Posts Tagged ‘Branislav Kisacanin’

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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The 2010-2011 season of Metroplex Math Circle will have a strong start with our first lecture by Dr. Branislav Kisačanin.

Dr. Kisačanin is a computer scientist at Texas Instruments working in the field of computer vision. In his spare time he likes to use computer vision for fun project such as his Tetris-playing robot. He loved math and physics competitions and nowadays likes to challenge his wife, kids, and friends with math problems and puzzles. Dr.Kisačanin wrote a book about selected mathematical gems:Mathematical Problems and Proofs.

Dr. Kisačanin has chosen Number Sequences as his first topic.  These sequences are critical parts of the tool kit of any middle school problem solver but also offer unexplored mysteries for professional mathematicians.  Following are some of the topics Dr. Kisačanin may cover in the course of his talk:

Triangular numbers

  • Derive the formula and the relation to square numbers both algebraically and geometrically
  • Sum of n squares (Gregory’s vanishing triangle, induction)
  • Sum of n cubes (connection back to triangular numbers)
  • Excercise: Sum of n odd numbers (again alg + geom)
  • OPTIONAL: Sums of higher powers (telescoping)

Fibonacci numbers

Binomial coefficients

  • Coefficients in (a+b)^n
  • Combinations
  • Pascal’s Triangle
  • Excercise: each row sums to 2^n, finding triangular and Fibonacci numbers, …

Other sequences and open problems

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We have had many firsts at MMC from our talented and varied speakers, but I think on September 18th we will hear from the very first MMC lecturer to have built a robot to play Tetris leveraging his advanced work in vision algorithms.

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