Bay Area Math Circle

Berkeley Math Circle	A Hilde L. Mosse program for education at Mathematical Sciences Research Institute.
	BerkeleyMathCircle
	Project of the Mathematical Sciences Research Institute and co-sponsored by the UC Berkeley Mathematics Department and partially supported through the NSF Career Grant to R. Vakil of Stanford University.


	Sessions and Homework The sessions of the Math Circle will be a combination of lectures on mathematical theory and problem solving techniques, discussions, and problem-solving practices. Depending on the particular topic and instructor, a session may emphasize one component, or it may incorporate all of these components equally; its style can be anything from ``lecture'' to ``seminar''. Each instructor will bring into the classroom his or her own style of teaching. We believe that such a diversity will greatly benefit the participants in terms of their own mathematical future. Some instructors will give you handouts, and some will require that you take notes; some may give you a 5-10 minute break in the middle of the session, and some will be so eager to continue with the session that they may simply skip the break. So, come to the Circle with open minds and expect the unexpected! The topics of the sessions will also cover various mathematical areas. A given student may find some areas far more difficult than other, more familiar areas. The level of the students in the Math Circle will also vary from beginners to nationally and internationally recognized problem solvers. Such diversity of mathematical background and competition experience should be welcomed by all participants and should be used as efficiently as possible for the exchange of ideas and for the mutual benefit of everyone. This diversity, however, will naturally require different amount and content of individual work outside of the Circle. There will be no mandatory homework assignments to be collected and graded . Ordinarily, each session will end with a few problems, on which students will be expected to work as their homework. If a session is part of a series of lectures given by the same instructor, it can be expected that the homework problems will be discussed in a later session, so students should review them in preparation for the upcoming lecture in the series. If you feel certain gaps in your background on some topics, be assured that probably you are not the only one. You can ask the instructors and assistant for relevant literature and problems. We have established an e-mail bulletin board for exchange of ideas on homework problems and discussion of related math topics at: http://clubs.yahoo.com/clubs/berkeleymathcircle Lecture Notes and Homework Problems, 2001-2002 "A Few Words About Proofs", Handout by Mira Bernstein HTML format Postscript format PDF format 1. Inversion in the Plane, Part I, by Zvezdelina Stankova Abstract Postscript format PDF format 2. Inversion in the Plane, Part II, by Zvezdelina Stankova Abstract Postscript format PDF format HTML format 3. Elliptic Curves by Bjorn Poonen Postscript format PDF format HTML format 4. Inversion, Part III by Zvezdelina Stankova Abstract 5. Combinatorial Identities - Euler, Gauss, Jacobi, McDonald and Others, by Dmitry fuchs 6. Projective Geometry by Tom Davis Postscript format PDF format Abstract 7. Colored Hats and Hamming Codes, by Paul ZeitzMira Bernstein Abstract 8. Fibonacci Numbers, by Austin Shapiro JPG format 9. Inequalities, by Bjorn Poonen Postscript format PDF format HTML format 10. Fixed Points and Fair Divisions, by Kiran Kedlaya Abstract Postscript format PDF format HTML format 11. Induction, by Ted Alper Abstract Postscript format PDF format HTML format 12. Polya's Counting Theory , by Tom Davis Abstract Postscript format PDF format HTML format 13. Games and Graphs, by Joe Buhler Abstract Gameboards (Postscript format): Bridgit Chess Chess 7x7 Hex 9x9 Hex 8x8 14. Evolutes and Involutes, by Dmitry Fuchs 15. Hilbert's Third Problem, by Inna Zakharevich Postscript format 16. Maxima and Minima Problems WITHOUT Calculus, by Tom Rike Abstract Postscript format PDF format HTML format 17. Homogenious Coordinates, by Tom Davis Abstract Postscript format PDF format 18. Convex Polytopes, by Serkan Hosten 19. Journey to the Center of Pascal's Triangle, by Paul Zeitz 20. Journey to the Center of Pascal's Triangle,Part II; BAMO practice (general), by Paul Zeits 21. BAMO practice (general), by Maksim Maydanskiy MS Word format 22. BAMO practice (general), by Zvezdelina Stankova Postscript format PDF format HTML format 23. BAMO Aftermath, by Neil Herriot and Inna Zakharevich 24. Generating Functions, by Andrew Dudzik 25. Infinite Series, by Tom Rike Abstract Postscript format PDF format HTML format 26. Theorems of Pappus and Pascal and Cubic Curves, by Carl Mautner and Maksim Maydanskiy Abstract MS Word format 27. Regular Polyhedra in 2D and 3D, by Alexander Givental 28. "This Talk Is Under Construction", by Kiran Kedlaya A paper mentioned in the talk can be found at http://www.nevada.edu/~baragar/papers/monthly151-164.pdf Abstract Postscript format PDF format HTML format 29. USAMO Practice Session, by Kiran Kedlaya Postscript format PDF format HTML format 30. An Intriguing Geometry Problem, by Tom Rike Abstract Postscript format PDF format HTML format Supplementary figures

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Special thanks to George Csicsery, producer and director, and MSRI, sponsor, for allowing the use of some images from the movie "Invitation to Discover". For more information about George Csicsery's films, please visit http://www.zalafilms.com.

Sessions and Homework

Lecture Notes and Homework Problems, 2001-2002

"A Few Words About Proofs", Handout by Mira Bernstein

1. Inversion in the Plane, Part I, by Zvezdelina Stankova

2. Inversion in the Plane, Part II, by Zvezdelina Stankova

3. Elliptic Curves by Bjorn Poonen

4. Inversion, Part III by Zvezdelina Stankova

5. Combinatorial Identities - Euler, Gauss, Jacobi, McDonald and Others, by Dmitry fuchs

6. Projective Geometry by Tom Davis

7. Colored Hats and Hamming Codes, by Paul ZeitzMira Bernstein

8. Fibonacci Numbers, by Austin Shapiro

9. Inequalities, by Bjorn Poonen

10. Fixed Points and Fair Divisions, by Kiran Kedlaya

11. Induction, by Ted Alper

12. Polya's Counting Theory , by Tom Davis

13. Games and Graphs, by Joe Buhler

14. Evolutes and Involutes, by Dmitry Fuchs

15. Hilbert's Third Problem, by Inna Zakharevich

16. Maxima and Minima Problems WITHOUT Calculus, by Tom Rike

17. Homogenious Coordinates, by Tom Davis

18. Convex Polytopes, by Serkan Hosten

19. Journey to the Center of Pascal's Triangle, by Paul Zeitz

20. Journey to the Center of Pascal's Triangle,Part II; BAMO practice (general), by Paul Zeits

21. BAMO practice (general), by Maksim Maydanskiy

22. BAMO practice (general), by Zvezdelina Stankova

23. BAMO Aftermath, by Neil Herriot and Inna Zakharevich

24. Generating Functions, by Andrew Dudzik

25. Infinite Series, by Tom Rike

26. Theorems of Pappus and Pascal and Cubic Curves, by Carl Mautner and Maksim Maydanskiy

27. Regular Polyhedra in 2D and 3D, by Alexander Givental

28. "This Talk Is Under Construction", by Kiran Kedlaya

29. USAMO Practice Session, by Kiran Kedlaya

30. An Intriguing Geometry Problem, by Tom Rike