Excursions in Modern Mathematics

Description

1 The Mathematics of Elections

1.1 The Basic Elements of an Election

1.2 The Plurality Method

1.3 The Borda Count Method

1.4 The Plurality-with-Elimination Method

1.5 The Method of Pairwise Comparisons

1.6 Fairness Criteria and Arrow’s Impossibility Theorem

2 The Mathematics of Power

2.1 An Introduction to Weighted Voting

2.2 Banzhaf Power

2.3 Shapley-Shubik Power

2.4 Subsets and Permutations

3 The Mathematics of Sharing

3.1 Fair-Division Games

3.2 The Divider-Chooser Method

3.3 The Lone-Divider Method

3.4 The Lone-Chooser Method

3.5 The Method of Sealed Bids

3.6 The Method of Markers

4 The Mathematics of Apportionment

4.1 Apportionment Problems and Apportionment Methods

4.2 Hamilton’s Method

4.3 Jefferson’s Method

4.4 Adams’s and Webster’s Methods

4.5 The Huntington-Hill Method

4.6 The Quota Rule and Apportionment Paradoxes

5 The Mathematics of Getting Around

5.1 Street-Routing Problems

5.2 An Introduction to Graphs

5.3 Euler’s Theorems and Fleury’s Algorithm

5.4 Eulerizing and Semi-Eulerizing Graphs

6 The Mathematics of Touring

6.1 What Is a Traveling Salesman Problem?

6.2 Hamilton Paths and Circuits

6.3 The Brute-Force Algorithm

6.4 The Nearest-Neighbor and Repetitive Nearest-Neighbor Algorithms

6.5 The Cheapest-Link Algorithm

7 The Mathematics of Networks

7.1 Networks and Trees

7.2 Spanning Trees, MSTs, and MaxSTs

7.3 Kruskal’s Algorithm

8 The Mathematics of Scheduling

8.1 An Introduction to Scheduling

8.2 Directed Graphs

8.3 Priority-List Scheduling

8.4 The Decreasing-Time Algorithm

8.5 Critical Paths and the Critical-Path Algorithm

9 Population Growth Models

9.1 Sequences and Population Sequences

9.2 The Linear Growth Model

9.3 The Exponential Growth Model

9.4 The Logistic Growth Model

10 Financial Mathematics

10.1 Percentages

10.2 Simple Interest

10.3 Compound Interest

10.4 Retirement Savings

10.5 Consumer Debt

11 The Mathematics of Symmetry

11.1 Rigid Motions

11.2 Reflections

11.3 Rotations

11.4 Translations

11.5 Glide Reflections

11.6 Symmetries and Symmetry Types

11.7 Patterns

12 Fractal Geometry

12.1 The Koch Snowflake and Self-Similarity

12.2 The Sierpinski Gasket and the Chaos Game

12.3 The Twisted Sierpinski Gasket

12.4 The Mandelbrot Set

13 Fibonacci Numbers and the Golden Ratio

13.1 Fibonacci Numbers

13.2 The Golden Ratio

13.3 Gnomons

13.4 Spiral Growth in Nature

14 Censuses, Surveys, Polls, and Studies

14.1 Enumeration

14.2 Measurement

14.3 Cause and Effect

15 Graphs, Charts, and Numbers

15.1 Graphs and Charts

15.2 Means, Medians, and Percentiles

15.3 Ranges and Standard Deviations

16 Probabilities, Odds, and Expectations

16.1 Sample Spaces and Events

16.2 The Multiplication Rule, Permutations, and Combinations

16.3 Probabilities and Odds

16.4 Expectations

16.5 Measuring Risk

17 The Mathematics of Normality

17.1 Approximately Normal Data Sets

17.2 Normal Curves and Normal Distributions

17.3 Modeling Approximately Normal Distributions

17.4 Normality in Random Events

Answers to Selected Exercises

Index

Photo Credits

About the Book

 

• Applet Byte exercises have been written to guide students through their exploration of the applets in MyLab™ Math. These exercises allow students to take advantage of the applets and glean a greater understanding of the concepts from them.

 

Also available with MyLab Math

MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

• New and improved applets designed by the author help students visualize the more difficult concepts and explore deeper understanding. Applets are assignable in MyLab Math and new Applet Byte exercises in the text have been written to guide students. These applets are now mobile-friendly, and can be accessed on any device.
• Applets include: Voting Methods – Banzhaf Power Index – The Method of Sealed Bids – Method of Markers – Apportionment Methods – Euler Paths and Circuits – Hamilton Paths and Circuits – Traveling Salesman – Minimum Spanning Trees (Kruskal’s Algorithm) – Priority Lists Scheduling – Finance Calculator  – Rigid Motions – Geometric Fractals – Data Sets – Frequency Tables – Shapley-Shubik Power Index
• Animated Whiteboard Concept Videos bring concepts to life in an exciting and compelling fashion using narration and animated drawing. Videos cover topics such as Fair Division, Eulerizing Graphs, Self-Similarity, The Golden Ratio, and Normal Curves. . Students will see math in a fresh, new way!
• Learning Catalytics in MyMathLab is an interactive, student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking. Now included in MyMathLab, Learning Catalytics enables instructors to generate classroom discussion, guide the lecture, and promote peer-to-peer learning with real-time analytics.
• LC annotations at point-of-use for instructors in the new Annotated Instructor’s Edition provide a corresponding code for each question as it becomes relevant to integrate into the classroom. Simply search for the question within Learning Catalytics using the code in the textbook’s annotation.
• StatCrunch, a powerful, web-based statistical software that allows users to perform complex analyses, share data sets, and generate compelling reports has been integrated into MyLab Math for the first time. The vibrant online community offers tens of thousands of data sets shared by users.
• Workspace Assignments allow students to work through an exercise step-by-step, allowing them to show their mathematical reasoning as they progress. Students receive feedback at each step when and where they need it most, and feedback adjusts to the path each student takes. When accessed via a mobile device, workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus.

