Download E-books Elliptic Tales: Curves, Counting, and Number Theory PDF

By Avner Ash

Elliptic Tales describes the most recent advancements in quantity idea by way of the most fascinating unsolved difficulties in modern mathematics--the Birch and Swinnerton-Dyer Conjecture. during this publication, Avner Ash and Robert Gross advisor readers during the arithmetic they should comprehend this eye-catching problem.

The key to the conjecture lies in elliptic curves, that could look easy, yet come up from a few very deep--and usually very mystifying--mathematical principles. utilizing purely uncomplicated algebra and calculus whereas proposing a number of eye-opening examples, Ash and Gross make those rules available to basic readers, and, within the procedure, enterprise to the very frontiers of contemporary arithmetic.

Show description

Read Online or Download Elliptic Tales: Curves, Counting, and Number Theory PDF

Best Abstract books

Introduction to Local Spectral Theory

Smooth neighborhood spectral idea is equipped at the classical spectral theorem, a primary lead to single-operator conception and Hilbert areas. This e-book offers an in-depth creation to the common enlargement of this interesting subject of Banach house operator conception. It supplies entire assurance of the sector, together with the basic fresh paintings by way of Albrecht and Eschmeier which supplies the entire duality thought for Banach house operators.

More Concise Algebraic Topology: Localization, Completion, and Model Categories (Chicago Lectures in Mathematics)

With company foundations courting basically from the Fifties, algebraic topology is a comparatively younger zone of arithmetic. There are only a few textbooks that deal with primary themes past a primary direction, and plenty of themes now necessary to the sphere aren't handled in any textbook. J. Peter May’s A Concise direction in Algebraic Topology addresses the traditional first direction fabric, resembling basic teams, masking areas, the fundamentals of homotopy thought, and homology and cohomology.

Lie Groups: An Approach through Invariants and Representations (Universitext)

Lie teams has been an expanding region of concentration and wealthy study because the center of the 20 th century. In Lie teams: An method via Invariants and Representations, the author's masterful strategy supplies the reader a finished therapy of the classical Lie groups in addition to an in depth creation to a variety of subject matters linked to Lie teams: symmetric capabilities, thought of algebraic kinds, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic teams, workforce representations, invariants, Hilbert thought, and binary types with fields starting from natural algebra to practical research.

Topological Methods in Group Theory (Graduate Texts in Mathematics)

This publication is ready the interaction among algebraic topology and the speculation of limitless discrete teams. it's a highly vital contribution to the sphere of topological and geometric crew idea, and is certain to turn into a regular reference within the box. to maintain the size moderate and the point of interest transparent, the writer assumes the reader understands or can simply research the required algebra, yet desires to see the topology performed intimately.

Additional info for Elliptic Tales: Curves, Counting, and Number Theory

Show sample text content

Rated 4.56 of 5 – based on 38 votes