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## September 18th – Analysis of Number Sequences

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