Algebra and number theory have been mainstays of mathematical research and interest for centuries. A combination of techniques and tools from commutative algebra with motivation and language from geometry has made algebraic geometry one of the most exciting and active fields of research in modern mathematics. Ideas from algebraic geometry now help inform developments in a range of disciplines from topology to cryptography and classical number theory. With an advanced degree in this field, you will develop the ability to apply complex mathematical theories, computational techniques and algorithms to solve economic, scientific, engineering, physics and business-related problems.