Adams, Colin

Why Knot?
An Introduction to the Mathematical Theory of Knots

2004, Approx. 100 p., Softcover
ISBN: 1-931914-22-2
A Key College Publishing book
Due: January 2004

About this textbook

Colin Adams, well-known for his advanced research in topology and knot theory, is the author of this exciting new book that brings his findings and his passion for the subject to a more general audience. This beautifully illustrated comic book is appropriate for many mathematics courses at the undergraduate level such as liberal arts math, and topology. Additionally, the book could easily challenge high school students in math clubs or honors math courses and is perfect for the lay math enthusiast. Each copy of Why Knot? is packaged with a plastic manipulative called the Tangle R. Adams uses the Tangle because "you can open it up, tie it in a knot and then close it up again." The Tangle is the ultimate tool for knot theory because knots are defined in mathematics as being closed on a loop. Readers use the Tangle to complete the experiments throughout the brief volume. Adams also presents a illustrative and engaging history of knot theory from its early role in chemistry to modern applications such as DNA research, dynamical systems, and fluid mechanics. Real math, unreal fun!

Written for:

Mathematics courses at the undergraduate level such as liberal arts math, and topology; high school students in math clubs or honors math courses; lay math enthusiast

Oertel, Herbert (Ed.)

Prandtl's Essentials of Fluid Mechanics,2nd ed.,

Series: Applied Mathematical Sciences, Vol. 158

2004, Approx. 600 p., Hardcover
ISBN: 0-387-40437-6

About this textbook

This book is an update and extension of the classic textbook by Ludwig Prandtl, Essentials of Fluid Mechanics. It is based on the 10th German edition with additional material included. Chapters on wing aerodynamics, heat transfer, and layered flows have been revised and extended, and there are new chapters on fluid mechanical instabilities and biomedical fluid mechanics. References to the literature have been kept to a minimum, and the extensive historical citations may be found by referring to previous editions. This book is aimed at science and engineering students who wish to attain an overview of the various branches of fluid mechanics. It will also be useful as a reference for researchers working in the field of fluid mechanics.

Written for:

Senior undergraduates, graduate students, researchers

Keywords:

fluid mechanics

Table of contents

Introduction.- Properties of Liquids and Gases.- Kinematics of Liquids and Gases.- Dynamics of Liquids and Gases.- Fundamental Equations of Fluid Mechanics.- Aerodynamics.- Turbulent Flows.- Fluid Mechanical Instabilities.- Convective Heat and Mass Transport.- Multi-Phase Flows.- Flows with Chemical Reactions.- Flows in the Atmosphere and in the Ocean.- Biofluid Mechanics.- Thermal Flow Machinery.

Izhboldin, O.T., Kahn, B., Karpenko, N.A., Vishik, A.
Tignol, Jean-Pierre (Ed.)

Geometric Methods in the Algebraic Theory of Quadratic Forms
Summer School, Lens, 2000

Series: Lecture Notes in Mathematics, Vol. 1835

2004, XIV,190p., Softcover
ISBN: 3-540-20728-7

About this book

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes an introduction to motives of quadrics by A. Vishik, with various applications, notably to the splitting patterns of quadratic forms, papers by O. Izhboldin and N. Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields with u-invariant 9, and a contribution in French by B. Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties.

Table of contents

Cohomologie non ramifiee des quadriques (B. Kahn).- Motives of Quadrics with Applications to the Theory of Quadratic Forms (A. Vishik).- Motives and Chow Groups of Quadrics with Applications to the u-invariant (N.A. Karpenko after O.T. Izhboldin).- Virtual Pfister Neigbors and First Witt Index (O.T. Izhboldin).- Some New Results Concerning Isotropy of Low-dimensional Forms (O.T. Izhboldin).- Izhboldin's Results on Stably Birational Equivalence of Quadrics (N.A. Karpenko).- My recollections about Oleg Izhboldin (A.S. Merkurjev).

Nastasescu, Constantin, Oystaeyen, Freddy van

Methods of Graded Rings

Series: Lecture Notes in Mathematics, Vol. 1836

2004, XII, 304 p., Softcover
ISBN: 3-540-20746-5

About this book

The topic of this book, graded algebra, has developed in the past decade to a vast subject with new applications in noncommutative geometry and physics. Classical aspects relating to group actions and gradings have been complemented by new insights stemming from Hopf algebra theory. Old and new methods are presented in full detail and in a self-contained way. Graduate students as well as researchers in algebra, geometry, will find in this book a useful toolbox. Exercises, with hints for solution, provide a direct link to recent research publications. The book is suitable for courses on Master level or textbook for seminars.

Table of contents

The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- Internal Homogenization.- External Homogenization.- Smash Products.- Localization of Graded Rings.- Application to Gradability.- Appendix A: Some Category Theory.- Appendix B: Dimensions in an Abelian Category.- Bibliography.- Index.

Arnold, Vladimir I.

Arnold's Problems

2004, Approx. 620 p., Hardcover
ISBN: 3-540-20614-0
Due: May 2004

About this book

Arnold's Problems contains mathematical problems which have been brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books. The invariable peculiarity of these problems was that mathematics was considered not as a game with deductive reasonings and symbols, but as a part of natural science (especially of physics), i.e. as an experimental science. Many of these problems are at the frontier of research still today and are still open, and even those that are mainly solved keep stimulating new research appearing every year in journals all over the world. The second part of the book is a collection of comments of mostly Arnold's former students about the current progress in the problems' solution (featuring bibliography inspired by them). This book will be of great interest to researchers and graduate students in mathematics and mathematical physics.

Written for:

Researchers and graduate students in mathematics and mathematical physics

Peitgen, Heinz-Otto, Jurgens, Hartmut, Saupe, Dietmar

Chaos and Fractals, 2nd ed.,
New Frontiers of Science

2004, XIII, 864 p. 606 illus., 40 in color., Hardcover
ISBN: 0-387-20229-3
Due: February 2004

About this textbook

The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot set, Julia sets, cellular automata, L-systems, percolation and strange attractors. This new edition has been thoroughly revised throughout. The appendices of the original edition were taken out since more recent publications cover this material in more depth. Instead of the focussed computer programs in BASIC, the authors provide 10 interactive JAVA-applets for this second edition.

Written for:
Teachers and students of main fields, teachers and students of secondary fields, interested lay people

Table of contents

Introduction: Causality Principle, Deterministic Laws and Chaos.- The Backbone of Fractals: Feedback and the Iterator.- Classical Fractals and Self-Similarity.- Limits and Self-Similarity.- Length, Area, and Dimension: Measuring Complexity and Scaling Properties.- Encoding Images by Simple Transformations.- The Chaos Game: How Randomness Creates Deterministic Shapes.- Recursive Structures: Growing Fractals and Plants.- Pascal's Triangle: Cellular Automata and Attractors.- Irregular Shapes: Randomness in Fractal Constructions.- Deterministic Chaos: Sensitivity, Mixing, and Periodic Points.- Order and Chaos: Period-Doubling and Its Chaotic Mirror.- Strange Attractors: The Locus of Chaos.- Julia Sets: Fractal Basin Boundaries.- The Mandelbrot Set: Ordering the Julia Set.