MAT 25: Advanced Calculus (Fall 2014)
(CRN 49287 (B1) and 49288 (B2))
     MWF 9:00-9:50AM, 2016 Haring

INSTRUCTOR: Janko Gravner
TA: Xiaochen Liu

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

TEXTBOOK: Understanding Analysis, by S. Abbott (Springer, 2001). Chapters 1-3 will be covered. Also recommended is a very similar book Elementary Analysis: The Theory of Calculus, by K. A. Ross (Springer, 1980).

GRADE: Course grade will be based on the following:

I will follow this grading curve:


Thursday meeting is a discussion session, lead by the TA, and devoted to homework and further elaboration on lecture material. Attendance of discussion sessions is mandatory (in the sense that you are responsible for the material covered there; your presence will not be verified)

Please bear in mind that talking, cellphone ringing, newspaper reading, etc. disrupt the lectures. Use of computers, cellphones, recorders, or any other electronic devices during lectures is not allowed.

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

Use of books, notes, calculators, 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. Late homework will not be accepted under any circumstances. See the Homework assignments page for homework information.

Also, 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. Be aware that, due to a recent policy change, the grade NS (Enrolled No Work Submitted) no longer exists, so you will receive an F if you submit no work.

Solutions for the midterms will be posted at the materials page.


  • Prof. John Hunter has written very nice lecture notes for this class (and 125AB).
  • Terrence Tao's home page for a similar course at UCLA. Many links do not work, but Tao's Lecture notes are superb and so is other supplementary material.
  • Duane Kouba's lecture notes from MAT 108 are an excellent introduction to abstract mathematics.
  • A great book to learn set theory is Classic Set Theory by D. C. Goldrei, and a good advanced book is Introduction to Set Theory by Hrbacek and Jech.
  • A tutorial on writing proofs by Larry Cusick at CSU Fresno.
  • Some tips on reading math books 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.
  • To read some of the most elegant proofs ever discovered, check out the Proofs from the Book by Martin Aigner and Günter M. Ziegler.
  • 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, although it will not be required in this course. Here is some information to get you started: MikTeX (TeX system for Windows), WinEdt (TeX Editor for Windows, not free), LEd (another TeX Editor for Windows, free), TeXnicCenter (yet another TeX Editor for Windows, free), GSView and Ghostscript (needed to handle PostScript files). A very good introduction is at the Art of Problem Solving website, and you can check out a LaTeX textbook by David R. Wilkins.