Math 4433

(Intro. to Analysis I)

Summer 2012

Northern mockingbird (Mimus polyglottos). If you're up late studying, one of these will sometimes serenade you till the wee hours of the morning. They seem to be able to go for hours, never singing the same thing twice. If you are good at bird calls, though, you can sometimes imitate one of its phrases and get it to sing it back to you again. This image from Wikipedia Commons, source is http://www.flickr.com/photos/bobistraveling/5446906068/.

Instructor: John Albert

Office: PHSC 1004

Office hours: Mondays, Tuesdays and Thursdays from 1:30 pm to 2:30 pm (or by appointment)

Phone: 325-3782

E-mail: jalbert@ou.edu

Course information

Questions and solutions for the third exam.
Solutions to problems on Assignment 16.
Review sheet for the third exam.
Questions on second exam.
Answers to questions on second exam.
Review sheet for the second exam.
Questions on first exam.
Answers to questions on first exam.
Review sheet for the first exam.
Here is a proof of the fact that the product of the limit of two sequences is the limit of the products. This fixes the problem in the proof we did in class.
Syllabus for the course.

Exams

Exam 1: Wednesday, June 6

Exam 2: Friday, June 22

Exam 3: Friday, July 6

Homework

Sometimes I post an assignment in advance but change it in class the day before it's due. If you miss a class you should check this web page after class for the final version of the next day's assignment.

Assignment	Due Date	Problems
1	Friday, May 18	2.2.2, 2.2.6, 2.2.12, 2.2.13, 2.2.18(a)
2	Tuesday, May 22	2.3.1., 2.3.2, 2.3.3, 2.3.7
3	Thursday, May 24	2.3.11, 2.5.7, 2.5.8
4	Tuesday, May 29	3.1.4, 3.1.8
5	Wednesday, May 30	3.1.5(b), 3.1.12
6	Friday, June 1	3.2.6(a,c), 3.2.9
7	Monday, June 4	3.2.5(a), 3.2.7
8	Monday, June 11	3.3.1, 3.3.3, 3.3.10
9	Wednesday, June 13	3.4.7, 3.5.10
10	Friday, June 15	3.7.7, 3.7.9(a,b)
11	Tuesday, June 19	4.1.3, 4.1.9(a,c)
12	Thursday, June 21	4.2.4(first part only, proving that the limit of cos (1/x) does not exist as x -> 0), 4.2.14
13	Wednesday, June 27	5.1.7, 5.1.8
14	Friday, June 29	5.1.11, 5.1.12, 5.1.13
15	Monday, July 2	6.1.1(a), 6.1.2, 6.1.4
16	Thursday, July 5	6.2.6, 6.2.7

References and Links

Click here to see pages for versions of this course I taught in previous semesters.
A Mathematician's Lament by Paul Lockhart.

You can consult these links for more information on analysis and the foundations of mathematics.

The Wikipedia articles on "Dedekind cut" and "Construction of the real numbers" are worth a look.
M.I.T. Open Courseware: ocw.mit.edu. Click on "Mathematics" and then "Analysis I, Fall 2006".
Wikipedia entry for "set theory": en.wikipedia.org/wiki/Set_theory.
There are many interesting articles on set theory and foundations of mathematics at the online Stanford Encyclopedia of Philosophy.
"A Primer for Logic and Proof", by H. P. Hirst and J. L. Hirst: www.mathsci.appstate.edu/~jlh/primer/hirst.pdf.
The website "Intro to Logic" by Ian Barland et al. contains a course on logic, and in particular a discussion of the proper use of quantifiers such as "for every" and "there exists". In our analysis course, we don't delve too much into the details of the rules of logic, and rely on our common sense to tell us whether a proof or argument is logically correct. But when you have to explain to someone else what you think is wrong with their proof, it's sometimes difficult: everybody has common sense, but not everybody can explain common sense to others. Courses in logic such as this one aim at making "common sense" rules explicit, so you can communicate with others about them.
Here is a site where fundamental theorems in many fields of mathematics are proved in complete detail, with proofs that are verifiable (and have been verified) by computer: us.metamath.org.
"Understanding Analysis", a textbook by Stephen Abbott.
"Analysis, Vol. 1", a textbook by Terence Tao.

The founder of the subject of analysis, as we learn it in this class, was the French mathematician Augustin-Louis Cauchy (1789-1857). Here is a nice article about what Cauchy did, and why.