<p>How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincaré argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time. The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.</p>

A First Course in Topology: Continuity and Dimension (Student Mathematical Library) (Student Mathematical Library, 31)

Science & Math

John McCleary

Mathematics

American Mathematical Society

<p>Winner of a CHOICE Outstanding Academic Title Award for 2017! What does style mean in mathematics? Style is both how one does something and how one communicates what was done. In this book, the author investigates the worlds of the well-known numbers, the binomial coefficients. The author follows the example of Raymond Queneau's Exercises in Style. Offering the reader 99 stories in various styles. The book celebrates the joy of mathematics and the joy of writing mathematics by exploring the rich properties of this familiar collection of numbers. For any one interested in mathematics, from high school students on up.</p>

Exercises in (Mathematical) Style (Anneli Lax New Mathematical Library) (Anneli Lax New Mathematical Library, 48)

Geometry From A Differentiable Viewpoint

Cambridge University Press

Exercises in (Mathematical) Style: Stories of Binomial Coefficients (Anneli Lax New Mathematical Library, 50)

Max Dehn

Jemma Lorenat

Volker R. Remmert

David E. Rowe

Providence, Rhode Island : American Mathematical Society

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Books by John McCleary