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Books > Science & Mathematics > Mathematics > Algebra > General

Galois Theory (Paperback, New edition): Emil Artin Galois Theory (Paperback, New edition)
Emil Artin
R149 R123 Discovery Miles 1 230 Save R26 (17%) Ships in 7 - 11 working days

Clearly presented elements of one of the most penetrating concepts in modern mathematics include discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 ed.

Galois Theory and Its Algebraic Background (Paperback, 2nd Revised edition): D.J.H. Garling Galois Theory and Its Algebraic Background (Paperback, 2nd Revised edition)
D.J.H. Garling
R900 Discovery Miles 9 000 Ships in 12 - 17 working days

Galois Theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects of pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals: that is, determining when and how a polynomial equation can be solved by repeatedly extracting roots using elementary algebraic operations. This textbook contains a fully detailed account of Galois Theory and the algebra that it needs and is suitable both for those following a course of lectures and the independent reader (who is assumed to have no previous knowledge of Galois Theory). The second edition has been significantly revised and re-ordered; the first part develops the basic algebra that is needed, and the second a comprehensive account of Galois Theory. There are applications to ruler-and- compass constructions, and to the solution of classical mathematical problems of ancient times. There are new exercises throughout, and carefully-selected examples will help the reader develop a clear understanding of the mathematical theory.

The Rules of Contagion - Why Things Spread--And Why They Stop (Paperback): Adam Kucharski The Rules of Contagion - Why Things Spread--And Why They Stop (Paperback)
Adam Kucharski
R384 R325 Discovery Miles 3 250 Save R59 (15%) Ships in 7 - 11 working days
All the Math You Missed - (But Need to Know for Graduate School) (Paperback, 2nd Revised edition): Thomas A. Garrity All the Math You Missed - (But Need to Know for Graduate School) (Paperback, 2nd Revised edition)
Thomas A. Garrity
R628 R523 Discovery Miles 5 230 Save R105 (17%) Ships in 7 - 11 working days

Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The explanations are accompanied by numerous examples, exercises and suggestions for further reading that allow the reader to test and develop their understanding of these core topics. Featuring four new chapters and many other improvements, this second edition of All the Math You Missed is an essential resource for advanced undergraduates and beginning graduate students who need to learn some serious mathematics quickly.

Math Without Numbers (Hardcover): Milo Beckman Math Without Numbers (Hardcover)
Milo Beckman
R501 R410 Discovery Miles 4 100 Save R91 (18%) Ships in 7 - 11 working days
Algebra - Notes from the Underground (Paperback): Paolo Aluffi Algebra - Notes from the Underground (Paperback)
Paolo Aluffi
R813 Discovery Miles 8 130 Ships in 12 - 17 working days

From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics - such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naive set theory.

Humble Pi - When Math Goes Wrong in the Real World (Paperback): Matt Parker Humble Pi - When Math Goes Wrong in the Real World (Paperback)
Matt Parker
R329 R275 Discovery Miles 2 750 Save R54 (16%) Ships in 7 - 11 working days
Numerical Ranges of Hilbert Space Operators (Hardcover): Hwa-Long Gau, Pei Yuan Wu Numerical Ranges of Hilbert Space Operators (Hardcover)
Hwa-Long Gau, Pei Yuan Wu
R2,923 Discovery Miles 29 230 Ships in 12 - 17 working days

Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.

Abstract Algebra - A Comprehensive Introduction (Hardcover): John W Lawrence, Frank A. Zorzitto Abstract Algebra - A Comprehensive Introduction (Hardcover)
John W Lawrence, Frank A. Zorzitto
R1,690 Discovery Miles 16 900 Ships in 12 - 17 working days

Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Groebner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.

Elementary Algebra (Hardcover): Harold Jacobs Elementary Algebra (Hardcover)
Harold Jacobs
R1,500 R1,157 Discovery Miles 11 570 Save R343 (23%) Ships in 5 - 10 working days
Linear Algebra for Everyone (Hardcover): Gilbert Strang Linear Algebra for Everyone (Hardcover)
Gilbert Strang
R1,269 Discovery Miles 12 690 Ships in 12 - 17 working days
The Ten Equations That Rule the World - And How You Can Use Them Too (Hardcover): David Sumpter The Ten Equations That Rule the World - And How You Can Use Them Too (Hardcover)
David Sumpter
R547 R447 Discovery Miles 4 470 Save R100 (18%) Ships in 7 - 11 working days
Perspectives on Projective Geometry - A Guided Tour Through Real and Complex Geometry (Hardcover, 2011 ed.): Jurgen... Perspectives on Projective Geometry - A Guided Tour Through Real and Complex Geometry (Hardcover, 2011 ed.)
Jurgen Richter-Gebert
R2,370 Discovery Miles 23 700 Ships in 7 - 11 working days

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author's experience in implementing geometric software and includes hundreds of high-quality illustrations.

