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Mathematics for Computer Science - MIT OpenCourseWare

Mcs 2015/5/18 1:43 page i #1 Mathematics for Computer Science revised Monday 18th May, 2015, 01:43 Eric Lehman Google Inc. F Thomson LeightonDepartment of Mathematics and the Computer Science and AI Laboratory, Massachussetts Institute of Technology; Akamai Technologies Albert R MeyerDepartment of Electrical Engineering and Computer Science and the Computer Science and AI Laboratory, Massachussetts Institute of Technology 2015, Eric Lehman, F Tom Leighton,Albert R Meyer. This work is available under the terms of theCreative CommonsAttribution-NonCommercial-ShareAl ike license. mcs 2015/5/18 1:43 page ii #2 mcs 2015/5/18 1:43 page iii #3 Contents I Proofs Introduction 3 References 4 1 What is a Proof?

12.7 Classifying Polyhedra 489 12.8 Another Characterization for Planar Graphs 492 III Counting Introduction 501 12.9 References 502 13 Sums and Asymptotics 503 13.1 The Value of an Annuity 504 13.2 Sums of Powers 510 13.3 Approximating Sums 512 13.4 Hanging Out Over the Edge 516 13.5 Products 522 13.6 Double Trouble 525

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