Math 131A: Real Analysis

General Information

Time and Place: MWF 9:00 am-9:50 am,  MS 5147

Instructor: Matthias Aschenbrenner

E-mail address:

MS 5614
Office Phone: (310) 206-8576
Office Hours: MW 10 am-10:50 am, or by appointment. (I will not hold 'virtual' office hours.)

Discussion Section: T 9:00 am-9:50 am, MS 5147
Teaching Assistant: Jeffrey Lin

Achtung!Click here to download the course handout.


Rigorous introduction to foundations of real analysis; real numbers; point-set topology in Euclidean space, functions, continuity.


32B, 33B. Recommended: 115A.

Course Text

Elementary Analysis: The Theory of Calculus, 2nd ed., by K. A. Ross, Springer-Verlag, New York, 2013.


There will be 9 problem sets assigned over the course of the quarter. The problems will range in difficulty from routine to more challenging. Completed solutions are to be handed in at the beginning of class on Friday's lecture, beginning in Week 2. No late homework will be accepted. However, your lowest homework score will be dropped when computing your grade. You are encouraged to work together on the exercises, but any graded assignment should represent your own work.

Put the following information in the upper right hand corner of the first page:

   Your Name
   Math 131A, Homework # number.

On each additional page, put your name in the upper right-hand corner. Work single-sided, that is, write on only one side of each sheet of paper. STAPLE any homework that is more than one page long. Remove all perforation before submitting. Write legibly. Label the chapter + section number as well as the problem number (e.g., 1.1 #1.12). Homework that fails to meet the above requirements will be marked "Unacceptable'' and returned unread.

Homework 1, due April 10.
Homework 2, due April 17.
Homework 3, due April 24.
Homework 4, due May 1.
Homework 5, due May 8.
Homework 6, due May 15.
Homework 7, due May 22.
Homework 8, due May 29.
Homework 9, due June 5.


There will be two hour examinations, on Friday, April 24 and Friday, May 22, in class. There will be a final exam on Tuesday, June 9, 11:30am-2:30pm, in our regular classroom. 

No make up exams will be given under any circumstances.

No books, calculators, scratch paper or notes will be allowed during exams.

Grading policy: Homework: 20%. Hour Exams: 20% each. Final Exam: 40%.

All scores and final grades will be available on the MyUCLA gradebook.

Historical Information

Click here for a brief history of calculus, and below to learn more about some of our real analysis heroes:

Archimedes of Syracuse
Bernard Bolzano
Georg Cantor
Richard Dedekind
Jacob Bernoulli
Johann Bernoulli
Augstin Louis Cauchy
Jean Gaston Darboux
Rene Descartes
Leonhard Euler
Pierre de Fermat
Guillaume de l'Hopital
Gottfried Wilhelm von Leibniz
Sir Isaac Newton
Bernhard Riemann
Thomas Stieltjes
Brook Taylor
Karl Weierstrass
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