Analysis I


The class syllabus can be found Real Analysis.

Class Times

9:20 – 10:30 (section I) on MWF and 1:20 – 2:30 (section II) on MWF

Click here to access the class calendar.


Homework will be due at the start of class on Wednesdays.  Weekly assignments will be posted here as well as on our class schedule.

If you want to download the .tex files for these assignments so that you can more easily type up your homework (something I strongly encourage everyone to do), then you will also need to download the “simplemargins.sty” file that I e-mailed to everyone on 8/31/2016.

Assignment 1 (due 9.7.16) — Assignment 1 .tex file + image file — solutions-1

Assignment 2 (due 9.14.16) — Assignment 2.tex file — solutions

Assignment 3 (due 9.21.16) — Assignment 3.tex file — solutions

Assignment 4 (due 10.5.16) — no .tex file this time, sorry! — solutions

Assignment 5 (due 10.14-ish.16) — Assignment 5.tex file — solutions

Assignment 6 (due 10.19.16) — Assignment 6.tex file — solutions

Assignment 7 (due 10.26.16) — Assignment 7.tex file — solutions

Assignment 8 (due 11.9.16) — Assignment 8.tex file

Assignment 9 (due 11.18.16) — .tex file coming soon!

Assignment 10 (due Monday after Thanksgiving)

Assignment 11


Exam 1 (due 9.28.16) — Solutions

Exam 2 (due 11.2.16) — Exam 2.tex fileSolutions — Link to Some Hints

Final Exam (the .tex file will be e-mailed to the entire class)


Our main textbook will be Introduction to Analysis (5th edition) by Edward D. Gaughan.  Copies are available in our bookstore as well as via Amazon and other online stores.

Blog Posts

I will occasionally write up some notes and thoughts on our class discussions / work and share them as blog posts.  I will also try to maintain a current list of posts, but even when I fail to organize them in this way, you can find all Analysis posts by clicking here (and, yes, if they are helpful you can use them as part of your notes when working on take-home exams).

Introductory Post (FOM + Real Numbers)

Proof that Completeness \Rightarrow NIP \Rightarrow BW Thm (coming soon!)

Completeness and the Archimedean Property

Picture of \displaystyle \lim_{x\to x_0} f(x) = L.

Summary Notes on “Monotone Functions have only countably many discontinuities” Theorem.