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Modern algebra has its roots in the mathematics of the ancient world, arising out of the basic problem of solving equations. Following an explosive development in the twentieth century, it is now a vibrant, multi-faceted and wide-ranging branch of mathematics, having ties with almost every field of mathematics and computer science. The interests of the algebra group at Northeastern include algebraic geometry, commutative algebra, representation theory, homological algebra, and quantum groups, with connections to combinatorics, singularities, Lie groups, topology, and physics.
Algebraic geometry generally uses tools from algebra to study objects called algebraic varieties that are solution sets to algebraic equations
Perhaps the fastest growing area of modern mathematics. It has a wealth of real-world applications, especially in computer science, which have greatly contributed to its rapid growth.
Differential geometry uses tools from analysis to study objects called manifolds that generalize Euclidean space.
Discrete geometry studies combinatorial properties of finite or discrete objects.