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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

BooksJournals

    • Quantum Theoretic Machines

      • 1st Edition
      • December 8, 2000
      • A. Stern
      • English
      • Hardback
        9 7 8 0 4 4 4 8 2 6 1 8 3
      • Paperback
        9 7 8 0 4 4 4 5 5 2 1 9 8
      • eBook
        9 7 8 0 0 8 0 5 4 0 1 3 9
      Making Sense of Inner Sense'Terra cognita' is terra incognita. It is difficult to find someone not taken abackand fascinated by the incomprehensible but indisputable fact: there are material systems which are aware of themselves. Consciousness is self-cognizing code. During homo sapiens's relentness and often frustrated search for self-understanding various theories of consciousness have been and continue to be proposed. However, it remains unclear whether and at what level the problems of consciousness and intelligent thought can be resolved. Science's greatest challenge is to answer the fundamental question: what precisely does a cognitive state amount to in physical terms?Albert Einstein insisted that the fundamental ideas of science are essentially simple and can be expressed in a language comprehensible to everyone. When one thinks about the complexities which present themselves in modern physics and even more so in the physics of life, one may wonder whether Einstein really meant what he said. Are we to consider the fundamental problem of the mind, whose understanding seems to lie outside the limits of the mind, to be essentially simple too? Knowledge is neither automatic nor universally deductive. Great new ideas are typically counterintuitive and outrageous, and connecting them by simple logical steps to existing knowledge is often a hard undertaking. The notion of a tensor was needed to provide the general theory of relativity; the notion of entropy had to be developed before we could get full insight into the laws of thermodynamics; the notice of information bit is crucial for communication theory, just as the concept of a Turing machine is instrumental in the deep understanding of a computer. To understand something, consciousness must reach an adequate intellectual level, even more so in order to understand itself. Reality is full of unending mysteries, the true explanation of which requires very technical knowledge, often involving notions not given directly to intuition. Even though the entire content and the results of this study are contained in the eight pages of the mathematical abstract, it would be unrealistic and impractical to suggest that anyone can gain full insight into the theory that presented here after just reading abstract.In our quest for knowledge we are exploring the remotest areas of the macrocosm and probing the invisible particles of the microcosm, from tiny neutrinos and strange quarks to black holes and the Big Bang. But the greatest mystery is very close to home: the greatest mystery is human consciousness. The question before us is whether the logical brain has evolved to a conceptual level where it is able to understand itself.

    • Mathematical and Conceptual Foundations of 20th-Century Physics

      • 1st Edition
      • Volume 100
      • April 1, 2000
      • G.G. Emch
      • English
      • Hardback
        9 7 8 0 4 4 4 8 7 5 8 5 3
      • Paperback
        9 7 8 0 4 4 4 5 5 7 9 4 0
      • eBook
        9 7 8 0 0 8 0 8 7 2 1 1 7
      This book is primarily intended for Mathematicians, but students in the physical sciences will find here information not usually available in physics texts.The main aim of this book is to provide a unified mathematical account of the conceptual foundations of 20th-Century Physics, in a form suitable for a one-year survey course in Mathematics or Mathematical Physics. Emphasis is laid on the interlocked historical development of mathematical and physical ideas.

    • Linear Algebra and Linear Operators in Engineering

      • 1st Edition
      • Volume 3
      • June 12, 2000
      • H. Ted Davis + 1 more
      • English
      • Hardback
        9 7 8 0 1 2 2 0 6 3 4 9 7
      • eBook
        9 7 8 0 0 8 0 5 1 0 2 4 8
      Designed for advanced engineering, physical science, and applied mathematics students, this innovative textbook is an introduction to both the theory and practical application of linear algebra and functional analysis. The book is self-contained, beginning with elementary principles, basic concepts, and definitions. The important theorems of the subject are covered and effective application tools are developed, working up to a thorough treatment of eigenanalysis and the spectral resolution theorem. Building on a fundamental understanding of finite vector spaces, infinite dimensional Hilbert spaces are introduced from analogy. Wherever possible, theorems and definitions from matrix theory are called upon to drive the analogy home. The result is a clear and intuitive segue to functional analysis, culminating in a practical introduction to the functional theory of integral and differential operators. Numerous examples, problems, and illustrations highlight applications from all over engineering and the physical sciences. Also included are several numerical applications, complete with Mathematica solutions and code, giving the student a "hands-on" introduction to numerical analysis. Linear Algebra and Linear Operators in Engineering is ideally suited as the main text of an introductory graduate course, and is a fine instrument for self-study or as a general reference for those applying mathematics.

    • SET THEORY

      • 1st Edition
      • Volume 53
      • April 1, 2000
      • Lev D. Beklemishev
      • English
      • eBook
        9 7 8 0 0 8 0 9 5 7 7 2 2

    • Lincos

      • 1st Edition
      • Volume 28
      • April 1, 2000
      • Lev D. Beklemishev
      • English
      • eBook
        9 7 8 0 0 8 0 9 5 7 4 8 7

    • Recent Topics in Nonlinear PDE

      • 1st Edition
      • Volume 98
      • April 1, 2000
      • M. Mimura + 1 more
      • English
      • eBook
        9 7 8 0 0 8 0 8 7 2 0 9 4
      This volume contains papers covering the theory of nonlinear PDEs and the related topics which have been recently developed in Japan.

Related subjects

Mathematics and applied mathematics

Statistics and probability