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The Art of Proof: Basic Training for Deeper Mathematics
Hardcover
Series: Undergraduate Texts in Mathematics
FictionAlgebraGeneral Mathematics
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ISBN10: 1441970223
ISBN13: 9781441970220
Publisher: Springer Nature
Published: Aug 31 2010
Pages: 182
Weight: 1.27
Height: 0.50 Width: 7.00 Depth: 10.00
Language: English
ISBN13: 9781441970220
Publisher: Springer Nature
Published: Aug 31 2010
Pages: 182
Weight: 1.27
Height: 0.50 Width: 7.00 Depth: 10.00
Language: English
The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.
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