Murty, M.R., Queen's University, Kingston, Ont., Canada
Problems in Analytic Number Theory
2001. Approx. 455 pp. Hardcover
0-387-95143-1
This book gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goal is to give a rapid introduction of how analytic methods are used to study the distribution of prime numbers. The book also includes an introduction to p-adic analytic methods. It is ideal for a first course in analytic number theory.
Contents: Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- References.
Series: Graduate Texts in Mathematics.VOL. 206
Sell, G.R., University of Minnesota, Minneapolis, MN, USA
You, Y., University of South Florida, Tampa, FL, USA.Dynamics of Evolutionary Equations
2001. Approx. 615 pp. 20 figs. Hardcover
0-387-98347-3
The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations which attempt to model phenomena that change with time, and the infinite dimensional aspects occur when forces that describe the motion depend on spatial variables. This book may serve as an entree for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations. It begins with a brief essay on the evolution of evolutionary equations and introduces the origins of the basic elements of dynamical systems, flow and semiflow.
Contents: Preface * 1 The Evolution of Evolutionary Systems * 2 Dynamical Systems: Basic Theory * 3 Linear Semigroups * 4 Basic Theory of Evolutionary Equations * 5 Nonlinear Partial Differential Equations * 6 Navier Stokes Dynamics * 7 Basic Principles of Dynamics * 8 Inertial
Manifolds and the Reduction Principle * Appendices: Basics of Functional Analysis * Bibliography * Notation Index * Subject Index
Series: Applied Mathematical Sciences.VOL. 143
Kinsey, L.C., Canisius College, Buffalo, NY, USA
Moore, T.E., Ithaca College, Ithaca, NY, USASymmetry, Shape and Space
Introduction to Geometry
2001. Approx. 390 pp. 161 figs., 1 in color. Hardcover
1-930190-09-3
The text is suitable for introductory students, perhaps in programs such as education, art and architecture. The text contains some traditional material from geometry as well as more innovative topics. Throughout th etext, the authors place strong emphasis on pedagogy-- hands-on model building, a guided discovery method of learning, etc. Much of the material is written in such a way that it can be used in the classroom for enrichment projects, by prospective mathematics teachers.
Contents: 1. The Basics; 2. Grids; 3. Constructions; 4. Tesselations; 5. Two- dimensional Symmetry; 6. Other Dimensions, Other Worlds; 7. Polyhedra; 8. Three-dimensional Symmetry; 9. Spiral growth; 10. Drawing three dimensions in two; 11. Shape; 12. Graph theory; 13. Topology; References; Index
Publication date: March 2001
College Teachers High School
Book category: Undergraduate Textbook
Publication language: English
Prestel, A., University of Konstanz, Germany
Delzell, C.N., Louisiana State University, Baton Rouge, LA, USAPositive Polynomials: from Hilbert's 17th Problem to Real Algebra
2001. Approx. 245 pp. Hardcover
3-540-41215-8
Positivity is one of the most basic mathematical concepts. In many areas of mathematics (like analysis, real algebraic geometry, functional analysis, etc.) it shows up as positivity of a polynomial on a certain subset of Rn which itself is often given by polynomial inequalities. The main objective of the book is to give useful characterizations of such polynomials. It takes as starting point Hilberts 17th Problem from 1900 and explains how E. Artin's solution of that problem eventually led to the development of real algebra towards the end of the 20th century. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed. Thus the monograph can also serve as the basis for a 2-semester course in real algebra.
Keywords: Positive Polynomials ; Hilbert ' s 17th problem ; Real Algebra ; Semialgebraic sets ; Valued Fields 12 D15 ; 14 P 10 ; 12 J15 ; 12 J10
Contents: I Real Fields.- II Semialgebraic Sets.- III Quadratic Forms over Real Fields.- IV Real Rings.- V Archimedean Rings.- VI Positive Polynomials on Semialgebraic Sets.- VII Sums of 2mth Powers.- VIII Bounds.- Appendix.
Series: Springer Monographs in Mathematics.
Segal, L., Menlo Park, CA, USA
The Dream of Reality, 2nd ed.
Heinz von Foerster's Constructivism
2001. Approx. 175 pp. 20 figs. Softcover
0-387-95130-X
What if there were no objective facts, no objective truth, no objectivity at all, only our belief in them? What if our consciousness itself is an unconsciousinvention, constructed out of logic and language? In this thought-provoking volume, Lynn Segal describes how the ideas of Heinz von Foerster compel us to explore the question, "Do we discover the world or do we invent it?" and suggests that we must first know how we think before we can claim knowledge of the world. The resulting philosophy, Constructivism, examines the limits of whatwe can know and argues that understanding these limits can lead us to be more responsible for our personal and collective behavior. After tracing the historical transition from religious belief to a belief in science, Segal examines objectivity from semantic, philosophical, and neurological perspectives. Segal shows that we can never achieve objectivity andthat the scientific method ensures only a consensus among observers. Next, he details how language and logic unwittingly predetermine the very conclusions we derive when we try to know the world. Finally, he describes a computational model of cognition that does not depend on first positing the world to account for cognition and consciousness.
While Constructivism may seem relevant only to those in the cognitive sciences,it is, in fact, highly relevant to everyone. Paradoxically, grasping the limits of our own under-standing can free us to live more creative and meaningful personal and professional lives.
Publication date: March 2001
Fields: Philosophy; Physics, general; Psychology
Written for: Scientists, philosophers, psychologists, students, laymen
Book category: Nonfiction
Publication language: English