Jean-Pierre Serre's mathematical contributions, leading to a Fields Medal in 1954, were largely in the field of algebraic topology, but his later work ranged widely--within algebraic geometry, group theory, and especially

number theory.

Zhang did so in spite of being a relative unkown in the field of

number theory.

GOING FOR GOLD:

Number Theory ridden by Russ Kennemore (second from the right) pictured winning the bet365 Old Newton Cup

Among the topics are partition functions and box-spline, the calculus of operator functions, toric Sasaki-Einstein geometry, automorphic representations, rigidity of polyhedral surfaces,

number theory techniques in the theory of Lie groups and differential geometry, the flabby glass group of a finite cyclic group, Green's formula in Hall algebras and cluster algebras, zeta functions in combinatorics and

number theory, and soliton hierarchies constructed from involutions.

SCHOOL ACTIVITIES: Fencing, Grades 10-12, rated E2010 by USFA; Track, Grades 10-12;

Number Theory and Puzzling Club, Grades 10-12, president, Grade 12; Harry Potter Club, Grades 9-12, co-president, Grade 12; National Honor Society, Grades 10-12, president, Grade 12.

In elementary

number theory, we call an arithmetical function f (n) as an additive function, if for any positive integers m, n with (m, n) = 1, we have f (mn) = f (m) + f (n).

Dave Penniston, Computational

Number Theory and Combinatorics 2006 REU, Clemson University, Clemson, SC 29634.

Topics covered include coding theory, cryptology, combinatorics, finite geometry, algebra, and

number theory.

Odorless, colorless--a

number theory of the universe weighs next to

A related subplot involves three young MIT math geniuses and offers some fascinating glimpses into the rarefied world of advanced

number theory and its personal and technical applications.

She was engaged in proving a statement of elementary

number theory.

The contest is open to secondary students and includes topics relating to Euclidian and analytic geometry, trigonometry, the binomial theorem, and elementary

number theory.

However, other sequences are sometimes encountered, especially in combinatorics and

number theory, which have application to several areas of computer science, and which often have an intriguing physical analogy.

As I read the book I marked in the margins where Stephenson found opportunities to explain the

number theory that underlies modern cryptography; "traffic analysis" (deriving military intelligence from where and when messages are sent and received, without actually decoding them); steganography (hiding secret messages within other, non-secret communications); the electronics of computer monitors (and the security problems created by those monitors); the advantages to Unix-like operating systems compared to Windows or the Mac OS; the theory of monetary systems; and the strategies behind high-tech business litigation.