Our last lecture of fall 2008 by Dr. Tanya Khovanova reprised many of the themes that made this semester memorable.
The very first lecture by Richard Rusczyk emphasized the importance of playfulness to encourage a deep understanding in problem solvers. Many of our speakers continued this theme, and Dr. Khovanova’s first lecture on binary numbers was a perfect example.
She encouraged the students to work together in small groups and issued them the challenge to guess a day in the month by asking only 5 yes or no questions. Using binary she was able to teach them a memorable “trick” to always getting the right answer. She followed this with an exercise with playing cards which by applying a binary technique quickly sorted the deck into order.
After the break, Dr. Khovanova showed some of the web sites she had developed and others that are used by professional mathematicians:
Number Gossip is a particularly interesting web site developed by Dr. Khovanova that lists multiple interesting properties for any number the user enters. This recalls Dr. Paul Stanford’s own book of interesting numbers which he shared with us earlier in the semester.
The Online Encyclopedia of Integer Sequences is a tool sponsored by AT&T Research which contains many documented sequences from the well-known Fibonacci numbers to more obscure sequences.
The Pi-Search Page is a fun tool which allows the user to find a sequence of digits anywhere in the number Pi.
The Secret Lives of Numbers is a tool based upon all of the number references collected by Google. It is an interesting way to see how frequently specific numbers occur in our daily lives.
Dr. Khovanova’s Own Site has many useful essays and references for young problem solvers.
We are very grateful to Dr. Khovanova and all of our speakers for making this an excellent Fall semester and we look forward to the Spring.
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After Dr. Benjamin’s special November 19 presentation, Metroplex Math Circle will be on break for the next two Saturdays to allow people to travel for the Thanksgiving holiday.
We will return for our last lecture of the semester December 6 with Dr. Tanya Khovanova who will deliver two talks:
1. Binary Numbers
I will teach binary numbers, show a magic trick and we will play with binary dollars.
2. Integers and Sequences
Have you ever heard of untouchable numbers? How about aspiring numbers? I will tell you what they are. I will talk about perfect numbers and how they are connected to Mersenne primes. I will talk about the biggest known prime number. Have you ever wondered what is the most famous number sequence? What is the most versatile sequence? We will discuss that. What is the largest amount of coin money you can have without being able to make change for a dollar? You can bring your answer to this seminar. What is so special about 1089? You will learn that too. Is 42 (The Answer to Life, the Universe, and Everything) more famous than 47 (the secret Star Trek TNG number)? You will get the answer to that. I will also show you the Internet resources about numbers. You will be able to find out many things about your favorite numbers.
Dr. Khovanova has had a varied and interesting career. She grew up in Russia where she participated in many math competitions, winning 3 gold medals at the national level and one gold and a silver at the IMO. She earned her PhD in Mathematics at Moscow State University.
Until recently Dr. Khovanova worked in Battle Management until recently deciding to return to academia. She currently holds a position as a Visiting Scholar at Math Dept at MIT. In addition, Dr. Khovanova is a math competition coach at the Advanced Math and Sciences Academy.
You can read more about Dr. Tanya Khovanova on her blog.
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