# The Art of Proof : Basic Training for Deeper Mathematics

Language: English

Pages: 203

ISBN: 1441970223

Format: PDF / Kindle (mobi) / ePub

*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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Binghamton, NY 13902 USA ross@math.binghamton.edu K.A. Ribet Mathematics Department University of California at Berkeley Berkeley, CA 94720-3840 USA ribet@math.berkeley.edu M. Beck and R. Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics, Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_1, © Matthias Beck and Ross Geoghegan 2010 3 M. Beck and R. Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics, Undergraduate Texts

Binghamton, NY 13902 USA ross@math.binghamton.edu K.A. Ribet Mathematics Department University of California at Berkeley Berkeley, CA 94720-3840 USA ribet@math.berkeley.edu M. Beck and R. Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics, Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_1, © Matthias Beck and Ross Geoghegan 2010 3 M. Beck and R. Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics, Undergraduate Texts

Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_7, © Matthias Beck and Ross Geoghegan 2010 M. Beck and R. Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics, Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_8, © Matthias Beck and Ross Geoghegan 2010 M. Beck and R. Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics, Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_9, © Matthias Beck and Ross

Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_7, © Matthias Beck and Ross Geoghegan 2010 M. Beck and R. Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics, Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_8, © Matthias Beck and Ross Geoghegan 2010 M. Beck and R. Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics, Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_9, © Matthias Beck and Ross

Mathematics, Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_12, © Matthias Beck and Ross Geoghegan 2010 M. Beck and R. Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics, Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_13, © Matthias Beck and Ross Geoghegan 2010 M. Beck and R. Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics, Undergraduate Texts in Mathematics, DOI 10.1007/978-1-4419-7023-7_14, © Matthias