Dr. Zuming Feng, coach of the US IMO team and author of multiple books on Olympiad problem solving, shared valuable techniques for solving the Diophantine Equations which occur frequently in problem solving contests.
The students worked through a series of increasingly difficult problems and Dr. Feng guided them through ways to leverage their number sense and algebra to limit the number of possible solutions saving them invaluable time in a contest situation.
If you missed Dr. Feng this weekend we are happy to say that he will be returning to Metroplex Math Circle on March 7th. The video below shows Dr. Feng discussing solutions to the 2006 International Mathematics Olympiad.
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.
It might be interesting to look at several of the thriving Math Circles around the country. The Berkeley Math Circle has an excellent site with monthly contest problems available for download. Berkeley is also an excellent example of the positive impact that a Math Circle can have on its community. Here is some information from the Berkeley site on their outstanding alumni:
The success of Berkeley Math Circle in identifying and fostering talent is striking. Although the BMC only started in 1998, the 6-member team at the International Math Olympiad (held in Washington, D.C., July 2001) included 3 members from this program:
Gabriel Carroll, graduated from Harvard as a math major and currently attending the Ph.D. program in Economics at MIT. He has won 2 Gold and 1 Silver medals at the IMO (including one perfect score in 2001), and won the Putnam competition 4 times. He was the grand prize BAMO winner 3 times.
Tiankai Liu, now at Harvard, won 3 Gold medals at the IMO. He attended the Research Experience for Undergraduates Program at Duluth, Minnesota in Summer 2007.
Oaz Nir has won 1 gold and 1 silver medal and has graduated from Duke University as a math major.
The three Berkeley Math Circle students contributed to the USA’s second-place finish among over 80 countries at the International Mathematics Olympiad in 2001. In 2002, students from the Berkeley Math Circle and BAMO continued to do exceptionally well in mathematics competitions. Over the years, a number of Berkeley Math Circle students were among the top twelve winners of the USA Math Olympiad, and one was among the five students in the US with a perfect score: Inna Zakharevich (Henry Gunn High School, Palo Alto, Currently a student at Harvard University). Several other Circle students qualified for the summer training program of the US team several years in a row. Evan O’Dorney, only in 8th grade, qualified among the top 24 students for the training of the USA Math Team in Summer 2007. He further won the Grand Prize at BAMO 2007 with a perfect score. Additionally, he has been a three-time finalist and 2007 Champion at the Scripps National Spelling Bee in Washington D.C.
Among other famous alumni of BMC and BAMO, it is worth mentioning Maxim Maydanskiy who tied for first place with Gabriel Carroll at BAMO 2001. Maxim was admitted to UC Berkeley, and upon recommendation from the BMC circle coordinator, Dr. Stankova, his Circle and Olympiad activities played a major role in awarding him the Regent’s scholarship, the most prestigious UC Berkeley scholarship for entering undergraduates. While at UC Berkeley, he also attended the Research Experience for Undergraduates Program at Duluth, Minnesota, and is currently a Ph.D. student in Mathematics at MIT.
This is the continuation of the interviews with the 2006 US IMO team. The first speaker, is ZEB Brady. ZEB spent part of his summer at UT Dallas working at Dr. Andreescu’s prestigious summer camp, AwesomeMath. ZEB was a gold medalist at the 2006 IMO.
These particular problems are much harder than the level normally discussed at math circles, but the strategies of problem solving can be very similar. It is interesting to hear how even these brilliant students struggled with problem number 6.
Several postings have concerned the International Math Olympiad which is a bold aspiration for many Math Circle participants. But there are several steps on the road to representing the US on the IMO team and each one of those steps has its own challenges and rewards.
The USAMO is a six question, two day, 9 hour essay/proof examination. All problems can be solved with pre-calculus methods. Approximately 500 of the top scoring AMC participants (based on a weighted average) are invited to take the USAMO.
Just sitting for the USAMO requires a distinguished performance on the AIME, AMC 12 or AMC 10 tests.
