Matters mathematical
著者
書誌事項
Matters mathematical
Chelsea Pub. Co., c1978
2d ed
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注記
Contains same text as 1st ed. with minor additions and corrections
Includes bibliographies and index
内容説明・目次
内容説明
From the Preface: 'This book is based on notes prepared for a course at the University of Chicago. The course was intended for non majors whose mathematical training was somewhat limited...Mastery of the material requires nothing beyond algebra and geometry normally covered in high school...It could be used in courses designed for students who intend to teach mathematics...We want the reader to see mathematics as a living subject in which new results are constantly being obtained'.
目次
- Sets and Functions: 1 Sets 2 Sets and counting 3 Functions Number Theory: 1 Prime numbers 2 Some formal aspects 3 Some formal consequences 4 Some basic properties 5 Equivalence relations 6 Congruence 7 Applications of the pigeon-hole principle 8 Waring's problem 9 Fermat and Mersenne primes Permutations: 1 The set $A(S)$ 2 Cycle decomposition 3 Even and odd 4 The interlacing shuffle 5 The Josephus permutation Bibliography Group Theory: 1 Definition and examples of groups 2 Some beginning notions and results 3 Subgroups 4 Lagrange's theorem 5 Isomorphism Finite Geometry: 1 Introduction 2 Affine planes 3 Counting arguments 4 Planes of low order 5 Coordinate affine planes 6 Parallelograms and midpoints 7 The nonexistence of planes of order 6 Suggestions for further reading Game Theory: 1 Probability 2 Mathematical expectation 3 Preliminary remarks on games 4 Examples 5 The general two-by-two game 6 Simplified poker 7 The game without a name 8 Goofspiel Suggestions for further reading Infinite Sets: 1 Infinite numbers
- countable sets 2 Uncountable sets Index.
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