Burger, E., Williams College, Williamstown, MA, USA
Starbird, M., University of Texas, Austin, TX, USA
The Heart of Mathematics
A Guide to Effective Thinking
2000. Approx. 680 pp. 700 figs., 100 in color.
1-55953-407-9
The power and attractiveness of the subject of mathematics is often hidden from students who are in introductory courses. In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, chanllenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.
Contents: Ch. 0: Welcome!; Ch. 1: Surfing the book; Ch. 2: Fun and Games: A Introduction to rigorous
thought; Ch. 3: Number Theory: The secret and hidden power of numbers; Ch. 4: Infinity; Ch. 5: Geometric
Gems; Ch. 6: Contortions of Space; Ch. 7: Chaos and Fractals; Ch. 8: Risky Business; Ch. 9: Farewell
Series: Textbooks in Mathematical Sciences.
Fields: Mathematics, general
Written for: College students
Book category: Undergraduate Textbook
Publication language: English
Hopf, H.
Eckmann, B., Eidgenessische Technische Hochschule Zurich, Switzerland
Collected Papers - Gesammelte Abhandlungen
2000. Etwa 1240 S.
3-540-57138-8
From the preface: "Hopf algebras, Hopf fibration of spheres, Hopf-Rinow complete Riemannian manifolds, Hopf
theorem on the ends of groups - can one imagine modern mathematics without all this? Many other concepts and methods, fundamental in various mathematical disciplines, also go back directly or indirectly to the work of Heinz Hopf: homological algebra, singularities of vector fields and characteristic classes, group-like spaces, global differential geometry, and the whole algebraisation of topology with its influence on group theory, analysis and algebraic geometry. It is astonishing to realize that this oeuvre of a whole scientific life consists of only about 70 writings. Astonishing also the transparent and clear style, the concreteness of the problems, and how abstract and far-reaching the methods Hopf invented."
Schlagworte: Heinz Hopf, Collected Papers
Inhalt: Table of Contents.- List of Publications of Heinz Hopf.- Editor's Preface - Papers of Heinz Hopf.- Heinz
Hopf Selecta Fachgebiete: Algebraische Topologie; Kategorien, Homologische Algebra, Algebraische
K-Theorie; Gruppentheorie
geschrieben fur: mathematicians
Buchkategorie: Werkausgabe
Publikationssprache: Deutsch
Poizat, B., Universite Claude Bernard Lyon I, Villeurbanne, France
A Course in Model Theory
An Introduction to Contemporary Mathematical Logic
2000. Approx. 450 pp.
0-387-98655-3
This book, translated from the French, is an introduction to first-order model theory. The first six chapters are
very basic: starting from scratch, they quickly reach the essential, namely, the back-and-forth method and
compactness, which are illustrated with examples taken from algebra. The next chapter introduces logic via the
study of the models of arithmetic, and the following is a combinatorial tool-box preparing for the chapters on
saturated and prime models. The last ten chapters form a rather complete but nevertheless accessible exposition of stability theory, which is the core of the subject.
Fields: Mathematical Logic and Set Theory
Written for: Graduate mathematics students, logicians, mathematicians
Book category: Graduate Textbook
Publication language: English
Mordeson, J.N., Creighton University, Omaha, NE, USA
Nair, P.S., Creighton University, Omaha, NE, USA
Fuzzy Graphs and Fuzzy Hypergraphs
2000. XIV, 248 pp. 29 figs., 10 tabs.
3-7908-1286-2
The authors present an up-to-date account of results from fuzzy graph theory and fuzzy hypergraph theory and give applications of the results. The book should be of interest to research mathematicians and to engineers and computer scientists interested in applications. Some specific application areas presented from fuzzy graph theory are cluster analysis, pattern classfication, database theory, and the problem concerning group structure. Applications of fuzzy hypergraph theory to portfolio management, managerial decision making with an example to waste management, and to neural cell-assemblies are given. It is shown how (fuzzy) hypergraphs and rough sets are related in such a way that ideas may be carried back and forth between the two areas.