The AIME (American Invitational Mathematics Examination) is an intermediate examination between the AMC 10 or AMC 12 and the USAMO. All students who took the AMC 12 and achieved a score of 100 or more out of a possible 150 are invited to take the AIME. All students who took the AMC 10 and had a score of 120 or were in the top 1% also qualify for the AIME.
The AMC 10 and AMC 12 test are administered to hundreds of thousands of high school students. Many of the universities who routinely reject applicants with 800 SAT Math scores are requiring submission of AMC test scores.
A special purpose of the AMC 12 is to help identify those few students with truly exceptional mathematics talent. Students who are among the very best deserve some indication of how they stand relative to other students in the country and around the world .
To prepare for these challenging and potentially life altering tests, AMC offers the AMC 8 eligible to students through the 8th grade.
The AMC 8 is a 25 question, 40 minute multiple choice examination in junior high school (middle school) mathematics designed to promote the development and enhancement of problem solving skills. The examination provides an opportunity to apply the concepts taught at the junior high level to problems which not only range from easy to difficult but also cover a wide range of applications. Many problems are designed to challenge students and to offer problem solving experiences beyond those provided in most junior high school mathematics classes.
Math Circles have a great deal to offer beyond improving performance on this series of tests. However, Metroplex Math Circle is particularly fortunate to have as its Director, Dr. Titu Andreescu, the former Director of AMC and Coach of the US IMO team. He has generously shared his experience with MMC students to help them prepare for these critical steps on the road to the IMO.
“Count Down” is a narrative account of the 2002 International Mathematical Olympiad, which was held at George Mason University just outside Washington, D.C. It follows the six members of the U.S. team, their coach, and their guide (who was a team member several years ago), describing the qualities that led the Olympians to be among the best high-school-aged mathematical problem solvers in the world. More broadly, Count Down explores the following question: How does anyone learn how to do something extremely well?
The book prominently features the Director of MMC, Dr. Andreescu, as well as many other friends of the Metroplex Math Circle.
This video gives some insight into the thought process of Olympiad problem solvers. The first speaker, Dr. Zuming Feng, is a good friend of the Metroplex Math Circle and is a regular speaker. Zach Abel, the first student speaker, is a Dallas native and an alumnus of Greenhill School.
These particular problems are much harder than the level normally discussed at math circles, but the strategies of problem solving can be very similar. Exposure to former Olympiad winners and coaches is a great inspiration to math circle participants.
The 2008 Olympics in Beijing were exciting but we should also take pride in the excellentshowing of the US team in the International Math Olympiad this summer in Spain.
U.S.A. Team Results
Paul Christiano, 23, Silver
Shaunak Kishore, 32, Gold
Evan O’Dorney, 26, Silver
Colin Sandon, 35, Gold
Krishanu Sankar, 32, Gold
Alex Zhai, 42, Gold
Achieving a Gold medal at the IMO is among the highest honors for high school aged problem solvers. In addition, Alex Zhai was one of only 3 competitors to write a perfect paper. The US came in third behind the formidable Chinese and Russian teams.
Dr. Titu Andreescu, Director of the Metroplex Math Circle, has co-authored yet another book designed for students and coaches preparing for high-school-level mathematical Olympiads, national or international.
If you have not already seen it the Hard Problems movie is terrific and features many friends of MMC. You can buy it from the Art of Problem Solving or we may arrange for a showing during the upcoming semester.
Posted by Metroplex Math Circle 
Posted by Metroplex Math Circle 
Posted by Metroplex Math Circle 
“Count Down” is a narrative account of the 2002 International Mathematical Olympiad, which was held at George Mason University just outside Washington, D.C. It follows the six members of the U.S. team, their coach, and their guide (who was a team member several years ago), describing the qualities that led the Olympians to be among the best high-school-aged mathematical problem solvers in the world. More broadly, Count Down explores the following question: How does anyone learn how to do something extremely well?
