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AuthorBloch, Ethan D. author
TitleProofs and Fundamentals [electronic resource] : A First Course in Abstract Mathematics / by Ethan D. Bloch
ImprintBoston, MA : Birkhรคuser Boston, 2003
Connect tohttp://dx.doi.org/10.1007/978-1-4612-2130-2
Descript XXI, 424 p. online resource

SUMMARY

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 forยญ 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 excesยญ 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


CONTENT

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


Mathematics Mathematical logic Mathematics Mathematical Logic and Foundations Mathematics general



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