Intermediate Analysis I

• Text: Principles of Mathematical Analysis
• Author: Walter Rudin
• ISBN: 007054235X
  This book will also be used for the second semester
• Publisher: McGraw-Hill

Look up your grades

1. Install Mozilla from Page for obtaining the Mozilla browser
   It will also be necessary to install math fonts for this browser. Information on how to install these can be found on
   The MathML Fonts Page
   For linux users, the necessary fonts can be found in: mozilla-math.tar.gz (these should be installed in X windows).

Note: Other web pages for this course will not necessarily even show up in other browsers! Once you have installed Mozilla and the fonts, you can check your installation by viewing:

The MathML Start Page

Use this to check whether MathML is working properly on your web browser. Unfortunately, the Windows version of Mozilla seems to have a bug that will cause it to complain about missing fonts even though the fonts are there (and Mozilla is using them correctly).

The term Analysis refers to advanced calculus as it was developed in the 19th and 20th centuries. It involves several broad topics including: the Lebesgue Integral, Complex Analysis and Functional Analysis. The methods and results of this work are needed for advanced work in fields as diverse as Topology, Quantum Mechanics and Ergodic Theory.

Topics covered

1. Real numbers
   • Dedekind Cuts
   • The real field
   • nth roots exist
   • The extended real number system
   • Complex numbers
   • Euclidean spaces
2. Topology
   • Orders of infinity
   • Uncountable sets exist
   • Metric spaces
   • Open and closed sets, Limit points
   • Compact sets
   • Connected sets
3. Numerical sequences and series
   • Convergent sequences
   • Subsequences
   • Cauchy sequences

Links

1. Countable and Uncountable sets
2. Cantor set
   This is an uncountable set of measure 0.

Grading

Grades will be based on graded homework assignments given each week (mostly taken from the textbook).

1. p.22 #7; p.43 #2,3
2. p.43 #4, 5, 6, 8; p.44 #11, 17
3. p.78 #1, 2, 3, 6; p.82 #24
4. p. 78 6, 7; p. 79 11
5. p. 100 #18; p.114 # 1, 2, 4, 6

Lecture Notes

Note: you may have to zoom on these images to see them clearly

1. 1-6-2005
2. 1-13-2005
3. 1-20-2005
4. 1-27-2005
5. 2-3-2005
6. 2-10-2005
7. 2-17-2005
8. 3-3-2005
9. 3-10-2005