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– The description and notation for integers ( Z, Z+, Z-, Z nonneg), rational numbers (with Z replaced by Q), and real numbers (with Z replaced by R) are introduced early (in Section 1.1, Sets). – Makes sets available for proofs in examples and exercises, thus providing more interesting examples earlier than in the previous editions. – Permits the use of set terminology throughout the book. Earlier introduction of sets – Now the first section of the book.– Except for the section on sets, Chapters 2 (The Language of Mathematics) and 3 (Relations) in the sixth edition have been combined into Chapter 3 (Functions, Sequences, and Relations) in this revision. – The first chapter from the previous edition (Logic and Proofs) has been divided into two chapters – Logic (Chapter 1) and Proofs (Chapter 2). – Nearly every proof is preceded by a Discussion section and/or accompanied by a figure. – There are expanded subsections on proofs of equivalence and existence proofs (including constructive and nonconstructive existence proofs). – Sections 2.1 and 2.2 are new extended sections on mathematical systems and proof techniques. – Two new Problem-Solving Corners have been added, one on quantifiers, the other on proofs (see Proving Some Properties of Real Numbers).
#Discrete mathematics with graph theory 3rd edition chapter 0.2 how to#
– Problem-Solving Tips sections include expanded advice and examples on how to do proofs, how to write up proofs, and common errors in proofs. – More examples and exercises are included to highlight common errors – Also expands discussion and adds motivation for most of the examples. Increased number of examples and exercises throughout:.Summaries of the mathematical and algorithm notation used in the book on the inside covers.
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Figure captions provide additional explanation and insight into figures accompanying proofs.
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Extensive applications with an emphasis on computer science.Over 3500 exercises – Approximately one third have answers at the back of the book.Over 500 worked examples throughout the text.
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