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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. With a great variety in topics
and instructors, a session may emphasize one component, or it
may incorporate all of these components equally; the resulting
style can range from a participatory seminar to a cozy lecture.
Each instructor will bring into the classroom his or her own style
of teaching. Such diversity will greatly benefit the participants
in terms of their own mathematical future. Some in structors 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 usually varies 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.
Lecture
Notes - 2002-2003
First Meeting:
Sept. 15, 2002
Meetings 1 and 2. Vectors: Applications in Problems Handout
by Zvezdelina Stankova
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Postscript format
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PDF format
Meeting 3. Inversion in the Plane by Zvezdelina
Stankova
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Postscript format
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PDF format
4. Fractions and Repeating Decimals by Tom Davis
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Postscript format
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PDF format
5. Four Points on a Circle by Tom Davis
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Postscript format
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PDF format
6. Classical Theorems in Geometry by Maksim Maydanskiy
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Word document format
7. Is This Number Prime? by Kiran S. Kedlaya
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Postscript format
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PDF format
8. Infinity by Bjorn Poonen
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PDF format
9 - 10. Graph Theory by Paul Zeitz
11. "How to make a Moebius band out of paper?"
by Dmitry Fuchs
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Abstract
12. "Accidental Summations" by Joshua Zucker
13. "Perennial Problems from Geometry" by Tom Rike
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Postscript format
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PDF format
14. "A Formula for Cubic Equations, Does it Exist?"
by Dmitry Fuchs
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Abstract
15. Binary Numbers and Error Correcting Codes in Message
Sending by Quan Lam
No Handouts were Given
16. "Equations in Degree 5" by Dmitry Fuchs
17. Symmetry by Joshua Zucker
18.
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BAMO Practice Beginners by Paul Zeitz
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BAMO Practice Advanced by Kiran S. Kedlaya
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BAMO 2003 Practice
19. BAMO Practice General by Zvezdelina Stankova
The Handout was based on the National Math Olympiad from 1991
20. BAMO Aftermath by Maksim Maydansky
21 & 22. Loose Ends by Tom Rike
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Abstract
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Postscript Handout
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Postscript Figure
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PDF Handout
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PDF Figure
23.
The smallest prime factor (and other objects from number
theory) by Kiran S. Kedlaya
24. Combinatorial Identities: Euler, Gauss, Jacobi,
McDonald, Leibenzon and others. by Dmitry Fuchs
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abstract
24. Group and Crytals by Tatiana Shubin
25. Olympiad Problem Solving for USAMO by Zvezdelina
Stankova
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