LN01 Book - Center for Economic Research and Graduate...

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Unformatted text preview: Center for Economic Research and Graduate Education Charles University Economics Institute Academy of Science of the Czech Republic A COOK-BOOK OF MATHEMATICS Viatcheslav VINOGRADOV June 1999 CERGE-EI LECTURE NOTES 1 A Cook-Book of MAT HEMAT ICS Viatcheslav Vinogradov Center for Economic Research and Graduate Education and Economics Institute of the Czech Academy of Sciences, Prague, 1999 CERGE-EI 1999 ISBN 80-86286-20-7 To my Teachers He liked those literary cooks Who skim the cream of others’ books And ruin half an author’s graces By plucking bon-mots from their places. Hannah More, Florio (1786) Introduction This textbook is based on an extended collection of handouts I distributed to the graduate students in economics attending my summer mathematics class at the Center for Economic Research and Graduate Education (CERGE) at Charles University in Prague. Two considerations motivated me to write this book. First, I wanted to write a short textbook, which could be covered in the course of two months and which, in turn, covers the most significant issues of mathematical economics. I have attempted to maintain a balance between being overly detailed and overly schematic. Therefore this text should resemble (in the ‘ideological’ sense) a “hybrid” of Chiang’s classic textbook Fundamental Methods of Mathematical Economics and the comprehensive reference manual by Berck and Sydsaeter (Exact references appear at the end of this section). My second objective in writing this text was to provide my students with simple “cook- book” recipes for solving problems they might face in their studies of economics. Since the target audience was supposed to have some mathematical background (admittance to the program requires at least BA level mathematics), my main goal was to refresh students’ knowledge of mathematics rather than teach them math ‘from scratch’. Students were expected to be familiar with the basics of set theory, the real-number system, the concept of a function, polynomial, rational, exponential and logarithmic functions, inequalities and absolute values. Bearing in mind the applied nature of the course, I usually refrained from presenting complete proofs of theoretical statements. Instead, I chose to allocate more time and space to examples of problems and their solutions and economic applications. I strongly believe that for students in economics – for whom this text is meant – the application of mathematics in their studies takes precedence over das Glasperlenspiel of abstract theoretical constructions. Mathematics is an ancient science and, therefore, it is little wonder that these notes may remind the reader of the other text-books which have already been written and published. To be candid, I did not intend to be entirely original, since that would be impossible. On the contrary, I tried to benefit from books already in existence and adapted some interesting examples and worthy pieces of theory presented there. If theadapted some interesting examples and worthy pieces of theory presented there....
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LN01 Book - Center for Economic Research and Graduate...

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