| 本书详细讨论数学的读写和证明，将学习数学的过程在某种意义下程序化，以使学习者培养出极好的学习习惯，以及学会如何应付面对的问题。 本书努力将读者培养成独立思考研究型的学习者，并试图将这个过程程序化，同时通过大量的实例让读者接受这个程序。这也许代表了西方教育的一个特征，这个特征也许在中国是缺少的，在教科书中也是缺少的。 本书对初学高等数学的读者来说特别有意义。 |
| contents preface xi 1 the how,wnen. and why of mathematics spotlight: george p61ya tips on doing homework 2 logically speaking 3 introducing the contrapositivc and converse 4 set notation and opantificrs tips on quantification 5 proof techniques tips on definitions 6 sets spotlight:paradoxs 7 operations on sets 8 more on operations on sets 9 the power set and the cartesian product tips on writing mathematics 10 relations tips on reading mathematics 11 partitions tips on putting it all together 12 order in the reals tips:you solved it now what? 13 functions, domain, and range spotlight:the definition of function 14 functions, one-to-one, and onto 15 inverses 16 images and inverse images spotlight. minimum or infimum 17 mathematical induction …… 18 sequences 19 convergence of sequences of real numbers 20 equivalent sets 21 finite sets and an infinite set 22 countable and uncountable sets 23 metric spaces 24 getting to know open and closed sets 25 modular arithmetic 26 fermat's little theorem 27 projects 28 appendix references index |
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