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＜電子ブック＞
Introduction · to Mathematical Structures and · Proofs / by Larry Gerstein
(Textbooks in Mathematical Sciences)

版	1st ed. 1996.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1996
本文言語	英語
大きさ	X, 350 p : online resource
著者標目	*Gerstein, Larry author SpringerLink (Online service)
件　名	LCSH:Social sciences LCSH:Humanities FREE:Humanities and Social Sciences
一般注記	1 Logic -- 2 Sets -- 3 Functions -- 4 Finite and Infinite Sets -- 5 Permutations and Combinations -- 6 Number Theory -- Hints and Partial Solutions to Selected Odd-Numbered Exercises This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper­ division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci­ pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu­ dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them­ selves questions that will lead them in the right direction HTTP:URL=https://doi.org/10.1007/978-1-4684-6708-6

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