DEVELOPMENTAL MATHEMATICS - Hawkes Learning
DEVELOPMENTALMATHEMATICSSECOND EDITIOND. Franklin WrightInstructor PreviewDEV 2e Preface.indd 110/11/2017 12:16:56 PM
WIEEditor: Nina WaldronVEProject Manager: Patrick Vande BosscheYLNOAssistant Editors: Chelsey Cooke, S. Rebecca Johnson, Barbara Miller,RRDesigners: D. Kanthi, E. Jeevan Kumar, U. Nagesh, James Smalls,Patrick Thompson, Tee Jay ZajacFOCover Design: Patrick ThompsonVP Research & Development: Marcel PrevuznakDirector of Content: Kara RochéRFOA division of Quant Systems, Inc.WEIVYLNOER546 Long Point Road, Mount Pleasant, SC 29464Copyright 2017 by Hawkes Learning / 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.Printed in the United States of AmericaISBN: 978-1-946158-71-0DEV2e Marketing Booklet.indb 210/11/2017 10:25:07 AM
Instructor Sample ContentsDevelopmental Mathematics Second Edition Table of Contents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vDevelopmental Mathematics: Content Highlights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixStrategies for Academic SuccessYLNHow to Read a Math Textbook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Tips for Success in a Math Course. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2OTips for Improving Math Test Scores. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Practice, Patience, and Persistence! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4WIENote Taking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5VEDo I Need a Math Tutor?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Tips for Improving Your Memory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7RROvercoming Anxiety. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Online Resources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9FOPreparing for a Final Math Exam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10YLNChapter ProjectBefore and After. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12CHAPTER 2WEIVFractions and Mixed NumbersO2.1 Introduction to Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Multiplication with Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28CHAPTER 10RFOERGraphing Linear Equations and Inequalities10.1 The Cartesian Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4110.2 Graphing Linear Equations in Two Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5810.3 Slope‑Intercept Form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68CHAPTER 17Exponential and Logarithmic Functions17.3 Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8417.4 Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97DEV2e Marketing Booklet.indb 310/11/2017 10:25:07 AM
RRFOVERFODEV2e Marketing Booklet.indb 4WIEYLNOWEIVYLNOER10/11/2017 10:25:07 AM
Developmental Mathematics Second Edition Table of ContentsvPrefaceDevelopmental Mathematics Second Edition Table of Contents Note: Content subject to changeCHAPTER 1CHAPTER 3Whole NumbersDecimal Numbers1.1Introduction to Whole Numbers3.1Introduction to Decimal Numbers1.2Addition and Subtractionwith Whole Numbers3.2Addition and Subtractionwith Decimal Numbers1.3Multiplication with Whole Numbers3.3Multiplication with Decimal Numbers1.4Division with Whole Numbers3.41.5Rounding and Estimatingwith Whole Numbers1.6Problem Solving with Whole Numbers1.7Exponents and Order of Operations1.8Tests for DivisibilityRRFO1.9WIE3.5VE3.6YLNODivision with Decimal NumbersEstimating and Order of Operationswith Decimal NumbersDecimal Numbers and FractionsCHAPTER 4Ratios, Proportions, and PercentsPrime Numbers and Prime Factorizations4.1Ratios and Unit Rates4.2ProportionsFractions and Mixed Numbers4.3Decimals and Percents2.1Introduction to Fractionsand Mixed Numbers4.4Fractions and Percents2.2Multiplication with Fractions4.5Solving Percent ProblemsUsing Proportions2.3Division with Fractions2.4Multiplication and Divisionwith Mixed NumbersCHAPTER 2ER2.5Least Common Multiple (LCM)2.6Addition and Subtraction with Fractions2.7Addition and Subtractionwith Mixed Numbers2.8Comparisons and Order ofOperations with FractionsDEV2e Marketing Booklet.indb 5RFOWEIVYLNO4.6Solving Percent Problems Using Equations4.7Applications of Percent4.8Simple and Compound InterestCHAPTER 5Measurements5.1US Measurements5.2The Metric System: Length and Area5.3The Metric System: Capacity and Weight5.4US and Metric Equivalents10/11/2017 10:25:07 AM
