Instructor’s Annotated Edition Denley ∙ Hall Viewing Life Mathematically A Pathway to Quantitative Literacy © All Rights Reser ved.Executive Editor: Susan Fuller Co-Editor: Barbara Miller Assistant Editors: Margaret Gibbs, Robin Hendrix Executive Project Manager: Kimberly Cumbie Vice President, Research and Development: Marcel Prevuznak Editorial Assistants: Danielle C. Bess, Claudia Vance, Nina Waldron Review Coordinators: Lisa Young, Jessica O’Leary Senior Graphic Designers: Jennifer Moran, Tee Jay Zajac Digital Production Editors: Robert Alexander, Doug Chappell QSI (Pvt.) Ltd: E. Jeevan Kumar, D. Kanthi, U. Nagesh, B. Syam Prasad Art: Jennifer Moran Cover Design: Jennifer Moran A Division of Quant Systems, Inc. 546 Long Point Road, Mount Pleasant, SC 29464 Copyright © 2020, 2016 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written consent of the publisher. Library of Congress Control Number: 2014948152 Printed in the United States of America 10 9 8 7 6 5 4 3 ISBN: 978-1-935782-05-6 Textbook and Software Bundle: 978-1-935782-06-3 AIE ISBN: 978-1-64277-218-0 VLM_FrontMatter.indd 25/14/2019 3:02:05 PM © All Rights Reser ved.Table of Contents Preface Purpose and Style vi Special Features vi Content viii Hawkes Learning Systems: Courseware ix Acknowledgements x About the Authors xi 1 2 3 4 ved. 5 6 7 8 9 Rights Reser ved. Supplemental Calculator 10 11 12 13 14 © All Rights ReserViewing Life Mathematically Preface vi Preface Purpose and Style We created Viewing Life Mathematically: A Pathway to Quantitative Literacy as an alternative college-level mathematics pathway for students whose majors are neither calculus-based nor statistics-based. It is assumed that students taking the course will have sufficient knowledge of basic algebraic manipulation, ability to graph functions, and ability to solve algebraic equations. The material includes a variety of fields within mathematics that allow the course to be tailored to an institution’s specific objectives. Each topic engages students in developing mathematical skills and techniques that can be applied in their everyday lives and their own programs of study. The unifying theme is the introduction of concepts and ideas that encourage students to view aspects of life by thinking mathematically. We strive to make these applications of mathematics interesting to students and accessible through a clear, conversational writing style that leads students through the mathematics. The content is neatly organized, utilizing text boxes to emphasize the location of important definitions, theorems, and formulas. Numerous visual displays and diagrams are provided to support the quantitative reasoning process. We often present alternate ways to approach a problem and clearly explain the thinking process behind the steps, so that students can choose the process that works best for them. To further develop analytical skills, we encourage students to use technological resources, including calculators, spreadsheet programs, and online resources, to perform calculations for them, so that they are able to focus on interpreting the output and understanding the contextual implications of the mathematics. Our goal for this text is to develop the quantitative reasoning skills that students majoring in liberal arts disciplines need to succeed. With these students in mind, Viewing Life Mathematically: A Pathway to Quantitative Literacy focuses on building practical knowledge and problem-solving skills in everyday real-world contexts. The ability to analyze and interpret data is essential for all students to become informed citizens of a complex, technological world, regardless of their chosen discipline. Special Features Chapter Opener Each chapter begins with a list of sections and a list of chapter objectives to prepare students for the topics that will be covered. The objectives list also helps students identify the most important concepts in the chapter, enabling students to focus their time and effort appropriately. Chapter Introduction An application of the chapter content is introduced on the first page of each chapter to inspire student interest and provide an understanding of how the topics to be studied are useful. Examples Examples are presented in a step‑by‑step manner that is easy for students to follow. Titles are given to alert students to the concept they will be learning throughout the example. Examples make use of tables, diagrams and graphs, and technology where applicable, giving clarification to the mathematical skill being presented. Tech Training Tech Training boxes appear throughout the text, providing step‑by‑step instructions for using a calculator, spreadsheet program, or online resource to solve problems. Calculator instructions are given for a TI‑83/84 Plus graphing calculator and a TI‑30 scientific calculator with the Equation Operation System (EOS). All spreadsheet directions are written for Microsoft Excel 2010. The online resource used is Wolfram|Alpha (Wolfram Alpha LLC. 2009. Wolfram|Alpha. http://www.wolframalpha.com). Wolfram|Alpha is a free resource that can be utilized by any student with internet access. Students may use other types of technology, but may need to consult a user manual to troubleshoot any differences. © All Rights Reser ved.Viewing Life Mathematically Preface vii Definitions and Formulas Definitions and formulas are presented in highly visible boxes for easy reference. Skill Check Skill Check questions allow students to test their knowledge as they progress through a chapter to ensure that they understand the material. Solutions to these problems are located at the end of the section in which they appear before the section exercises. Think Back Think Backs are just‑in‑time information located in the margins of the text to remind students of important concepts that they may have forgotten from previous math courses or previous chapters in this course. Z Z Helpful Hint Helpful Hints appear in the margins of the text and provide students with extra insightful pieces of information to help them avoid common mistakes and understand concepts more deeply. Fun Fact Fun Facts appear in the margin with additional information to pique student interest and make mathematics more relatable. Math Milestone Math Milestones appear in the margins to give more information about mathematicians and the history of mathematics to help students connect further with the material. Section Exercises Each section includes a variety of exercises to give students practice applying and reinforcing the skills they learned in the section. The exercises exhibit a wide range of difficulty levels and applications, often using real‑world data. Chapter Summary Each chapter features a Chapter Summary that highlights important definitions, properties, processes, and formulas given in the chapter. Material is listed by section in the order that it appears, allowing students to quickly find the information they need when studying for a test