Linear Algebra and Optimization for Machine Learning - A Textbook (Paperback, 1st ed. 2020): Charu C. Aggarwal Linear Algebra and Optimization for Machine Learning - A Textbook (Paperback, 1st ed. 2020)
Charu C. Aggarwal
R1,083 Discovery Miles 10 830 Ships in 7 - 11 working days

This textbook introduces linear algebra and optimization in the context of machine learning. Examples and exercises are provided throughout the book. A solution manual for the exercises at the end of each chapter is available to teaching instructors. This textbook targets graduate level students and professors in computer science, mathematics and data science. Advanced undergraduate students can also use this textbook. The chapters for this textbook are organized as follows: 1. Linear algebra and its applications: The chapters focus on the basics of linear algebra together with their common applications to singular value decomposition, matrix factorization, similarity matrices (kernel methods), and graph analysis. Numerous machine learning applications have been used as examples, such as spectral clustering, kernel-based classification, and outlier detection. The tight integration of linear algebra methods with examples from machine learning differentiates this book from generic volumes on linear algebra. The focus is clearly on the most relevant aspects of linear algebra for machine learning and to teach readers how to apply these concepts. 2. Optimization and its applications: Much of machine learning is posed as an optimization problem in which we try to maximize the accuracy of regression and classification models. The "parent problem" of optimization-centric machine learning is least-squares regression. Interestingly, this problem arises in both linear algebra and optimization, and is one of the key connecting problems of the two fields. Least-squares regression is also the starting point for support vector machines, logistic regression, and recommender systems. Furthermore, the methods for dimensionality reduction and matrix factorization also require the development of optimization methods. A general view of optimization in computational graphs is discussed together with its applications to back propagation in neural networks. A frequent challenge faced by beginners in machine learning is the extensive background required in linear algebra and optimization. One problem is that the existing linear algebra and optimization courses are not specific to machine learning; therefore, one would typically have to complete more course material than is necessary to pick up machine learning. Furthermore, certain types of ideas and tricks from optimization and linear algebra recur more frequently in machine learning than other application-centric settings. Therefore, there is significant value in developing a view of linear algebra and optimization that is better suited to the specific perspective of machine learning.

What's the Use? - How Mathematics Shapes Everyday Life (Hardcover): Ian Stewart What's the Use? - How Mathematics Shapes Everyday Life (Hardcover)
Ian Stewart
R570 R474 Discovery Miles 4 740 Save R96 (17%) Ships in 7 - 11 working days
The Math of Life and Death - 7 Mathematical Principles That Shape Our Lives (Paperback): Kit Yates The Math of Life and Death - 7 Mathematical Principles That Shape Our Lives (Paperback)
Kit Yates
R318 R262 Discovery Miles 2 620 Save R56 (18%) Ships in 7 - 11 working days
Operators and Representation Theory - Canonical Models for Algebras of Operators Arising in Quantum Mechanics (Paperback,... Operators and Representation Theory - Canonical Models for Algebras of Operators Arising in Quantum Mechanics (Paperback, Dover)
Palle E. T. Jorgensen; Foreword by William Klink
R404 R342 Discovery Miles 3 420 Save R62 (15%) Ships in 7 - 11 working days

Algebras of operators arise frequently in the study of representations of Lie groups, both finite-dimensional and infinite-dimensional. This book begins with extensive background material that covers definitions and terminology, operators in Hilbert space, and the imprimitivity theorem.
Advancing to considerations of the algebras of operators in Hilbert space, the heart of the text examines domains of representations, operators in the enveloping algebra, and spectral theory. The final section explores covariant representations and connections, with a particular focus on infinite-dimensional Lie algebras. A helpful Appendix on the integrability of Lie algebras concludes the text.

Abstract Lie Algebras (Paperback): David J Winter Abstract Lie Algebras (Paperback)
David J Winter
R225 R186 Discovery Miles 1 860 Save R39 (17%) Ships in 7 - 11 working days

Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. It also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. Contents include introductory material on prerequisites for modules and basic material on nonassociative algebras. 1972 edition.

A Gentle Course in Local Class Field Theory - Local Number Fields, Brauer Groups, Galois Cohomology (Paperback): Pierre Guillot A Gentle Course in Local Class Field Theory - Local Number Fields, Brauer Groups, Galois Cohomology (Paperback)
Pierre Guillot
R759 Discovery Miles 7 590 Ships in 12 - 17 working days

This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology. The book culminates with the description of the abelian extensions of local number fields, as well as the celebrated Kronecker-Weber theory, in both the local and global cases. The material will find use across disciplines, including number theory, representation theory, algebraic geometry, and algebraic topology. Written for beginning graduate students and advanced undergraduates, this book can be used in the classroom or for independent study.

An Introduction to Linear Algebra (Paperback): L. Mirsky An Introduction to Linear Algebra (Paperback)
L. Mirsky
R456 R384 Discovery Miles 3 840 Save R72 (16%) Ships in 7 - 11 working days

Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter. "The straight-forward clarity of the writing is admirable."-American Mathematical Monthly. Bibliography.

I Will Tell You Algebra Stories You'Ve Never Heard before (Paperback): Z.P. Dienes I Will Tell You Algebra Stories You'Ve Never Heard before (Paperback)
Z.P. Dienes
R335 Discovery Miles 3 350 Ships in 12 - 17 working days

In this work Zoltan Paul Dienes enlivens the world of algebra and examines some of the mysteries of mathematical constructions in a new and exciting fashion. Step by step, equation by equation, diagram by diagram, he strips away all the unintelligible jargon and brings each task and problem to life. If algebra lessons were viewed with dread at school, this is the book to make you reconsider. The informal style, clear diagrams and comprehensive explanations make understanding easy, while innovative games and intriguing puzzles ensure that learning is no longer a chore but a pleasure. Although predominantly aimed at those already equipped with basic algebra skills, beginners and experts alike will find much to interest and test them.

The Genesis of the Langlands Program (Paperback): Julia Mueller, Freydoon Shahidi The Genesis of the Langlands Program (Paperback)
Julia Mueller, Freydoon Shahidi
R1,475 Discovery Miles 14 750 Ships in 12 - 17 working days

Robert Langlands formulated his celebrated conjectures, initiating the Langlands Program, at the age of 31, profoundly changing the landscape of mathematics. Langlands, recipient of the Abel Prize, is famous for his insight in discovering links among seemingly dissimilar objects, leading to astounding results. This book is uniquely designed to serve a wide range of mathematicians and advanced students, showcasing Langlands' unique creativity and guiding readers through the areas of Langlands' work that are generally regarded as technical and difficult to penetrate. Part 1 features non-technical personal reflections, including Langlands' own words describing how and why he was led to formulate his conjectures. Part 2 includes survey articles of Langlands' early work that led to his conjectures, and centers on his principle of functoriality and foundational work on the Eisenstein series, and is accessible to mathematicians from other fields. Part 3 describes some of Langlands' contributions to mathematical physics.

Surveys in Combinatorics 2021 (Paperback): Konrad K. Dabrowski, Maximilien Gadouleau, Nicholas Georgiou, Matthew Johnson,... Surveys in Combinatorics 2021 (Paperback)
Konrad K. Dabrowski, Maximilien Gadouleau, Nicholas Georgiou, Matthew Johnson, George B. Mertzios, …
R1,468 Discovery Miles 14 680 Ships in 12 - 17 working days

This volume contains nine survey articles based on plenary lectures given at the 28th British Combinatorial Conference, hosted online by Durham University in July 2021. This biennial conference is a well-established international event, attracting speakers from around the world. Written by some of the foremost researchers in the field, these surveys provide up-to-date overviews of several areas of contemporary interest in combinatorics. Topics discussed include maximal subgroups of finite simple groups, Hasse-Weil type theorems and relevant classes of polynomial functions, the partition complex, the graph isomorphism problem, and Borel combinatorics. Representing a snapshot of current developments in combinatorics, this book will be of interest to researchers and graduate students in mathematics and theoretical computer science.

Modular Theory in Operator Algebras (Hardcover): Serban-Valentin Stratila Modular Theory in Operator Algebras (Hardcover)
Serban-Valentin Stratila
R2,810 Discovery Miles 28 100 Ships in 7 - 11 working days

The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by S.V. Stratila and L. Zsido) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu's result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.

A Course in Algebraic Error-Correcting Codes (Paperback, 1st ed. 2020): Simeon Ball A Course in Algebraic Error-Correcting Codes (Paperback, 1st ed. 2020)
Simeon Ball
R997 Discovery Miles 9 970 Ships in 7 - 11 working days

This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon's theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.

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