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Posts Tagged ‘number theory’


crawfordteachIn addition to the Metroplex Math Circle, the Dallas Metroplex will soon be home to another unique institution which will help students develop their mathematical and problem solving skills.  Mathew Crawford, well-known to the global problem solving community for his early work on the Art of Problem Solving and two books in the library of almost every competitive problem solver (Introduction to Number Theory and Intermediate Algebra)  is opening his new school, Daedalus Education.

The new facility is being built out in a convenient location along 75:  3303 North Central Expressway, Suite 270, Plano, TX

Through his previous school and online resources, Mathew Crawford has helped many young problem solvers to realize their full potentialDaedalus Education offers a curriculum designed to inspire and challenge the most gifted problem solvers and evolved from years of working with a wide variety of students.

Mr. Crawford has been interviewing students and teaching assistants for his inaugural courses beginning in the fall.  Families interested in meeting with Mr. Crawford and applying for a spot in one of his classes should contact Daedalus Education as soon as possible.

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More Vi Hart doodles, this time exploring number theory.

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Number Theory is one of the cornerstones of math competitions and a vast field explored by professional mathematicians.  We are very fortunate to have Dr. Josh Nichols-Barrer present to us next week.  Dr. Nichols-Barrer was a very accomplished teenage competitive problem solver who has earned his doctorate at MIT.  In addition to Number Theory our students can learn a great deal from his personal experiences.  Here is a description of the session in Dr. Nichols-Barrer’s own words:

As you know, each positive integer may be factored uniquely into a product of powers of primes.  Do you know why?   In this class we will look at the structure of the integers in the simplest terms, and use that for a foundation from which we might actually prove that what we know to be true actually is.  In the first half we will recall some things about arithmetic that we know intuitively and can name (with maybe a surprise or two), and in the second half we will proceed to prove (along with some other things which are no less key) unique prime factorization in the integers.

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Our September 18th speaker, Dr. Branislav Kisacanin,  is an accomplished author.  His book, Mathematical Problems and Proofs, has enjoyed very favorable reviews on Amazon:

This is a very interesting book. If you have mastered the bare essentials of set theory (through the upside down A for “for all” and the backwards E for “there exists”), AND either 1) the bare essentials of combinatorics (through Pascal’s triangle), or 2) the bare essentials of number theory (through the definition of the Moebius function and the statement of the Chinese Remainder theorem), or 3) the bare essentials of geometry (through the law of cosines), AND if you are very talented in mathematics, then this book is a “MUST READ”. It matters not whether you are a high school student or a professional mathematician. You will find new and fruitful insights and quite a few interesting problems in this book. For the beginner, there are several tantalizing (but somewhat oversimplified) references to advanced topics such as Paul Cohen’s proof of the independence of the continuum hypotheses and Wiles’ proof of Fermat’s last theorem. For the professional there are footnotes with references to little known and suprising results obtained in the 20th century. But, unlike the claims in the “editorial review”, this book neither prepares you to read the literaure nor is it a store house of exercises which will help you take your problem solving abilities to the next level. The “editorial review” is “off”, but the book is “right on”. Only the title is unfortunate. Where it will help the career mathematician is in the “beer hall” or “coffee house” or “tea time” discussions with other mathematicians. It is just chock full of beautiful little “gems” which can be shared with one’s friends. This is the kind of beautiful stuff that makes mathematics truly interesting and exciting and though I have searched for a book like this for the last 35 years, this is by far the best in its class which I have found. Dr. John Aiken, Jan 5, 2003.

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This is a particularly beautiful movie showing how famous series from Number Theory underlie much of the structure in nature.

Information about the theory behind the movie is available here.

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A professor in the University of Texas system has received a significant and lucrative honor:

American wins $1 million math prize

Texas professor receives Norway’s Abel Prize for work in number theory

OSLO, Norway – An American professor at the University of Texas at Austin has won the 6 million kroner ($1 million) Abel Prize for mathematics. 

The prize jury praised John Tate as “a prime architect” of number theory, a branch of mathematics that has played a key role in the development of modern computers. 

The award citation issued Wednesday says Tate “has truly left a conspicuous imprint on modern mathematics” by advancing “one of (its) most elaborate and sophisticated branches.” 

Tate’s scientific accomplishments span six decades. A wealth of essential mathematical ideas and constructions were initiated by Tate and later named after him, such as the Tate module, Tate curve, Tate cycle, Hodge-Tate decompositions, Tate cohomology, Serre-Tate parameter, Lubin-Tate group, Tate trace, Shafarevich-Tate group and Néron-Tate height. 

In 2002-2003, Tate was a recipient of the Wolf Prize in Mathematics. The mathematician turned 85 this month and recently retired from his position as professor, becoming professor emeritus. 

The annual Abel Prize was created by the Norwegian government in 2003 and is awarded to candidates who have contributed to the mathematical sciences. The winner is selected by an international committee of five mathematicians. 

The prize will be given to Tate at a May 25 ceremony in Oslo. 

This report includes information from The Associated Press and msnbc.com. 
© 2010 msnbc.com

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discrete mathA good friend of the Metroplex Math Circle, Dr. Arthur Benjamin, has just released a new lecture course through the Teaching Company titled “Discrete Mathematics.” We have our pre-ordered copy and its seems to have the unique combination of humor and depth that we know from Dr. Benjamin’s excellent “mathemagic” presentations.

For any students just starting with Math Circles, they will benefit greatly from becoming familiar with the topics on these DVDs: number theory,  combinatorics and graph theory.

Here is the description of the course from the Teaching Company:

Welcome to Discrete Mathematics, a subject that is off the beaten track that most of us followed in school but that has vital applications in computer science, cryptography, engineering, and problem solving of all types.

Most of the mathematics taught after elementary school is aimed at preparing students for one subject—calculus, which is the mathematics of how things grow and change continuously, like waves in the water or clouds in the sky. Discrete mathematics, on the other hand, deals with quantities that can be broken into neat little pieces, like pixels on a computer screen, the letters or numbers in a password, or directions on how to drive from one place to another.

While continuous mathematics resembles an old-fashioned analog clock, whose second hand sweeps continuously across a dial, discrete mathematics is like a digital watch, whose numbers proceed one second at a time. As a result, discrete mathematics achieves fascinating mathematical results using relatively simple means, such as counting.

Explore this modern realm of digital math in Discrete Mathematics, 24 mind-expanding lectures by veteran Teaching Company Professor Arthur T. Benjamin, an award-winning educator and mathemagician who has designed a course that is mathematically rigorous and yet entertaining and accessible to anyone with a basic knowledge of high school algebra.

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