Algebra books

Examines seventeen groundbreaking equations that have altered the course of human history. This book explores how Pythagoras' Theorem led to GPS and SatNav; how logarithms are applied in architecture; why imaginary numbers were important in the development of the digital camera, and what is really going on with Schrodinger's cat.

This text provides a lively introduction to pure mathematics. It begins with sets, functions and relations, proof by induction and contradiction, complex numbers, vectors and matrices, and provides a brief introduction to group theory.

This bestelling introductory course covers all the key areas of algebra including elementary operations, linear equations, formulae, simultaneous equations, quadratic equations, logarithms, variation, laws and sequences.

Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments.

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces.

Schaum's Outlines present all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget.

A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections.

Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem....

With problems from National and International Mathematical Olympiads

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. This title presents the foundations of this theory.

In this classic graduate text, first published in 1999, the theory of distributions is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces; and also in this edition, the notion of the wavefront set of a distribution is introduced.

This book discusses quantized enveloping algebras (or variations thereof) introduced by Drinfeld and Jimbo. Coverage includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the Kac-Moody Lie algebras.

This book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets;

This book begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form.

This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises

Written specifically to introduce advanced undergraduate and beginning graduate students to an important area of mathematics, this book is far more accessible than previous books on Lie algebras. The emphasis is on special cases and explicit calculation, with many examples and exercises with full solutions provided.

This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear...

This text offers a friendly and concise introduction to algebra, with an emphasis on its real-world applications. It is intended for students who are less theoretically inclined. This text can be used for an undergraduate course in abstract algebra or modern algebra for mathematics, engineering, and computer science majors.