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Additive and Cancellative Interacting Particle Systems (Lecture Notes in Mathematics) by David Griffeath (Repost)
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Advances in Complex Function Theory (Lecture Notes in Mathematics) by W. E. Kirwan (Repost)
Matrix Mathematics - Theory, Facts, and Formulas, Second Edition
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Algebraic Aspects of Cryptography (Algorithms and Computation in Mathematics) by Neal Koblitz (Repost)
Mathematics Mathematical Foundations of Computer Science 2004 [Repost]
Mathematics Mathematical Logic for Computer Science (3rd edition)
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Mathematics Symmetry Theory in Molecular Physics with Mathematica: A new kind of tutorial book (Repost)
-Mathematics for the Physical Sciences- by Herbert S. Wilf
Mathematics for Elementary Teachers - A Conceptual Approach, 9 edition
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How to Fold It - The Mathematics of Linkages, Origami and Polyhedra
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Mathematics Maverick Mathematician: The Life and Science of J.E. Moyal
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Topology (Allyn and Bacon Series in Advanced Mathematics) by James Dugundji
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Mathematics Hypercomplex Numbers: An Elementary Introduction to Algebras
Posted on 2010-03-16
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After complex numbers appeared as an extension of the real number system, the question arose as to whether further extensions might be made and what would they look like. To do an extension of the complex numbers involves introducing additional symbols and forming polynomials from the new symbols and the complex numbers. Such an extension is a vector space over the complex numbers. When a product of such polynomials is introduced, the resulting structure is called an "algebra". During the nineteenth century, it was shown that (1) normed (norm means a magnitude, such as the absolute value, is defined) algebras, with an identity and (2) alternative (a weak version of the associate property) division (means can divide = reciprocal of a number is defined) algebras over the reals must be of dimension 2 to the n power. For n=1, we have the complex numbers, n = 2 are the quaternions and n = 3 are the octonions or Cayley numbers. There are none for n = 4 or greater. These results ( (1) is Hurwitz's Theorem and (2) is Frobenius' Theorem) are of great significance in a wide range of mathematical disciplines (topology, number theory, geometry, etc.) Quaternion products are the origin of dot and cross products in vector analysis and, indeed, of almost all vector analysis, itself. Quaternions are used for calculations for orbital mechanics of space vehicles and for computer vision develpoment. This book covers these systems well enough to give the reader a good start on such systems. Clifford algebras, a series of hypercomplex number systems, are increasingly being used as the proper way to express physics - Maxwell's equations are much more naturally expressed in this form and subatomic particle "spin" is best expressed as "spinors", which are intimately associated with Clifford algebra. The author also discusses hypercomplex systems in general and the "doubling" process which produces the complex numbers from the reals, the quaternions from the complex numbers and the octonions from the quaternions. "Doubling" can be continued indefinately, but the results beyond octonions are difficult for the less experienced reader to understand. If you have only a modest mathematics background, but want to learn about quaternions and octonions, read this book.
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