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This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with many important applications. The new edition has been thoroughly rewritten, both in the text and exercise sets, and contains new chapters on convexity and separation, positive solutions to linear systems, singular values and QR decompostion. Treatments of tensor products and the umbral calculus have been greatly expanded and discussions of determinants, complexification of a real vector space, Schur's lemma and Gersgorin disks have been added. The author is Emeritus Professor of Mathematics, having taught at a number of universities, including MIT, UC Santa Barabara, the University of South Florida, the California State University at Fullerton and UC Irvine. He has written 27 books in mathematics at various levels and 9 books on computing. His interests lie mostly in the areas of algebra, set theory and logic, probability and finance.

Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Matrix theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Algebra. --- Mathematics

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Mathematical control systems --- 621.39 --- 519.72 --- Telecommunication. Telecontrol --- Information theory: mathematical aspects --- Coding theory. --- Information theory. --- 519.72 Information theory: mathematical aspects --- 621.39 Telecommunication. Telecontrol --- Coding theory --- Information theory --- Communication theory --- Communication --- Cybernetics --- Data compression (Telecommunication) --- Digital electronics --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Entropy (Information theory) --- Entropie (théorie de l'information) --- Codage

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Object-oriented programming (Computer science) --- Programmation orientée objet (Informatique) --- Microsoft Visual Basic for applications. --- Microsoft Visual Basic for applications --- Programmation orientée objet (Informatique)

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Calculus. --- Calcul infinitésimal --- Calculus --- Calcul infinitésimal --- Analyse combinatoire --- Fonctions speciales --- Polynomes orthogonaux

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The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed. The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options.

Capital assets pricing model. --- Investments -- Mathematics. --- Options (Finance) -- Prices. --- Portfolio management -- Mathematical models. --- Investments --- Capital assets pricing model --- Portfolio management --- Options (Finance) --- Finance --- Commerce --- Business & Economics --- Accounting --- Economic Theory --- Investment & Speculation --- Mathematics --- Mathematical models --- Prices --- Business mathematics. --- Mathematical models. --- Mathematics. --- Mathematics of investment --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance. --- Economics, Mathematical. --- Probabilities. --- Quantitative Finance. --- Probability Theory and Stochastic Processes. --- Finance, general. --- Business mathematics --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical . --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mathematical economics --- Econometrics --- Methodology