Posted in meeting, tagged angle bisector, Branislav Kisacanin, Cassini Identity, direct proofs, Euclid, Fibonnacci, Mathematical Problems and Proofs, proof by contradiction, proof by induction, USAMO, USAMTS on October 10, 2010 |
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Computing a correct answer is sufficient for most grade school work, but proving that something must be true is one of the most important skills our students can learn. This ability has immediate benefits for such important tests as USAMTS or the USAMO as well as teaching the skills of reasoning and communication that can help in any profession.
We are very fortunate to once again have a lecture by Dr. Branislav Kisačanin. Here is his description of the upcoming session:
Introduction to Mathematical Proofs
In addition to a few more problems of historical significance, we will work on relatively simple problems that illustrate various proof techniques. In order to make things more interesting, we will let the students figure out which technique to use for each problem.
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Our September 18th speaker, Dr. Branislav Kisacanin, is an accomplished author. His book, Mathematical Problems and Proofs, has enjoyed very favorable reviews on Amazon:
This is a very interesting book. If you have mastered the bare essentials of set theory (through the upside down A for “for all” and the backwards E for “there exists”), AND either 1) the bare essentials of combinatorics (through Pascal’s triangle), or 2) the bare essentials of number theory (through the definition of the Moebius function and the statement of the Chinese Remainder theorem), or 3) the bare essentials of geometry (through the law of cosines), AND if you are very talented in mathematics, then this book is a “MUST READ”. It matters not whether you are a high school student or a professional mathematician. You will find new and fruitful insights and quite a few interesting problems in this book. For the beginner, there are several tantalizing (but somewhat oversimplified) references to advanced topics such as Paul Cohen’s proof of the independence of the continuum hypotheses and Wiles’ proof of Fermat’s last theorem. For the professional there are footnotes with references to little known and suprising results obtained in the 20th century. But, unlike the claims in the “editorial review”, this book neither prepares you to read the literaure nor is it a store house of exercises which will help you take your problem solving abilities to the next level. The “editorial review” is “off”, but the book is “right on”. Only the title is unfortunate. Where it will help the career mathematician is in the “beer hall” or “coffee house” or “tea time” discussions with other mathematicians. It is just chock full of beautiful little “gems” which can be shared with one’s friends. This is the kind of beautiful stuff that makes mathematics truly interesting and exciting and though I have searched for a book like this for the last 35 years, this is by far the best in its class which I have found. Dr. John Aiken, Jan 5, 2003.
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