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Elements of Logic via Numbers and Sets (Springer Undergraduate Mathematics Series) Paperback – 25 Sep 1998


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Product details

  • Paperback: 188 pages
  • Publisher: Springer; 1st ed. 1998. Corr. 2nd printing 1998 edition (25 Sep 1998)
  • Language: English
  • ISBN-10: 3540761233
  • ISBN-13: 978-3540761235
  • Product Dimensions: 17.8 x 1.1 x 23.5 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 773,513 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

From the reviews: “It took me a while to appreciate the need for a course intended to introduce mathematics undergraduates to advanced mathematics after they finish the calculus sequence. … This was the first book I found that seems really close to the core. It is well-written and very well suited to such a course.” (James M. Cargal, UMAP Journal, Vol. 31 (1), 2010)

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This book is based on a module given to first-year undergraduates at the University of Nottingham with the aim of bridging the gap between school and university in mathematics. Read the first page
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Most Helpful Customer Reviews

By C. R. Long VINE VOICE on 29 July 2013
Format: Paperback Verified Purchase
This book clearly lays out the language and techniques of logic applied to material familiar to a UK A-Level or First-year undergraduate student; numbers and series. It then introduces potentially unfamiliar key ideas such as well-ordering, partitioning of sets and equivalence relations. The book ties together logic and sets so the student can see why the algebra of sets is valid rather than some plausible results based on Venn diagrams. I especially liked how the key techniques for proof : modus ponens, modus tollens, proof by contradiction and proof by contraposition were expressed using logic operators then shown to yield tautologies by truth tables. Good mathematical style is introduced by worked examples that the student can follow and try to emulate.

The exercises are of a suitable standard and presented regularly throughout the text. I really felt it was important to tackle the exercises as they arose to check whether I had understood (or not) the preceding material. There are solutions to most exercise questions. The book , like other Springer-Verlag texts, is reasonably priced for most students and clearly organised and printed.
For me the material on syllogisms was less successful and less easy to follow, but maybe that is me.

I still think the gold-standard for an accessible yet exhaustive treatment of logic applied to proofs is “How to Prove it” by Velleman. That book does not yield its rewards instantly but after working through the exercises and really coming to grips with the material you really feel you understand (or begin to understand) what a valid argument actually is.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 2 reviews
13 of 14 people found the following review helpful
The Best Introduction To Logic and Set Theory 12 Dec 2001
By Dino - Published on Amazon.com
Format: Paperback
This is the clearest and most thorough introduction to the subject matter I've read. The beginner interested in logic, sets, relations, maps and cardinal numbers cannot do better than to read this text.
It also has solutions to most exercises, a very good index and a guide to all of the symbols and notation that appear.
2 of 2 people found the following review helpful
Great Text 25 Sep 2012
By Simon - Published on Amazon.com
Format: Kindle Edition Verified Purchase
I have an amateur interest in logic and math. I found this text to be very methodical and terse while remaining accessible. This is a book that I will keep going back to. If like me you don't like the new fad popular science presentation of academic material but rather something a bit more stripped away then you will really enjoy this text.
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