For courses in Liberal Arts Mathematics.

Math: Applicable, Accessible, Modern

Excursions in Modern Mathematics introduces readers to the power and beauty of math. By developing an appreciation for the aesthetics and applicability of mathematics, readers who previously felt math was an “unknowable” subject can approach it with a new perspective. Contemporary topics ranging from elections, to networks, to analyzing data show readers that math is an accessible tool that can be applicable and interesting for anyone. Refinement and updating of examples and exercises, plus increased resources, makes the 9th Edition a relevant, accessible, and complete program.

Also available with MyLab Math.

MyLabTM Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

NOTE: You are purchasing a standalone product; MyLab Math does not come packaged with this content. If you would like to purchase both the physical text and MyLab Math, search for:

0134765826 / 9780134765822 Excursions in Modern Mathematics Plus MyLab Math — Title-Specific Access Card Package, 9/e

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• 0134751817 / 9780134751818 MyLab Math with Pearson eText — Standalone Access Card — for Excursions in Modern Mathematics

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For courses in Liberal Arts Mathematics.

 

Math: Applicable, Accessible, Modern

Excursions in Modern Mathematics introduces non-majors to the power and beauty of math. By developing an appreciation for the aesthetics and applicability of mathematics, students who previously felt math was an “unknowable” subject can approach it with a new perspective. Contemporary topics ranging from elections, to networks, to analysing data show students that math is an accessible tool that can be applicable and interesting for anyone. Refinement and updating of examples and exercises, plus increased resources for students and instructors, makes the 9th Edition a relevant, accessible, and complete program.

About the Book

• Carefully chosen topics explaining real life applications motivate students to dive into the math. With chapters categorized by social choice – management science – growth – shape and form – and statistics -each part touches on a different area where mathematics and the real world interface. Chapters can be used in any order to fit any syllabi for liberal arts math.
• Relevant examples integrate real data and interesting applications to show students that math is a relevant, applicable tool.
• Diverse and extensive exercises appear at the end of chapter and are divided into three levels: Walking, Jogging, and Running.
• Walking exercises test a basic understanding to ensure mastery of the main concepts from the chapter. These exercises are organized by section number to make it easier for instructors to build assignments.
• Jogging exercises apply the basic ideas at a higher level of complexity and require critical thinking skills.
• Running exercises challenge students’ ability by asking them to combine concepts and think at a higher level. These are often used for extra credit or group work.
• NEW! Applet Byte exercises have been written to guide students through their exploration of the applets in MyLabTM Math. These exercises allow students to take advantage of the applets and glean a greater understanding of the concepts from them.
• Key Concepts charts at the end of every chapter make it easy to study and review the material.

Also available with MyLab Math

MyLabTM Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

• UPDATED! New and improved applets designed by the author help students visualize the more difficult concepts and explore deeper understanding. Applets are assignable in MyLab Math and new Applet Byte exercises in the text have been written to guide students. These applets are now mobile-friendly, and can be accessed on any device.
• Applets include: Voting Methods – Banzhaf Power Index – The Method of Sealed Bids – Method of Markers – Apportionment Methods – Euler Paths and Circuits – Hamilton Paths and Circuits – Traveling Salesman – Minimum Spanning Trees (Kruskal’s Algorithm) – Priority Lists Scheduling – Finance Calculator – Rigid Motions – Geometric Fractals – Data Sets – Frequency Tables – Shapley-Shubik Power Index
• NEW! Animated Whiteboard Concept Videos bring concepts to life in an exciting and compelling fashion using narration and animated drawing. Videos cover topics such as Fair Division, Eulerizing Graphs, Self-Similarity, The Golden Ratio, and Normal Curves. . Students will see math in a fresh, new way!
• NEW! Learning Catalytics in MyMathLab is an interactive, student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking. Now included in MyMathLab, Learning Catalytics enables instructors to generate classroom discussion, guide the lecture, and promote peer-to-peer learning with real-time analytics.
• LC annotations at point-of-use for instructors in the new Annotated Instructor’s Edition provide a corresponding code for each question as it becomes relevant to integrate into the classroom. Simply search for the question within Learning Catalytics using the code in the textbook’s annotation.
• NEW! StatCrunch, a powerful, web-based statistical software that allows users to perform complex analyses, share data sets, and generate compelling reports has been integrated into MyLab Math for the first time. The vibrant online community offers tens of thousands of data sets shared by users.
• NEW! Workspace Assignments allow students to work through an exercise step-by-step, allowing them to show their mathematical reasoning as they progress. Students receive feedback at each step when and where they need it most, and feedback adjusts to the path each student takes. When accessed via a mobile device, workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus.