Course Details

X-treme Thinking

Spring 2008 - Math 98/198 - Units: 1

Shortcuts:     decal.org/619     decal.org/thinking

If you are not an upper division math major, you probably have never thought about questions like these:

• How are numbers, functions, and all other mathematical objects defined in terms of sets?

• How come it's possible to make an infinite list of all the numbers that have a certain property, but impossible to make a list of all the numbers that don't have that property?

• What is the relationship between truth and provability in mathematics, and why are there true statements that can never be proven?

• How do we know that there are infinitely many prime numbers?

• Why does the security of credit card number encryption rely on the assumption that there is no efficient strategy for playing Minesweeper?

If you want to be exposed to profound insights in advanced mathematics without spending years learning all the technical details, then X-treme Thinking is the Decal for you.

Prerequisites:

There are no prerequisites, and the class is not hard to pass, but be advised: 

X-treme Thinking is the hardest you can possibly think in a 1-unit course. 

Course Topics:

1. Numbers
2. Proof
3. Sets and Counting
   
4. Foundations of Math
5. Infinity
6. Computability
7. Algorithms
8. Complexity
9. Paradoxes

Meeting Time:

Mondays 5-7, starting Week 3 (February 4). 

See the course syllabus for more information (below).

Lesson Notes

Lesson notes can be found at the course website (see link below).

Enrollment Info:

If you want to enroll, send me an email with:
1. Name
2. Year
3. Major
4. A sentence about why you want to take the class.

Also email me if you have any questions. 

Course Contact: liron AT berkeley.edu

Website: http://base.google.com/base/a/wiseguy/1361797/D7472106773329947327

Faculty Sponsor: William M. Kahan

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Course info last modified February 6, 2008. This page has been viewed 3570 times.