Intro to Analysis (Fall 2010)

recent posts to forum

Quick discussion of the cardinality of an Infinite Set
WillTheSeriousWillTheSerious | 08 Dec 2010 15:42 | Comments: 11
Is the cardinality of the Natural Numbers really less then the cardinality of the Real numbers?

Problem 2.21
WillTheSeriousWillTheSerious | 29 Oct 2010 19:07 | Comments: 1
Show that the union of two closed point sets can not be a closed interval.

Problem 2.19
WillTheSeriousWillTheSerious | 29 Oct 2010 16:12 | Comments: 3
Proving that a set of numbers x is closed where f(x)=f(p) within a closed interval.

Another Attempt at Rigor
WillTheSeriousWillTheSerious | 28 Oct 2010 17:32 | Comments: 7
Attempt #2 at proving 0.999... is not equal to 1

"may" versus "can"
Dana ErnstDana Ernst | 22 Oct 2010 20:37 | Comments: 1

An Attempt at Rigor
WillTheSeriousWillTheSerious | 17 Oct 2010 03:25 | Comments: 9
A proof that 0.999... is not equal to 1

Each versus every
Dana ErnstDana Ernst | 11 Oct 2010 19:44 | Comments: 3


Welcome to the course wiki for the Fall 2010 manifestation of MA4510: Introduction to Analysis at Plymouth State University. This wiki is viewable by anyone, but content can only be added and edited by authorized users, which basically means students registered in the class.

This course is an introduction to Real_analysis, which is a subject area of mathematics that deals with the set of real numbers. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real numbers, and continuity, and related properties of real-valued functions.

We will spend most of our time studying sequences and the continuity of functions. We will take an axiomatic approach (definition, theorem, and proof) to the subject, but along the way, you will develop intuition about the objects of real analysis and pick up more proof-writing skills. The emphasis of this course is on your ability to read, understand, and communicate mathematics in the context of real analysis.

For more details, see the syllabus.

Using the Wiki

In the Web2.0 world, more and more of reading, writing, and communicating mathematics occurs online. What is a wiki, you ask? According to Wikipedia, the world's largest wiki site:

A Wiki ([ˈwiː.kiː] <wee-kee> or [ˈwɪ.kiː] <wick-ey>) is a type of website that allows users to add, remove, or otherwise edit and change most content very quickly and easily.

As a part of the network, this site is a customizable piece of the internet where users can edit content, upload files, communicate and collaborate. Using the wiki will provide an opportunity for you (as students) to collaborate together, and for me (the instructor) to provide feedback visible to all.

During the first week of classes, I will send you an invite to join the wiki. To join, you will need to sign up for a free Wikidot account. Please use your real name when signing up. (As a Wikidot member, you can create your own free wiki or web page.)

Getting Help

There are many resources available to get help. First, I recommend that you work on homework in groups as much as possible, and to come see me whenever necessary. Also, you are strongly encouraged to ask questions in the course forum, as I will post comments there for all to benefit from.

To effectively post to the course forum, you will need to learn the basics of LaTeX, the standard language for typesetting in the mathematics community. See the quick LaTeX guide for help with $\LaTeX$. If you need additional help with $\LaTeX$ or editing/posting content to the wiki, post a question in the course forum.

There are substantial resources available online to help you learn the Wikidot markup, which is quite simple. I regularly consult Wikidot's Wiki Syntax page and Wikidot's Quick Reference Guide. Lastly, you can always contact me.