MAT 127A: Real Analysis (Fall 2019), CRN 48776 (A01), 48777 (A02)
     MWF 9:00-9:50AM, 168 Hoagland



PREREQUISITES: A good working knowledge of calculus (courses MAT 21ABC) and the ability to follow and write mathematical proofs (course MAT 108). You are responsible for satisfying the prerequisites!

TEXTBOOK: Understanding Analysis, by S. Abbott, 2nd Edition (Springer, 2016). The e-book is freely available through the library. 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. If you miss the final because of illness or other emergency, please petition for the Retroactive Drop.

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


  • Prof. John Hunter has written very nice lecture notes for Math 127ABC.
  • Jiří Lebl has developed a free online textbook that covers Math 127ABC and more.
  • 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), 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.