Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page vi — #6
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Contents
III Counting
Introduction 545
14 Sums and Asymptotics 547
14.1 The Value of an Annuity 548
14.2 Sums of Powers 554
14.3 Approximating Sums 556
14.4 Hanging Out Over the Edge 560
14.5 Products 566
14.6 Double Trouble 569
14.7 Asymptotic Notation 572
15 Cardinality Rules 597
15.1 Counting One Thing by Counting Another 597
15.2 Counting Sequences 598
15.3 The Generalized Product Rule 601
15.4 The Division Rule 605
15.5 Counting Subsets 608
15.6 Sequences with Repetitions 610
15.7 Counting Practice: Poker Hands 613
15.8 The Pigeonhole Principle 618
15.9 Inclusion-Exclusion 627
15.10 Combinatorial Proofs 633
15.11 References 637
16 Generating Functions 675
16.1 Infinite Series 675
16.2 Counting with Generating Functions 677
16.3 Partial Fractions 683
16.4 Solving Linear Recurrences 686
16.5 Formal Power Series 691
16.6 References 694
IV Probability
Introduction 713
17 Events and Probability Spaces 715
17.1 Let’s Make a Deal 715