# Math Xperience

For high school students participating in Virginia Tech's Math Xperience

Networks are all around us. They appear in our daily lives in various forms such as in the way we communicate with our friends, or the way our brains communicate with different parts of the body. Mathematics provides a great avenue for us to study the different types of networks. In this video, I will give a brief introduction about networks along with a couple of fun examples.

Note that this activity will require each student to have about 60 toothpicks (or maybe dry speghetti noodles). Students will use toothpicks as Chinese rods to perform row reduction and solve systems of equations. They should see how the Chinese number system – the earliest base-10 system – led to the invention of Gaussian elimination 1600 years before Gauss was born!

The study of infinite series is one of the most challenging topics in modern mathematics. The Greek philosopher, Zeno, almost 2400 years ago, devised some paradoxes to challenge and criticize our understanding of the physical world. The flaws of his paradoxes can be shown by studying the infinite series. Applications of the infinite series in mathematics, probability, physics, engineering, finance and computer science makes this subject absolutely fascinating. During this 30-minute presentation, we will discuss some fun facts and computations about infinite series. It may even blow your mind!

Oscillations are all around us, from predator-prey interactions in the animal kingdom, to business cycles in the corporate world. The most basic functions that describe oscillations are the trigonometric functions. Interestingly, arbitrary functions can be decomposed into basic trigonometric functions, and we explore that theme in this activity.

In 1978, two American computer scientists and cryptographers, Merkle and Hellman, published the earliest examples of a cryptosystem based on the knapsack problem. Before that, in 1976, the idea of public key cryptography was introduced by Diffie and Hellman. A public key cryptosystem has 2 keys: a public key for encryption, and a private key for decryption. In this presentation, I try to represent the idea of knapsack ciphers with some simple examples.