This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity. ELEMENTARY CONCEPTS. Numbers, Sets and Functions. Language and Proofs. Properties of Functions. Induction. PROPERTIES OF NUMBERS. Counting and Cardinality. Divisibility. Modular Arithmetic. The Rational Numbers. DISCRETE MATHEMATICS. Combinatorial Reasoning. Two Principles of Counting. Graph Theory. Recurrence Relations. CONTINUOUS MATHEMATICS. The Real Numbers. Sequences and Series. Continuity. Differentiation. Integration. The Complex Numbers. For anyone interested in learning how to understand and write mathematical proofs, or a reference for college professors and high school teachers of mathematics.
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This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity. ELEMENTARY CONCEPTS. Numbers, Sets and Functions. Language and Proofs. Properties of Functions. Induction. PROPERTIES OF NUMBERS. Counting and Cardinality. Divisibility. Modular Arithmetic. The Rational Numbers. DISCRETE MATHEMATICS. Combinatorial Reasoning. Two Principles of Counting. Graph Theory. Recurrence Relations. CONTINUOUS MATHEMATICS. The Real Numbers. Sequences and Series. Continuity. Differentiation. Integration. The Complex Numbers. For anyone interested in learning how to understand and write mathematical proofs, or a reference for college professors and high school teachers of mathematics.
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Seller: World of Books (was SecondSale), Montgomery, IL, U.S.A.
Hardback. Condition: Good. Aims to prepare students in the logical thinking skills, necessary to understand the fundamental ideas and proofs in mathematics. This text discusses mathematical language and proof techniques, applies them to questions in elementary number theory, and then develops additional techniques of proof through discrete and continuous mathematics. Seller Inventory # 00108676404
Seller: World of Books (was SecondSale), Montgomery, IL, U.S.A.
Hardback. Condition: Very Good. Aims to prepare students in the logical thinking skills, necessary to understand the fundamental ideas and proofs in mathematics. This text discusses mathematical language and proof techniques, applies them to questions in elementary number theory, and then develops additional techniques of proof through discrete and continuous mathematics. Seller Inventory # CIN0130144126VG
Seller: World of Books Inc, Montgomery, IL, U.S.A.
Hardback. Condition: Good. Aims to prepare students in the logical thinking skills, necessary to understand the fundamental ideas and proofs in mathematics. This text discusses mathematical language and proof techniques, applies them to questions in elementary number theory, and then develops additional techniques of proof through discrete and continuous mathematics. Seller Inventory # CIN0130144126G
Seller: World of Books Inc, Montgomery, IL, U.S.A.
Hardback. Condition: Very Good. Aims to prepare students in the logical thinking skills, necessary to understand the fundamental ideas and proofs in mathematics. This text discusses mathematical language and proof techniques, applies them to questions in elementary number theory, and then develops additional techniques of proof through discrete and continuous mathematics. Seller Inventory # CIN0130144126VG
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