Feb 3rd, 2012
Studypool Tutor
Northwestern University
Price: $20 USD

Tutor description

As mathematics continues to expand so will topology. Topology will most likely give way to even more complex and abstract areas of mathematics. It is hard to imagine what may be the next branch of topology, considering that much of this field can only be explained mathematically. It is exciting to think that eventually these principles might have real life applications in a time when we are comfortable dealing with more than three dimensional space.

Word Count: 1467
Showing Page: 1/6
Subject- MathematicsTopic-TopologyUniversity Name- Northwestern UniversityTopologyMathematics is a field so vast and diverse that it is impossible to be an expert in all areas. It is also a field that is constantly evolving and branching outward. The field of topology is one of the newest intensively studied branches of mathematics. "A simple way to describe topology is as rubber sheet geometry" [2]. "Topology is an offshoot of geometry that originated during the 19th century and that studies those properties an object retains under deformation - specifically, bending, stretching and squeezing, but not breaking or tearing" [1]. Under these conditions, one could say that a square is topologicallyequivalentto a circle because a square can be bent and stretched into a circle [3]. However, a square is not topologically equivalent to a torus because a torus cannot be formed unless a hole is bored through the medium, or two pieces are joined together. Topologists obviously have expanded upon these simple concepts over time to create theorems further removed from our ordinary experiences. Some of these shapes and objects exist in fourdimensionalspace or higher dimensions and cannot exist inour world. Theoretically these shapes would be as commonplace as a tree or rock in a higher dimensional universe. However, in our universe topologists turn to mathematics to understand these shapes [6].The first mathematical problem, which led to the origins

Review from student

Studypool Student
" Thanks for the help. "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1825 tutors are online

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors