In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler’s polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment “undergraduate topology” proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l’isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.
Classical Topology and Combinatorial Group Theory Free Download
April 7, 2022
![Classical Topology and Combinatorial Group Theory Classical Topology and Combinatorial Group Theory](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghn9TIqFuWQJg-pfvZExm7QmtvTKSTouEUciTEiOWXc0ZK1ew6UMLQ_NrUYT961mpJnbWM17USccgrG-pzKEBbZQURrG7cqQjZu-mQAQGqiCvyMQI242CHQKQ1PzQp-wZtjng-rKkL3ejx1kpvw4lgrWslnl7MODOmTmjtQQNau2Z_1Oc3lrCEo1ESeg/s320/Classical%20Topology%20and%20Combinatorial%20Group%20Theory.jpg)
You may also like
Number theory has a long and distinguished history and the concepts and problems relating to the subject have been instrumental in the foundation of much of...
Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis...
A new text for the liberal arts math course by a seasoned author team, Mathematical Excursions, is uniquely designed to help students see math at work in the...
Recent Posts
- Nuclear Physics Exploring the Heart of Matter PDF
- Applied Physics Crash Course by Arthur Beiser PDF
- Variational Principles in Physics by Jean-Louis Basdevant PDF
- Analytical Chemistry by Dhruba Charan Dash PDF
- Handbook of Modern Sensors Physics, Designs, and Applications 3rd Edition by Jacob Fraden PDF
Add Comment