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Computer science --- Mathematics --- Math --- Science --- Computer mathematics --- Electronic data processing --- Discrete mathematics --- discrete wiskunde
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Discrete mathematics --- Computer science --- Mathematics --- Math --- Science --- Computer mathematics --- Electronic data processing
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To write everything about nothing, or to write nothing about everything: this is the problem. (Anonym, circa 1996-97) The first idea to write a book on M athematical Economics, more or less ordered in a historical sequence, occurred to me in 1995, when I was asked, by Istituto delta Enciclopedia Italiana, to write the entry "Storia dell'economia 1 2 matematica" , for the collective work "Storia deI XX Secolo". I thought that it would be interesting to elaborate on the text presented to the editors, to turn it into a book aiming at giving a panorama of what, in my opinion, are the main 20th century contributions to mathematical eco nomics. Of course, only a narrow set of the contributions made by economic theorists could be included, both for space limitations and necessity, because 3 of the limited competence of any single author. For instance, I have paid very limited attention to what is now called Macroeconomics, and also to Game Theory, which actually has grown so much as to acquire scientific in dependence as a living branch of applied mathematics. For the same reason, I have also left completely untouched such fields as Mathematical Finance, Public Economics, Theory of Taxation, etc. I have always based my presentation on published material only, assuming that what is contained in working papers still waits to be confirmed, possibly in the first years of the 21st century.
Quantitative methods (economics) --- Economics, Mathematical --- History --- Economic theory. --- Computer mathematics. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Computational Mathematics and Numerical Analysis. --- Computer mathematics --- Electronic data processing --- Mathematics --- Economic theory --- Political economy --- Social sciences --- Economic man --- Economics, Mathematical - History - 20th century
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Mathematics --- Computer science --- Informatique --- Congresses. --- Mathématiques --- Congrès --- Mathématique discrète. --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Computer Science
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Mathematics --- Mathématiques --- Research --- Periodicals --- Recherche --- Périodiques --- Computer science --- Mathematics. --- Research. --- Mathematical research --- Math --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Science --- Mathematical Theory
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Number theory --- Number theory. --- Computer science --- Mathematics --- Number study --- Numbers, Theory of --- Algebra --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing
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Computer science --- Discrete mathematics --- System design --- Design, System --- Systems design --- Electronic data processing --- System analysis --- Computer mathematics --- Mathematics --- Informatique --- Systèmes, Conception de --- Mathématiques --- Mathematics.
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This book can be understood as a model for teaching commutative algebra, taking into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, it is shown how to handle it by computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The text starts with the theory of rings and modules and standard bases with emphasis on local rings and localization. It is followed by the central concepts of commutative algebra such as integral closure, dimension theory, primary decomposition, Hilbert function, completion, flatness and homological algebra. There is a substantial appendix about algebraic geometry in order to explain how commutative algebra and computer algebra can be used for a better understanding of geometric problems. The book includes a CD with a distribution of Singular for various platforms (Unix/Linux, Windows, Macintosh), including all examples and procedures explained in the book. The book can be used for courses, seminars and as a basis for studying research papers in commutative algebra, computer algebra and algebraic geometry.
Algebraic geometry --- Ordered algebraic structures --- Commutative algebra. --- 512.55 --- 512.55 Rings and modules --- Rings and modules --- Algebra --- Commutative algebra --- Algebra. --- Algebraic geometry. --- Algorithms. --- Computer mathematics. --- Computer science—Mathematics. --- Algebraic Geometry. --- Computational Mathematics and Numerical Analysis. --- Symbolic and Algebraic Manipulation. --- Computer mathematics --- Electronic data processing --- Mathematics --- Algorism --- Arithmetic --- Geometry --- Mathematical analysis --- Foundations
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Mathematics --- Computer science --- Informatique --- Periodicals --- Mathématiques --- Périodiques --- Mathématiques --- Périodiques. --- Mathematical Sciences --- Combinatorics --- Applied Mathematics --- Mathematical Sciences. --- Combinatorics. --- Périodiques --- EJINFOR EJMATHE ELSEVIER-E EPUB-ALPHA-D EPUB-PER-FT --- Matematikk --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing
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Mathematical analysis --- Numerical analysis --- Computer science --- Mathematical analysis. --- Numerical analysis. --- Mathematics. --- Mathematics --- Advanced calculus --- Analysis (Mathematics) --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- 517.1 Mathematical analysis --- Algebra --- Mathematical Sciences --- Applied Mathematics
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