This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics.
Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.
Finitely Generated Algebras
The K-Spectrum and the Zariski Topology
Prime Spectra and Dimension
Schemes
Projective Schemes
Regular, Normal and Smooth Points
Riemann*Roch Theorem
220pp Pub. date: Mar 2010
ISBN: 978-981-4304-56-6
ISBN: 978-981-4307-58-1(pbk)
Paperback (ISBN-13: 9780521535830)
Page extent: 348 pages
Size: 244 x 170 mm
Weight: 0.56 kg
This book was originally published in 2004. Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.
* Self-contained textbook, suitable for self-study or as a supplement, with problems and worked-out examples * Previously unpublished material: original results and a chapter on the shape of a random walk * Copious use of supplements gives reader ready access to important background material
Preface; 1. Introduction to techniques; 2. Generating functions I; 3. Generating functions II: recurrence, sites visited, and the role of dimensionality; 4. Boundary conditions, steady state, and the electrostatic analogy; 5. Variations on the random walk; 6. The shape of a random walk; 7. Path integrals and self-avoidance; 8. Properties of the random walk: introduction to scaling; 9. Scaling of walks and critical phenomena; 10. Walks and the O(n) model: mean field theory and spin waves; 11. Scaling, fractals, and renormalization; 12. More on the renormalization group; References; Index.
Hardback (ISBN-13: 9780521192484)
Paperback (ISBN-13: 9780521122542)
18 b/w illus. 94 exercises
Page extent: 240 pages
Size: 228 x 152 mm
The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive, and this is captured by saying that P is different from NP. Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.
* Book focuses on the P versus NP Question, which is the most fundamental question of computer science * Book clarifies the importance of the P versus NP Question and the theory of NP-completeness in general terms
1. Computational tasks and models; 2. The P versus NP Question; 3. Polynomial-time reductions; 4. NP-completeness; 5. Three relatively advanced topics; Epilogue: a brief overview of complexity theory.
2010, Approx. 1000 p. 2-volume-set.
ISBN: 978-3-0346-0163-4
The first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.
The second volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.
Keywords ≫ complex analysis - integral equations - matrix theory - operator theory - systems theory
2012, Approx. 7000 p. In 9 volumes, not available separately., Hardcover
ISBN: 978-3-540-70528-4
Due: January 2012
There do not exist any comprehensive, up-to-date encyclopedias in Mathematics. Thus, EACM is without competition and will be a landmark in Mathematics publishing. The EACM team of editors consists of scientists of the highest level, all are leaders in their fields of research. Besides mathematicians, all types of scientists and engineers will use EACM as a standard working tool.
EACM is a comprehensive reference work covering the vast field of applied and computational mathematics. Applied mathematics itself accounts for at least 60 per cent of mathematics, and the emphasis on computation reflects the current and constantly growing importance of computational methods in all areas of applications. EACM emphasizes the strong links of applied mathematics with major areas of science, such as physics, chemistry, biology, and computer science, as well as specific fields like atmospheric ocean science. In addition, the mathematical input to modern engineering and technology form another core component of EACM.
Content Level ≫ Research
Related subjects ≫ Applications - Computational Science & Engineering - Engineering - Foundations of Computing - Physics