In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.
Elements of Logic via Numbers and Sets
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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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9 of 10 people found the following review helpful:
5.0 out of 5 stars
The Best Introduction To Logic and Set Theory,
This review is from: Elements of Logic via Numbers and Sets (Springer Undergraduate Mathematics Series) (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.
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Inside This Book
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First Sentence:
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 Key Phrases - Capitalized Phrases (CAPs): (learn more)
Elements of Logic, Lewis Carroll, Proof Let, Use Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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 Key Phrases - Capitalized Phrases (CAPs): (learn more)
Elements of Logic, Lewis Carroll, Proof Let, Use Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 19
books:
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1
book
cites this book:
- The Higher Arithmetic: An Introduction to the Theory of Numbers by H. Davenport in Back Matter
- Elementary Number Theory by Gareth A. Jones in Front Matter
- Linear Algebra by Jin Ho Kwak in Front Matter
- Introductory Mathematics: Applications and Methods (Springer Undergraduate Mathematics Series) by Gordon S. Marshall in Front Matter
- Set Theory and the Continuum Hypothesis by Paul J. Cohen in Back Matter
See all 19 books this book cites
- Gateway to Higher Mathematics by Jason H. Goodfriend in Back Matter
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