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Math 55 is a two-semester freshman undergraduate mathematics course at Harvard University founded by Lynn Loomis and Shlomo Sternberg.The official titles of the course are Studies in Algebra and Group Theory (Math 55a) [1] and Studies in Real and Complex Analysis (Math 55b). [2]
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism , though usually most classify up to homotopy equivalence .
Algebra includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called group. Outline of algebra; Glossary of field theory; Glossary of ...
Since 2002 Cohen has been one of the developers and contributors to the theory of String topology, which was introduced originally by Moira Chas and Dennis Sullivan. In 1995, Cohen was a founder of the Stanford University Math Camp (SUMaC), a summer camp for mathematically talented high school students.
Finite mathematics – Syllabus in college and university mathematics; Graph theory – Area of discrete mathematics; Digital geometry – Deals with digitized models or images of objects of the 2D or 3D Euclidean space; Digital topology – Properties of 2D or 3D digital images that correspond to classic topological properties
Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces Subcategories. This category has the following ...
Chain (algebraic topology) Betti number; Euler characteristic. Genus; Riemann–Hurwitz formula; Singular homology; Cellular homology; Relative homology; Mayer–Vietoris sequence; Excision theorem; Universal coefficient theorem; Cohomology. List of cohomology theories; Cocycle class; Cup product; Cohomology ring; De Rham cohomology; Čech ...
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...