23 Mathematical Examples 23. 1 Sequences and Series 23.2 Arithmetic Sequences and Series 23.3 Geometric Sequences and Series aylor serl 23.4 The area under a function 23.5 The Slope of a Function 24 Intermezzo 4: Defining functions on the fly Syntax of lambda Scope and Semantics of lambda Pragmatics of lambda V Generative Recursion 25 A New form of recursion 25 1 Modeling a Ball on a Table 5.2 Sorting Quickly 26 Designing algorithms 26.1 Termination 26.2 Structural versus Generative recursion 26.3 Making choices 27 Variations on a theme 27.1 Fractals 27.2 From Files to Lines, from Lists to Lists ofLists 27.3 Binary Search 27.4 Newton's Method 27.5 Extended Exereise Gaussian Elimination 28 Algorithms that backtrack 28.1 Traversing Graphs 28.2 Extended Exercise: Checking(on) Queens 29 Intermezzo 5: The Cost of Computing and vectors 29.2 Concrete Time. Abstract Time 29 3 The Definition of"on the order of 29 4 A First look at vectors VI Accumulating knowledge 30 The loss of knowledge 30. 1 A Problem with Structural Processing 30.2 A Problem with Generative Recursion 31 Designing accumulator -Style functions 31.1 Recognizing the Need for an Accumulator 31.2 Accumulator-Style Functions 31.3 Transforming Functions into Accumulator-Style TEAM FLY PRESENTS-5- 23 Mathematical Examples 23.1 Sequences and Series 23.2 Arithmetic Sequences and Series 23.3 Geometric Sequences and Series Taylor Series 23.4 The Area Under a Function 23.5 The Slope of a Function 24 Intermezzo 4: Defining Functions on the Fly Syntax of lambda Scope and Semantics of lambda Pragmatics of lambda V Generative Recursion 25 A New Form of Recursion 25.1 Modeling a Ball on a Table 25.2 Sorting Quickly 26 Designing Algorithms 26.1 Termination 26.2 Structural versus Generative Recursion 26.3 Making Choices 27 Variations on a Theme 27.1 Fractals 27.2 From Files to Lines, from Lists to Lists of Lists 27.3 Binary Search 27.4 Newton's Method 27.5 Extended Exercise: Gaussian Elimination 28 Algorithms that Backtrack 28.1 Traversing Graphs 28.2 Extended Exercise: Checking (on) Queens 29 Intermezzo 5: The Cost of Computing and Vectors 29.2 Concrete Time, Abstract Time 29.3 The Definition of ``on the Order of'' 29.4 A First Look at Vectors VI Accumulating Knowledge 30 The Loss of Knowledge 30.1 A Problem with Structural Processing 30.2 A Problem with Generative Recursion 31 Designing Accumulator-Style Functions 31.1 Recognizing the Need for an Accumulator 31.2 Accumulator-Style Functions 31.3 Transforming Functions into Accumulator-Style TEAMFLY TEAM FLY PRESENTS