A Gentle Introduction to the Art of Mathematics
by Joseph Fields
Publisher: Southern Connecticut State University 2009
Number of pages: 428
The point of this book is to help you with the transition from doing math at an elementary level (which is concerned mostly with solving problems) to doing math at an advanced level (which is much more concerned with axiomatic systems and proving statements within those systems).
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by Ted Sundstrom - Pearson Education, Inc.
'Mathematical Reasoning' is designed to be a text for the first course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics.
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Contents: Logic (Logical Operations, De Morgan's Laws, Logic and Sets); Proofs (Direct Proofs, Existence proofs, Mathematical Induction); Number Theory (The Euclidean Algorithm); Functions (Injections and Surjections, Cardinality and Countability).
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The book helps students make the transition from freshman-sophomore calculus to more proof-oriented upper-level mathematics courses. Another goal is to train students to read more involved proofs they may encounter in textbooks and journal articles.
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This is a small (98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs. The book takes a straightforward, no nonsense approach to explaining the core technique of mathematics.