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Discrete Mathematics Mathematics Discrete mathematics is the branch of mathematics that involves finite or discontinuous quantities. In this unit, you will learn about sequences, series, probability, and statistics. Richard Kaye Professor of Mathematics University of Birmingham Chapter 11 Sequences and Series Chapter 12 Probability and Statistics 574 Unit 4 Discrete Mathematics ‘Minesweeper’: Secret to Age-Old Puzzle? Source: USA TODAY, November 3, 2000 “Minesweeper, a seemingly simple game included USA TODAY Snapshots® on most personal computers, could help mathematicians crack one of the field’s most intriguing problems. Why teens use PCs at home The buzz began after Richard Kaye, a mathematics The leading purposes teens age 12 to 17 gave for using a PC at home: professor at the University of Birmingham in England, started playing Minesweeper. After playing the Educational program 93% game steadily for a few weeks, Kaye realized that School 80% Minesweeper, if played on a much larger grid, has the assignments Games 70% same mathematical characteristics as other problems Word processing 63% deemed insolvable.” In this project, you will research Internet 32% a mathematician of the past and his or her role in the 25% E-mail development of discrete mathematics. Log on to www.algebra2.com/webquest. Begin your WebQuest by reading the Task. Source: U.S. Census Bureau Current Population Report (Sept. ’99) By Mark Pearson and Jerry Mosemak, USA TODAY Then continue working Lesson 11-7 12-1 on your WebQuest as Page 616 635 you study Unit 4. Unit 4 Discrete Mathematics 575 Sequences and Series • Lessons 11-1 through 11-5 Use arithmetic and Key Vocabulary geometric sequences and series. • arithmetic sequence (p. 578) • Lesson 11-6 Use special sequences and iterate • arithmetic series (p. 583) functions. • sigma notation (p. 585) • Lesson 11-7 Expand powers by using the • geometric sequence (p. 588) Binomial Theorem. • geometric series (p. 594) • Lesson 11-8 Prove statements by using mathematical induction. Many number patterns found in nature and used in business can be modeled by sequences, which are lists of numbers. Some sequences are classified by the method used to predict the next term from the previous term(s). When the terms of a sequence are added, a series is formed. In Lesson 11-2, you will learn how the number of seats in the rows of an amphitheater can be modeled using a series. 576 Chapter 11 Sequences and Series Prerequisite Skills To be successful in this chapter, you’ll need to master these skills and be able to apply them in problem-solving situations. Review these skills before beginning Chapter 11. For Lessons 11-1 and 11-3 Solve Equations Solve each equation. (For review, see Lessons 1-3 and 5-5.) 1. 36 12 4x 2. 40 10 5x 3. 12 3x 27 4. 162 2x4 1 5. 4x5 6. 3x3 4 20 8 For Lessons 11-

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