当今的计算机和其他信息处理设备使用对物理定律的经典近似来操纵信息。然而
Combinatorics is the study of discrete structures and their properties. Many modern scientific advances have employed combinatorial structures to model the physical world, and recent advances in computational technology have made such investigations feasible. In particular, since computers process discrete data, combinatorics has become indispensable to computer science. Optimization, or mathematical programming, is the study of maximizing and minimizing functions subject to specified boundary conditions or constraints. With the emergence of computers, optimization experienced a dramatic growth as a mathematical theory, enhancing both combinatorics and classical analysis. The functions to be optimized arise in engineering, the physical and management sciences, and in various branches of mathematics. The MMath degree involves about a year of graduate courses and either a research report or thesis supervised by a faculty member.<br><br>Today's computers and other information processing devices manipulate information using what is known as the classical approximation to the laws of physics. However, we have known for some time that there is a more accurate description of the laws - the one provided by quantum mechanics. The study of how the laws of quantum mechanics affect computing, cryptography, and similar information processing tasksis known as quantum information processing. In the 1990s, a sequence of results culminated in an efficient quantum algorithm for decomposing integers into their prime factors. No efficient classical algorithm is known for this problem, and its apparent hardness for classical computers is the foundation of the RSA encryption protocol widely used for e-commerce. Since then, fast quantum algorithms have been discovered for a variety of important problems. Quantum phenomena have a dramatic, and often counter-intuitive effect on other aspects of information processing as well. For instance, they enable cryptographic tasks such as secret key expansion with the guarantee that its security rests solely on the validity of quantum theory, as opposed to the conjectured hardness of a computational problem.