Gerald Jay Sussman and Jack Wisdom
Structure and Interpretation of Classical Mechanics
This textbook takes an innovative approach to the teaching of classical mechanics, emphasizing the
development of general but practical intellectual tools to support the analysis of nonlinear Hamiltonian
systems. The development is organized around a progressively more sophisticated analysis of particular
natural systems and weaves examples throughout the presentation. Explorations of phenomena such as
transitions to chaos, nonlinear resonances, and resonance overlap to help the student to develop
appropriate analytic tools for understanding. Computational algorithms communicate methods
used in the analysis of dynamical phenomena Expressing the methods of mechanics in a computer
language forces them to be unambiguous and computationally effective. Once formalized as a
procedure, a mathematical idea also becomes a tool that can be used directly to compute results.
The student actively explores the motion of systems through computer simulation and experiment. This
active exploration is extended to the mathematics. The requirement that the computer be able to
interpret any expression provides strict and immediate feedback as to whether an expression is
correctly formulated. The interaction with the computer uncovers and corrects many deficiencies in
understanding.
March 2001
ISBN 0-262-19455-4
526 pp., 50 illus.
Michael Hoy, John Livernois, Chris McKenna, Ray Rees, and ThanasisStengos
Mathematics for Economics - 2nd Edition
This book offers a comprehensive presentation of the mathematics required to tackle problems in economic
analysis. To give a better understanding of the mathematical concepts, the text follows the logic of
the development of mathematics rather than that of an economics course. After a review of the fundamentals
of sets, numbers, and functions, the book covers limits and continuity, the calculus of functions of one
variable, linear algebra, multivariate calculus, and dynamics. To develop the student's problem-solving
skills, the book works through a large number of examples and economic applications. The second
edition includes simple game theory, l'Hital's rule, Leibniz's rule, and a more intuitive development of the
Hamiltonian. An instructor's manual is available.
June 2001
ISBN 0-262-08294-2
1072 pp., 321 illus.
Kirillov, A. et al (eds.)
Physics and Combinatorics
This volume contains research and review papers on different branches of mathematics and mathematical physics, written by the reading specialists. Among the contributed papers are articles on: (i) multiple basic hypergeometric functions with applications to the number theory, (ii) birational representations of affine Weyl groups with applications to discrete integrable systems, (iii) algebraic geometry and Painleve VI, and (iv) combinatorics of Kostka-Foulkes polynomials. Contents: Monodromy Problem Related to Wu-Sutherland Equations (K Aomoto); Quantum Integrable Lattice Field Theory and Quantum Dilogarithm Function (K Hikami); Symmetric Spaces over Finite Fields, Frobenius-Schur Indices, and Symmetric Function Identities (N Kawanaka); Ubiquity of Kostka Polynomials (A Kirillov); Kashaev's Invariant and the Volume of a Hyperbolic Knot after Y Yokota (H Murakami); Birational Weyl Group Actions Arising from a Nilpotent Poisson Algebra (M Noumi & Y Yamada); Two Relations That Generalize the q-Serre Relations and the Dolan-Grady Relations (P Terwilliger); and other papers.
981-02-4578-5
Maejima Makoto et al (eds.)
Stochastic Processes.
Selected Papers of Hiroshi Tanaka
Hiroshi Tanaka is noted for his discovery of the "Tanaka formula", which is a generalization of the It formulain stochastic analysis. This important book is a selection of his brilliant works on stochastic processes andrelated topics. It contains Tanaka's papers on (i) Brownian motion and stochastic differential equations(additive functionals of Brownian paths and stochastic differential equations with reflecting boundaries), (ii)mathematical physics and the probabilistic treatment of nonlinear equations (the Boltzmann equation,homogenization and propagation of chaos), and (iii) stochastic processes in random environments (especiallylimit theorems on the stochastic processes in one-dimensional random environments and their refinements).
981-02-4591-2
Mills,T.
Problems in Probability
Probability theory is an important part of contemporary mathematics. It plays a key role in the insurance industry, in the modelling of financial markets, and in statistics generally - including all those fields of endeavour to which statistics is applied (e.g. health, physical sciences, engineering, economics). The 20th century has been an important period for the subject, because we have witnessed the development of a solid mathematical basis for the study of probability, especially from the Russian school of probability under the leadership of A N Kolmogorov. We have also seen many new applications of probability - from applications of stochastic calculus in the financial industry to Internet gambling. At the beginning of the 21st century, the subject offers plenty of scope for theoretical developments, modern applications and computational problems. There is something for everyone in probability!
981-02-4598-X
Taketani Mituo
The Formation and Logic of Quantum Mechanics (3 vols.set)
This book analyzes the intricate logical process through which the quantum theory was developed, and shows that the quantum mechanics thus established is governed by stereo-structural logic. The method of analysis is based on Mituo Taketani's three-stage theory of scientific cognition, which was presented and developed in close connection with Yukawa's theory of the meson. According to the three-stage theory, scientific cognition proceeds through a series of coiling turns of the phenomenological, substantialistic and essentialistic stages. The old quantum mechanics is shown to be in a substantialistic stage, followed by the quantum mechanics in the corresponding essentialistic stage.
981-02-4601-3
Irwin, M.
Smooth Dynamical Systems
(Advanced Series in Dynamical Systems,vol.17)
This is a reprint of M C Irwin's beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential leading for all who want to master this area. Content: Some Simple Examples; Equivalent Systems; Integration of Vector Fields; Linear Systems, Linearization, Stable Manifolds; Stable Systems; and appendices.
981-02-4599-8