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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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Contenuti
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.
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- EditoreSpringer
- Data di pubblicazione2012
- ISBN 10 1468467107
- ISBN 13 9781468467109
- RilegaturaCopertina flessibile
- LinguaInglese
- Numero di pagine364
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Introduction · to Mathematical Structures and · Proofs (Textbooks in Mathematical Sciences)
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9781468467109
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Introduction to Mathematical Structures and Proofs (Textbooks in Mathematical Sciences)
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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. Withou. Codice articolo 4204557
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Introduction to Mathematical Structures and Proofs
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Introduction to Mathematical Structures and Proofs
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ISBN 13: 9781468467109
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 364 pp. Englisch. Codice articolo 9781468467109
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