New Books Recommended by Dr. Adorna Now Available @ EnggLib2 Circulation


Dr. Henry Adorna
Recommending Faculty

A guide to advanced linear algebra
(Dolciani mathematical expositions no. 44. ; MAA guides # 6)

Author Steven H. Weintraub
Place of Publication Washington, D.C
Date of Publication 2011
Publisher Mathematical Association of America

Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level, and is directed at graduate students and professional mathematicians. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Students in algebra, analysis, and topology will find much of interest and use to them, and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives.

Topics treated in this book include: vector spaces and linear transformations; dimension counting and applications; representation of linear transformations by matrices; duality; determinants and their uses; rational and especially Jordan canonical form; bilinear forms; inner product spaces; normal linear transformations and the spectral theorem; and an introduction to matrix groups as Lie groups.

The book treats vector spaces in full generality, though it concentrates on the finite dimensional case. Also, it treats vector spaces over arbitrary fields, specializing to algebraically closed fields or to the fields of real and complex numbers as necessary.

Algebraic theories : a categorical introduction to general algebra

Authors J. Adámek, J. Rosický, E.M. Vitale
Place of Publication New York
Date of Publication 2011
Publisher Cambridge University Press

Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved very useful in various areas of mathematics and computer science. This carefully developed book gives a systematic introduction to algebra based on algebraic theories that is accessible to both graduate students and researchers. It will facilitate interactions of general algebra, category theory and computer science. A central concept is that of sifted colimits – that is, those commuting with finite products in sets. The authors prove the duality between algebraic categories and algebraic theories and discuss Morita equivalence between algebraic theories. They also pay special attention to one-sorted algebraic theories and the corresponding concrete algebraic categories over sets, and to S-sorted algebraic theories, which are important in program semantics. The final chapter is devoted to finitary localizations of algebraic categories, a recent research area.

Matrices and graphs in geometry
(Encyclopedia of Mathematics and its Applications 139)

Author Miroslav Fiedler
Place of Publication Cambridge, U.K.
Date of Publication 2011
Publisher Cambridge University Press

Simplex geometry is a topic generalizing geometry of the triangle and tetrahedron. The appropriate tool for its study is matrix theory, but applications usually involve solving huge systems of linear equations or eigenvalue problems, and geometry can help in visualizing the behaviour of the problem. In many cases, solving such systems may depend more on the distribution of non-zero coefficients than on their values, so graph theory is also useful. The author has discovered a method that in many (symmetric) cases helps to split huge systems into smaller parts. Many readers will welcome this book, from undergraduates to specialists in mathematics, as well as non-specialists who only use mathematics occasionally, and anyone who enjoys geometric theorems. It acquaints the reader with basic matrix theory, graph theory and elementary Euclidean geometry so that they too can appreciate the underlying connections between these various areas of mathematics and computer science.

Topology for analysis

Author Albert Wilansky
Place of Publication Mineola, N.Y.
Date of Publication 2008
Publisher Dover Publications

Appropriate for both students and professionals, this volume starts with the first principles of topology and advances to general analysis. Three levels of examples and problems, ordered and numbered by degree of difficulty, illustrate important concepts. A 40-page appendix, featuring tables of theorems and counter examples, provides a valuable reference.

From explorations of topological space, convergence, and separation axioms, the text proceeds to considerations of sup and weak topologies, products and quotients, compactness and compactification, and complete semimetric space. The concluding chapters explore metrization, topological groups, and function spaces. Each subject area is supplemented with examples, problems, and exercises that progress to increasingly rigorous levels. All examples and problems are classified as essential, optional, and advanced.

Foundations of quantum mechanics : from photons to quantum computers

Author Reinhold Blümel
Place of Publication Sudbury, Mass.
Date of Publication c2010
Publisher Jones and Bartlett Publishers

Quantum computers are the proposed centerpieces of a revolutionary, 21st century quantum information technology. Ideal for undergraduate and graduate courses in modern quantum physics, Foundations of Quantum Mechanics: From Photons to Quantum Computers takes the reader into the fascinating world of quantum mechanics and continues on an in-depth study of quantum information and quantum computing, including an entire chapter on the future of quantum technology. This accessible text with modern applications focuses on what is quantum about quantum mechanics; topics discussed include the EPR paradox, entanglement, teleportation, Bell’ s Theorem, quantum computing, and code-breaking with quantum computers.

Cell biology, 6th ed.

Author Gerald Karp
Place of Publication Hoboken, N. J.
Date of Publication c2010
Publisher Wiley

Karp continues to help biologists make important connections between key concepts and experimentation. The sixth edition explores core concepts in considerable depth and presents experimental detail when it helps to explain and reinforce the concepts. The majority of discussions have been modified to reflect the latest changes in the field. The book also builds on its strong illustration program by opening each chapter with “VIP” art that serves as a visual summary for the chapter. Over 60 new micrographs and computer-derived images have been added to enhance the material. Biologists benefit from these changes as they build their skills in making the connection.

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