Topology
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Topology
Topology is a significant part of mathematics that focuses on spatial properties preserved under continuous deformations of objects, like stretching. (Tearing or gluing would not be allowed.) The subject was engendered from concepts in geometry and set theory, such as space, dimension, and transformation.
If you think the study of topology is far removed from the "real" world in which we live, you are mistaken. Applications of topological studies pervade all areas of our lives. For example, the surface of a golf ball has interesting topology, and manufacturers of golf balls hire mathematicians to do research on the design of golf ball surfaces that will lead to cutting edge performance through improved flight characteristics.
Topics that students in topology will study include:
- Set Theory and Logic
- Topological Spaces and Continuous Functions
- Connectedness and Compactness
- Countability and Separation Axioms
- The Tychonoff Theorem
- Metrization Theorems and Paracompactness
- Complete Metric Spaces and Function Spaces
- Baire Spaces and Dimension Theory
- Algebraic Topology
- The Fundamental Group
- Separation Theorems in the Plane
- The Seifert-van Kampen Theorem
- Classification of Surfaces
- Classification of Covering Spaces
- Applications to Group Theory
MIT's Open Courseware has several entire courses in topology available to students for free, including Introduction to Topology. Many books on this subject can be found at Google Books and Amazon.com. Good tutorials on topology are available through the University of Illinois at Urbana-Champaign's Beckman Institute for Advanced Science and Technology, Topology Tutorial I. Journals that students should be following include Oxford University Press' Journal of Topology and Elsevier's Topology.
To fulfill our tutoring mission of online education, our college homework help and online tutoring centers are standing by 24/7, ready to assist college students who need homework help with all aspects of topology. Our mathematics tutors can help with all your projects, large or small, and we challenge you to find better online topology tutoring anywhere.
College Topology Homework Help
Since we have tutors in all Topology related topics, we can provide a range of different services. Our online Topology tutors will:
- Provide specific insight for homework assignments.
- Review broad conceptual ideas and chapters.
- Simplify complex topics into digestible pieces of information.
- Answer any Topology related questions.
- Tailor instruction to fit your style of learning.
With these capabilities, our college Topology tutors will give you the tools you need to gain a comprehensive knowledge of Topology you can use in future courses.
24HourAnswers Online Topology Tutors
Our tutors are just as dedicated to your success in class as you are, so they are available around the clock to assist you with questions, homework, exam preparation and any Topology related assignments you need extra help completing.
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