Algebraic Complexity Theory (Grundlehren der mathematischen Wissenschaften)1 review Peter Bürgisser, Michael Clausen, ... Springer, 1997 An Excellent Introduction and Reference This book presents an excellent and thorough introduction and overview of the field. It contains results of 573 papers in the field, but requires few prerequisites beyond basic abstract and linear algebra. It's perfect for independent study. The key parts of the book for those interested in ...             Algebraic Graph Theory1 review Chris Godsil, Gordon Royle Springer, 2001 an introduction to an interesting subject --The first part of the book is devoted to quite hard chapters on transitive, arc-transitive graph, homomorphism, etc. --The second part is about Matrix theory, interlacing, strongly regular graph, two graph, generalized line graph, etc it is the main part of the book. --The third part is about ...             Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications) Charles C. Sims Cambridge University Press, 1994 The book describes methods for working with elements, subgroups, and quotient groups of a finitely presented group. The author emphasizes the connection with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, from computational number theory, and from computational commutative algebra. The LLL lattice reduction algorithm and ...             Efficient Checking of Polynomials and Proofs and the Hardness of Approximation Problems (Lecture Notes in ... Springer, 1995 This book is based on the author's PhD thesis which was selected as the winning thesis of the 1993 ACM Doctoral Dissertation Competition. The author improved the presentation and included the progress achieved since the thesis was approved by the University of California at Berkeley. This work is a fascinating piece of theoretical computer science research building on deep results from different ...             Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative ...6 reviews David Cox, John Little, ... Springer, 2006 Easiest introduction to Algebraic Geometry + Symbolic computation + Straightforward and lucidly written + Good book + The best book on the topic             Algebraic Graph Theory (Cambridge Mathematical Library)1 review Norman Biggs Cambridge University Press, 1994 Well written, intriguing, but somewhat dated I found this book very clear, concise, and well written. Most proofs seemed effortless on both the author's and reader's part. Moreover, I found the content very interesting, especially the results on the spectrum of a graph, which simply represents the eigenvalues (and their multiplicities) of the ...             Undergraduate Commutative Algebra (London Mathematical Society Student Texts)1 review Miles Reid Cambridge University Press, 1996 "Undergraduate" in the best way The material in this book is not usually considered "undergraduate": Noether normalization, spectra of rings, discrete valuation rings, and more. But this book makes them very clear. It is more geometrical, and has more motivation, than Atiyah and MacDonald INTRODUCTION TO COMMUTATIVE ALGEBRA. It ...             Algebraic Codes for Data Transmission4 reviews Richard E. Blahut Cambridge University Press, 2002 A deep grasp of algebraic coding theory + Channel Coding gone wild The book is well organized and mathematically rigorous. It depicts a full picture of conventional algebraic coding theory in a systematic fashion. As a specialist in coding theory, I give my highest rank.             A Survey of Modern Algebra (AKP Classics) (Akp Classics)3 reviews Garrett Birkhoff; Saunders MacLane AK Peters, Ltd., 1997 This is how algebra texts ought to be written I have just started reading this book, and already I am enthralled by the beauty and elegance of the authors' exposition. Assuming nothing more than an acquaintance with school algebra and a little geometry, they develop the basic properties of central algebraic structures, including rings, ...             Undergraduate Algebraic Geometry (London Mathematical Society Student Texts)1 review Miles Reid Cambridge University Press, 1989 baked just right for the first timers ! There are many good books on the subject of algebraic geometry, so what was the use of one more - asks the author in the preface to this book. But there are none -at the UG level- which for the first time reveal to the younger mathematicians the secrets of this vast and growing subject. The book ...             Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties3 reviews G. Ausiello, P. Crescenzi, ... Springer, 2003 A great sequel to Garey and Johnson + Complexity book + A great sequel to Garey and Johnson This book is a great sequel to Garey and Johnson. The appendix of this book gives a list of all NP optimisation problems together with their current approximability (or inapproximability results) in a Garey Johnson fashion. Developing approximation algorithms for NP hard problems is now a very ...             Polynomials (Problem Books in Mathematics)4 reviews E.J. Barbeau Springer, 2003 5 stars as an introduction + Math pleasure + Polynomials Rule! + 6 stars! one of my favourites!             Abstract Algebra and Solution by Radicals7 reviews John E. Maxfield, Margaret W. Maxfield Dover Publications, 1992 Roots (as in square roots) + exelent book + Excellent text for a first course This charming little introit to abstract algebra is keyed on a theme of the algebraic equation, and the discovery of the insolubility of the quintic. This includes the history and final plight of the circle-squarers, and some of the history of Galois and Abel, working heroically and heuristically ...             Elementary Number Theory, Group Theory and Ramanujan Graphs (London Mathematical Society Student Texts) Giuliana Davidoff, Peter Sarnak, ... Cambridge University Press, 2003 This text is a self-contained study of expander graphs, specifically, their explicit construction. Expander graphs are highly connected but sparse, and while being of interest within combinatorics and graph theory, they can also be applied to computer science and engineering. Only a knowledge of elementary algebra, analysis and combinatorics is required because the authors provide the necessary ...             A First Course in Abstract Algebra, 7th Edition24 reviews John B. Fraleigh Addison Wesley, 2002 Fraleigh? awesome, sure + Fraleigh put into perspective This book was my introduction to algebra, and I can say that with me it hit its target - I not only learned and understood abstract algebra, but I grew to love it and be thrilled by it. If you are outside of mathematics and looking for the way in, I don't think you can do much better than ...             Gröbner Bases: A Computational Approach to Commutative Algebra (Graduate Texts in Mathematics) Thomas Becker, Volker Weispfenning Springer, 1998 This book provides a comprehensive treatment of Gr bner bases theory embedded in an introduction to commutative algebra from a computational point of view. The centerpiece of Gr bner bases theory is the Buchberger algorithm, which provides a common generalization of the Euclidean algorithm and the Gaussian elimination algorithm to multivariate polynomial rings. The book explains how the ...             Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative ...6 reviews David Cox, John Little, ... Springer, 2006 Easiest introduction to Algebraic Geometry + Symbolic computation + Straightforward and lucidly written + Good book + The best book on the topic             Undergraduate Algebraic Geometry (London Mathematical Society Student Texts)1 review Miles Reid Cambridge University Press, 1989 baked just right for the first timers ! There are many good books on the subject of algebraic geometry, so what was the use of one more - asks the author in the preface to this book. But there are none -at the UG level- which for the first time reveal to the younger mathematicians the secrets of this vast and growing subject. The book ...             Gröbner Bases: A Computational Approach to Commutative Algebra (Graduate Texts in Mathematics) Thomas Becker, Volker Weispfenning Springer, 1998 This book provides a comprehensive treatment of Gr bner bases theory embedded in an introduction to commutative algebra from a computational point of view. The centerpiece of Gr bner bases theory is the Buchberger algorithm, which provides a common generalization of the Euclidean algorithm and the Gaussian elimination algorithm to multivariate polynomial rings. The book explains how the ...             Algebraic Codes for Data Transmission4 reviews Richard E. Blahut Cambridge University Press, 2002 A deep grasp of algebraic coding theory + Channel Coding gone wild The book is well organized and mathematically rigorous. It depicts a full picture of conventional algebraic coding theory in a systematic fashion. As a specialist in coding theory, I give my highest rank.