices, or anything else but pencil and paper, will not be allowed on any exam.

Homework will be assigned about once a week and due the following week. The grader, Elysée Wilson-Egolf, will handle all aspects of homework submission and grading. See the Homework assignments page for homework information.

There will be no make-up exams. A missed exam counts as 0 points. If you miss the final you will automatically receive an F. The grade I (Incomplete) will not be given in any circumstances. If you miss much of the coursework because of illness or other emergency, please petition for the Retroactive Drop.

SOME USEFUL LINKS:

  • Duane Kouba's lecture notes from MAT 108.
  • A tutorial on writing proofs by Larry Cusick at CSU Fresno.
  • Some study tips by Mark Tomforde at University of Houston.
  • A very nice guide on how to write solutions to math problems, by Richard Rusczyk and Mathew Crawford at Art of Problem Solving.
  • Two freely available books that cover most of our topics are: A Transition to Advanced Mathematics (same title as our textbook, but a different book) by Darrin Doud and Pace P. Nielsen; Mathematical Reasoning: Writing and Proof by Theodore A. Sundstrom. If you want to explore in more depth, here are two additional book recommendations. Some of the most elegant proofs ever discovered are collected in Proofs from the Book by Martin Aigner and Günter M. Ziegler. The best self-study book for set theory I know is Classic Set Theory by Derek Goldrei.
  • TeX is the typesetting system used to write all mathematical texts nowadays. It is an excellent idea to learn the most commonly used variant of TeX called LaTeX as soon as possible. Here is some information to get you started: MikTeX (TeX system for Windows), Texmaker (a free TeX Editor for all platforms), Overleaf (an online LaTex editor). A very good introduction is at the Art of Problem Solving website, and you can check out a LaTeX textbook by David R. Wilkins.