Department of Mathematics
Box 395
Boulder, CO 80309
Office: Math 223
Email: thomas.gassert at colorado.edu

Teaching - Spring 2015

Analysis (Math 3001)

Text: Stephen Abbott's Understanding Analysis, Springer, 2000.

Syllabus

Resources

Proof writing tips
LaTeX guide
LaTeX template

Worksheets

1. Intro to proof
2. Subsets of the real line
3. Supremum and infemum
4. Sequences
5. Limits of sequences
6. Cauchy sequences
7. Series
8. Open and closed sets
9. Compact sets
10. Functional limits
11. Continuous functions
12. Uniform continuity
13. Derivatives
14. Mean value theorem
15. Riemann integration
16. Properties of integrals
17. Sequences of functions
18. Series of functions

Homework

Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Homework 8
Homework 9
Homework 10
Homework 11
Homework 12
Homework 13
Homework 14
Homework 15

Additional resources

Limits as birds
Cantor set