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＜電子ブック＞
Proofs and Fundamentals : A First Course in Abstract Mathematics / by Ethan D. Bloch

版	1st ed. 2003.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2003
本文言語	英語
大きさ	XXI, 424 p : online resource
著者標目	*Bloch, Ethan D author SpringerLink (Online service)
件　名	LCSH:Mathematical logic LCSH:Mathematics FREE:Mathematical Logic and Foundations FREE:Mathematics
一般注記	I PROOFS -- 1 Informal Logic -- 2 Strategies for Proofs -- II Fundamentals -- 3 Sets -- 4 Functions -- 5 Relations -- 6 Infinite and Finite Sets -- III Extras -- 7 Selected Topics -- 8 Number Systems -- 9 Explorations -- Appendix: Properties of Numbers -- Hints for Selected Exercises -- References In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for­ mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "transition" course, rather than in traditional courses such as linear algebra. A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. The presentation is straightforward and focuses on the essentials, without being too elementary, too exces­ sively pedagogical, and too full to distractions. Some of features of this text are the following: (1) Symbolic logic and the use of logical notation are kept to a minimum. We discuss only what is absolutely necessary - as is the case in most advanced mathematics courses that are not focused on logic per se HTTP:URL=https://doi.org/10.1007/978-1-4612-2130-2

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