Keywords: Fuzzy Graph Theory, Fuzzy Hypergraph Theory, Fuzzy Graphs, Fuzzy Mathematics
Contents: Fuzzy Subsets: Fuzzy Relations.- Fuzzy Equivalence Relations.- Pattern Classification.- Similarity
Relations.- References.- Fuzzy Graphs: Paths and Connectedness. Bridges and Cut Vertices. Forests and
Trees. Trees and Cycles. A Characterization of Fuzzy Trees. (Fuzzy) Cut Sets. (Fuzzy Chords, (Fuzzy) Cotrees, and (Fuzzy) Twigs. (Fuzzy) 1-Chain with Boundary 0, (Fuzzy) Coboundary, and (Fuzzy) Cocycles. (Fuzzy) Cycle Set and (Fuzzy) Cocycle Set.- Fuzzy Line Graphs.- Fuzzy Interval Graphs. Fuzzy Intersection Graphs. Fuzzy Interval Graphs. The Fulkerson and Gross Characterization. The Gilmore and Hoffman Characterization.- Operations on Fuzzy Graphs: Cartesian Product and Composition. Union and Join.- On Fuzzy Tree Definition.- References.- Applications of Fuzzy Graphs: Clusters.- Cluster Analysis. Cohesiveness. Slicing in Fuzzy Graphs.- Application to Cluster Analysis.- Fuzzy Intersection Equations. Existence of Solutions.- Fuzzy Graphs in Database Theory. Representation of Dependency Structure r(X,Y) by Fuzzy Graphs.- A Description of Strengthening and Weakening Members of a Group. Connectedness Criteria. Inclusive Connectedness Categories. Exclusive Connectedness Categories.- An Application of Fuzzy Graphs to the Problem Concerning Group Structure. Connectedness of a Fuzzy Graph. Weakening and Strenghtening Points of a Fuzzy Directed Graph.- References.- Fuzzy Hypergraphs: Fuzzy Hypergraphs.- Fuzzy Transversals of Fuzzy Hypergraphs. Properties of Tr(H). Construction of H3.- Coloring of Fuzzy Hypergraphs. beta-degree Coloring Procedures. Chromatic Values of Fuzzy Colorings.- Intersecting Fuzzy Hypergraphs. Characterization of Strongly Intersecting Hypergraphs. Simply Ordered Intersecting Hypergraphs. H-dominant Transversals.- Hebbian Structures.- Additional Applications.- References.
Series: Studies in Fuzziness and Soft Computing.VOL. 46
Fields: Combinatorial Mathematics/Graph Theory and Discrete Mathematics; Mathematics of
Computing; Information Systems/Business Data Processing
Written for: Research mathematicians, engineers, computer scientists in the fields of graph/hypergraph theory
Book category: Monograph
Publication language: English
Borwein, J., Simon Fraser University, Burnaby, BC, Canada
Lewis, A.S., University of Waterloo, ONT., Canada
Convex Analysis and Nonlinear Optimization
Theory and Examples
2000. Approx. 320 pp.
0-387-98940-4
Optimization is a rich and thriving mathematical discipline. The theory underlying current computational
optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis
unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis
and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises.
Contents: * Background * Inequality constraints * Fenchel duality * Convex analysis * Special cases *
Nonsmooth optimization * The Karush-Kuhn- Tucker Theorem * Fixed points * Postscript: infinite versus finite
dimensions * List of results and notation
Series: CMS Books in Mathematics. VOL. 3
Fields: Functional Analysis,Operator Theory
Written for: Graduate math students, mathematicians
Book category: Graduate Textbook
Publication language: English
Quarteroni, A., Ecole Polytechnique Federale de Lausanne, Switzerland
Sacco, R., Politecnico di Milano, Italy/Saleri, F., Politecnico di Milano, Italy
Numerical Mathematics
2000. Approx. 680 pp. 135 figs.
0-387-98959-5
Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions.
As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied
sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on
examples and counterexamples which outline their pros and cons. This is done using the MATLAB software
environment which is user-friendly and widely adopted. Within any specific class of problems, the most
appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the
expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples,
exercises and applications of the discussed theory to the solution of real-life problems.
This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in Engineering, Mathematics, Physics and Computer Sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields.
Series: Texts in Applied Mathematics.VOL. 37
Fields: Mathematics, general
Written for: Graduate students, researchers
Book category: Graduate Textbook
Publication language: English