Algebraic Geometry

Download E-books Basic Concepts of Algebraic Topology (Undergraduate Texts in Mathematics) PDF

By Fred H. Croom

This article is meant as a one semester advent to algebraic topology on the undergraduate and starting graduate degrees. essentially, it covers simplicial homology concept, the basic staff, protecting areas, the better homotopy teams and introductory singular homology thought. The textual content follows a vast ancient define and makes use of the proofs of the discoverers of the $64000 theorems while this is often in keeping with the straight forward point of the path. this technique of presentation is meant to minimize the summary nature of algebraic topology to a degree that's palatable for the start scholar and to supply motivation and harmony which are frequently missing in abstact remedies. The textual content emphasizes the geometric method of algebraic topology and makes an attempt to teach the significance of topological thoughts via making use of them to difficulties of geometry and research. the must haves for this direction are calculus on the sophomore point, a one semester advent to the speculation of teams, a one semester introduc­ tion to point-set topology and a few familiarity with vector areas. Outlines of the prerequisite fabric are available within the appendices on the finish of the textual content. it is recommended that the reader no longer spend time before everything engaged on the appendices, yet relatively that he learn from the start of the textual content, bearing on the appendices as his reminiscence wishes fresh. The textual content is designed to be used through collage juniors of standard intelligence and doesn't require "mathematical adulthood" past the junior point.

Show description

Read Online or Download Basic Concepts of Algebraic Topology (Undergraduate Texts in Mathematics) PDF

Similar Algebraic Geometry books

Fractured Fractals and Broken Dreams: Self-Similar Geometry through Metric and Measure (Oxford Lecture Series in Mathematics and Its Applications)

Fractal styles have emerged in lots of contexts, yet what precisely is a trend? How can one make certain the buildings mendacity inside items and the relationships among them? This e-book proposes new notions of coherent geometric constitution to supply a clean method of this accepted box. It develops a brand new idea of self-similarity known as "BPI" or "big items of itself," which makes the sector a lot more uncomplicated for individuals to go into.

The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The idea of elliptic curves is distinctive via its lengthy background and by means of the variety of the equipment which were utilized in its learn. This booklet treats the mathematics strategy in its glossy formula, by using simple algebraic quantity idea and algebraic geometry. Following a short dialogue of the required algebro-geometric effects, the booklet proceeds with an exposition of the geometry and the formal staff of elliptic curves, elliptic curves over finite fields, the advanced numbers, neighborhood fields, and worldwide fields.

A First Course in Modular Forms (Graduate Texts in Mathematics, Vol. 228)

This e-book introduces the idea of modular kinds, from which all rational elliptic curves come up, with an eye fixed towards the Modularity Theorem. dialogue covers elliptic curves as complicated tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner conception; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian kinds linked to Hecke eigenforms.

Extra info for Basic Concepts of Algebraic Topology (Undergraduate Texts in Mathematics)

Show sample text content

Rated 4.35 of 5 – based on 47 votes