Author | Gerstein, Larry J. author |
---|---|

Title | Introduction to Mathematical Structures and Proofs [electronic resource] / by Larry J. Gerstein |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1996 |

Connect to | http://dx.doi.org/10.1007/978-3-642-59279-9 |

Descript | X, 350 p. online resource |

SUMMARY

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 upperยญ 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 n

CONTENT

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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Mathematical Logic and Foundations