or doing homework assignments. Chapter Exercises At the end of each chapter, a set of Chapter Exercises provides extra problems for students to practice and to identify strengths and weaknesses before taking an exam. Answer Key The Answer Key in the back of the book contains the answers for odd‑numbered Section Exercises and all answers to Chapter Exercises. This allows students to check their work to ensure they are accurately applying the methods and skills that they have learned. © All Rights Reser ved.Viewing Life Mathematically Preface viii Content Chapter 1: Critical Thinking and Problem Solving For most students in college, thinking mathematically means thinking algebraically. This chapter aims to introduce thinking mathematically as creative problem solving through reasoning, processes, and techniques. Chapter 2: Set Theory From Twitter followers to pizza toppings; from understanding surveys to organizing a closet; from factors to prime numbers, looking at the way items are grouped provides a solid mathematical foundation. This chapter uses a systematic approach to organizing and analyzing information and groups of items in order to solve problems involving sets. Formal set theory is introduced, as well as its definitions and notation, as a means to express, analyze, and manipulate categories and groupings. Chapter 3: Logic Logic is the basic structure of thinking mathematically. This chapter introduces formal mathematical logic, along with its definitions and notation. The ultimate goal of the chapter is for the reader to create and critique valid and invalid logical arguments. Chapter 4: Rates, Ratios, Proportions, and Percentages Rates, ratios, proportions, and percentages are universal, from credit cards and mortgages to retail sales and tipping. This chapter develops the skills for understanding and calculating these important values. Chapter 5: The Mathematics of Growth Mathematical models use information about the past to create images of the future. In this chapter, methodology is developed to create, manipulate, and analyze how quantities change over time. The focus on real‑world applications involves linear, quadratic, exponential, and logarithmic growth. Chapter 6: Geometry From GPS navigation to rocket trajectories, it is important to be able to model situations geometrically. In this chapter, the mathematics behind the spatial relationships that exist between objects is developed in a way that engages students in elementary problem solving in Euclidean and non-Euclidean geometry. Chapter 7: Probability Little in life is certain. Behavioral economists suggest that many mistakes in everyday life stem from massively overestimating or underestimating chance. Being able to express and manipulate the uncertainties of random events is a crucial skill in life. This chapter introduces formal probability, as well as its definitions and notation, as a means to express, analyze, and calculate chance. Chapter 8: Statistics Being able to understand statistical concepts is an important part of mathematical literacy in every field of study at the college level. This chapter introduces the fundamental concepts behind collecting and analyzing statistical data. Chapter 9: Personal Finance Wise financial planning both for the short term and the long term is an important life skill. This chapter introduces the basic skills of mathematical finance for effective budgeting and long-term decision making. Topics include budgeting with Excel as well as computing sales prices, interest, compound interest, effective interest, and monthly payments. Chapter 10: Voting and Apportionment Making the right choice can be challenging. This chapter introduces the mathematics behind the way individual preferences affect the decisions groups make and how to ensure fair outcomes. Topics include apportionment, voting methods, and voting paradoxes. © All Rights Reser ved.Viewing Life Mathematically Preface ix Chapter 11: The Arts Art, architecture, and music are not necessarily known for their mathematical content by the novice observer. This chapter uses geometry and proportions to explore the mathematics of such beauty. Chapter 12: Sports Just as mathematics provides a language to describe and analyze other facets of life, the sporting world is no exception. Each sport in this chapter is covered in a way that will allow every student to learn how mathematics affects the decisions made in those sports, and how mathematics is used in the physical participation of each sport. This chapter explores how the world of sports incorporates problem solving skills, ratios, proportions, probability, and statistics into decision making. Chapter 13: Graph Theory This chapter includes a thorough coverage of introductory topics to graph theory and how they relate to real-world applications. The structure of networks including Facebook and the interstate highway system provide powerful mediums to connect people. This chapter looks at the mathematics behind these networks. Chapter 14: Number Theory From ISBN numbers to internet security, the properties of numbers plays an often unnoticed role throughout modern life. This chapter provides a gentle introduction into the power of number theory, covering topics from prime and composite numbers to modular arithmetic, as well as applications of public-key encryption. Hawkes Learning Systems: Courseware Hawkes Learning Systems specializes in interactive courseware with a unique mastery-based approach to student learning. The courseware is designed to help you develop a solid foundation of skills and has been proven to increase your overall success. Within each homework lesson you will find three learning modes: Learn, Practice, and Certify. Learn: Learn is a multimedia presentation that includes the information you need to successfully answer each question in your assignment. Each lesson includes definitions, rules, properties, and examples, along with instructional videos. Practice: Practice gives you unlimited opportunities to practice the types of problems you will receive in Certify. In Practice, you have access to learning aids through the Interactive Tutor. Step-By-Step breaks a problem down into smaller steps; Solution offers guided solutions to every problem; and Explain Error gives targeted feedback specific to your mistake. Certify: This is the credit component of your homework! You will answer your problem set by using your knowledge and the foundation you built in Learn and Practice. You will have the opportunity to try again with no penalty if you do not demonstrate Mastery in your initial attempt(s). Pay close attention to any due dates or benchmarks assigned by your instructor. Video: View instructional videos anytime, anywhere at HawkesTV.com. Feel free to contact support for questions or technical help. Support Center: support.hawkeslearning.com Chat: chat.hawkeslearning.com E-mail: support@hawkeslearning.com Phone: 843.571.2825 © All Rights Reser ved.Next >