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1 The Role of Algorithms in Computing 2 Getting Started 3 Growth of Functions 4 Divide-and-Conquer 5 Probabilistic Analysis and Randomized Algorithms 6 Heapsort 7 Quicksort 8 Sorting in Linear Time 9 Medians and Order Statistics 10 Elementary Data Structures 11 Hash Tables 12 Binary Search Trees 13 Red-Black Trees 14 Augmenting Data Structures 15 Dynamic Programming 16 Greedy Algorithms 17 Amortized Analysis 18 B-Trees 19 Fibonacci Heaps 20 van Emde Boas Trees 21 Data Structures for Disjoint Sets 22 Elementary Graph Algorithms 23 Minimum Spanning Trees 24 Single-Source Shortest Paths 25 All-Pairs Shortest Paths 26 Maximum Flow 27 Multithreaded Algorithms 28 Matrix Operations 29 Linear Programming 30 Polynomials and the FFT 31 Number-Theoretic Algorithms 32 String Matching 33 Computational Geometry 34 NP-Completeness 35 Approximation Algorithms

1 The How, When, and Why of Mathematics Spotlight: George Polya Tips on Doing Homework 2 Logically Speaking 3 Introducing the Contrapositive and Converse 4 Set Notation and Quantifiers Tips on Quantification 5 Proof Techniques Tips on Definitions …… 10 Relations Tips on Reading Mathematics 11 Partitions Tips on Putting It All Together 12 Order in the Reals 13 Consequences of the Completeness of R Tips: You Solved ItNow What? 14 Functions, Domain, and Range Spotlight: The Definition of Function 15 Functions, One-to-One, and Onto 16 Inverses 17 Images and Inverse Images Spotlight: Minimum or Infimum? 18 Mathematical Induction 19 Sequences 20 Convergence of Sequences of Real Numbers 21 Equivalent Sets 22 Finite Sets and an Infinite Set 23 Countable and Uncountable Sets 24 The Cantor–Schroder–Bernstein Theorem Spotlight: The Continuum Hypothesis ……