Posts Tagged ‘Dr. Branislav Kisačanin’

PascalsTriangleCoefficientThe first hour of this talk will be targeted primarily at the younger part of our audience (roughly in grades 4-7) – we will explain the fundamental rules of counting that can be used to solve even very hard problems: rule of sum (addition principle), rule of product (multiplication principle), pigeonhole principle, and the inclusion-exclusion principle. We will use them to solve a number of interesting problems from various competitions. For those students already familiar with these concepts, we will have a set of problems to keep them busy during the first hour.

The second hour will be targeted at the more experienced members of the Math Circle community (roughly grades 8-12). First, we will discuss several techniques used to prove combinatorial identities (combinatorial arguments, algebraic manipulations, and the method of generating functions). We will prove several important combinatorial identities using all of these techniques, illustrating the diversity of approaches found in combinatorics. After that we will look at applications of combinatorics in number theory, geometry, and graph theory, illustrating them with more interesting and challenging problems. While the younger part of our audience may not be able to follow everything during the second hour, it will be a great exposure to advanced mathematical topics, to show them they have a lot more to learn.

Throughout the talk we will highlight the mathematicians who developed this beautiful mathematical field, from its beginnings in gambling to modern applications in medicine, science, and technology.


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network-securityIn this talk we will learn about the art of protecting information, some incredible (but true) stories from the history of cryptography, and how the all-important RSA code works. To get there, we will need a bit of Number Theory, in particular Fermat’s Little Theorem and Euler’s Theorem. In the process we will also learn how to solve a class of problems that might be seen at AMC competitions, such as:
  • What is the remainder when 2^1000 is divided by 997?
  • Determine the last digit of 1^1 + 2^2 + 3^3 + … + 2009^2009.

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