viPrefaceDevelopmental Mathematics Second Edition Table of ContentsCHAPTER 6CHAPTER 9Geometry6.1Angles and TrianglesSolving Linear Equationsand Inequalities6.2Perimeter9.16.3AreaSolving Linear Equations:x b c and ax c6.4Circles9.2Solving Linear Equations: ax b c6.5Volume and Surface Area9.3Solving Linear Equations: ax b cx d6.6Similar and Congruent Triangles9.4Working with Formulas6.7Square Roots and thePythagorean Theorem9.5Applications: Number Problemsand Consecutive Integers9.6Applications: Distance‑Rate‑Time,Interest, Average9.7Solving Linear Inequalities in One Variable9.8Compound Inequalities9.9Absolute Value EquationsWIECHAPTER 7VEStatistics, Graphs, and Probability7.1Statistics: Mean, Median, Mode, and Range7.2Reading Graphs7.3Constructing Graphs from a Database7.4ProbabilityRRFOYLNO9.10 Absolute Value InequalitiesCHAPTER 10Graphing Linear Equationsand InequalitiesCHAPTER 8Introduction to AlgebraOThe Real Number Line and Absolute Value8.2Addition with Real Numbers10.2 Graphing Linear Equationsin Two Variables8.3Subtraction with Real Numbers10.3 Slope-Intercept Form8.4Multiplication and Divisionwith Real Numbers10.4 Point-Slope Form8.5Order of Operations with Real Numbers8.6Properties of Real Numbers8.7Simplifying and EvaluatingAlgebraic Expressions8.8Translating English Phrasesand Algebraic ExpressionsDEV 2e Preface.indd 6RFOYLN10.1 The Cartesian Coordinate System8.1WEIVER10.5 Introduction to Functionsand Function Notation10.6 Graphing Linear Inequalitiesin Two Variables10/11/2017 12:39:19 PM
Developmental Mathematics Second Edition Table of ContentsviiPrefaceCHAPTER 11CHAPTER 13Systems of Linear EquationsFactoring Polynomials11.1 Systems of Linear Equations:Solutions by Graphing13.1 Greatest Common Factor (GCF)and Factoring by Grouping11.2 Systems of Linear Equations:Solutions by Substitution13.2 Factoring Trinomials: x2 bx c13.3 Factoring Trinomials: ax2 bx c11.3 Systems of Linear Equations:Solutions by Addition13.4 Special Factoring Techniques11.4 Applications: Distance-Rate-Time,Number Problems, Amounts, and Costs13.6 Solving Quadratic Equations by FactoringO13.7 Applications: Quadratic Equations11.5 Applications: Interest and Mixture11.6 Systems of Linear Equations:Three VariablesYLN13.5 Review of Factoring TechniquesWIECHAPTER 14VE11.7 Matrices and Gaussian EliminationRational Expressions11.8 Systems of Linear Inequalities14.1 Introduction to Rational ExpressionsRRCHAPTER 12FO14.2 Multiplication and Divisionwith Rational Expressions14.3 Least Common Multiple of PolynomialsExponents and Polynomials14.4 Addition and Subtraction withRational Expressions12.1 Rules for Exponents12.2 Power Rules for Exponents14.6 Solving Rational Equations12.4 Introduction to Polynomials12.6 Multiplication with Polynomials12.8 Division with Polynomials12.9 Synthetic Division and theRemainder TheoremRFODEV2e Marketing Booklet.indb 7O14.7 Applications: Rational ExpressionsWEIV12.5 Addition and Subtraction with Polynomials12.7 Special Products of BinomialsYLN14.5 Simplifying Complex Fractions12.3 Applications: Scientific Notation14.8 Applications: VariationER10/11/2017 10:25:07 AM
viiiPrefaceDevelopmental Mathematics Second Edition Table of ContentsCHAPTER 15CHAPTER 17Roots, Radicals, andComplex NumbersExponential andLogarithmic Functions15.1 Evaluating Radicals17.1 Algebra of Functions15.2 Simplifying Radicals15.3 Rational Exponents17.2 Composition of Functionsand Inverse Functions15.4 Addition, Subtraction, andMultiplication with Radicals17.3 Exponential Functions17.4 Logarithmic Functions15.5 Rationalizing Denominators17.5 Properties of Logarithms15.6 Solving Radical Equations17.6 Common Logarithms andNatural Logarithms15.7 Functions with Radicals15.8 Introduction to Complex Numbers15.9 Multiplication and Divisionwith Complex NumbersCHAPTER 16RRFOQuadratic EquationsWIE17.8 Applications: Exponential andLogarithmic FunctionsCHAPTER 18Conic Sections16.1 Quadratic Equations:The Square Root Method18.1 Translations and Reflections18.3 Distance Formula, MidpointFormula, and Circles16.3 Quadratic Equations:The Quadratic Formula18.4 Ellipses and Hyperbolas16.4 More Applications of Quadratic Equations16.7 More on Graphing Functionsand ApplicationsRFO16.8 Solving Polynomial andRational InequalitiesDEV2e Marketing Booklet.indb 8YLN18.2 Parabolas as Conics16.2 Quadratic Equations:Completing the Square16.6 Graphing Quadratic FunctionsO17.7 Logarithmic and ExponentialEquations and Change-of-BaseVE16.5 Equations in Quadratic FormYLNWEIVO18.5 Nonlinear Systems of EquationsER10/11/2017 10:25:07 AM
Developmental Mathematics: Content HighlightsPrefaceixDevelopmental Mathematics:Content HighlightsNew FeaturesStrategies for Academic SuccessChapter ProjectsA new section has been included to help studentshone their skills in note taking, time management, testtaking, and reading. This section also provides tipsfor improving memory, overcoming test anxiety, andfinding a math tutor. (See page 19 for more)This new feature promotes collaboration and showsstudents the practical side of mathematics throughactivities using real-world applications of the conceptstaught in the chapter. (See page 24 for more)Strategies for Academic Success Note TakingGeneral TipsExample:RRFO Write the date and the course name at the top ofeach page. Write the notes in your own words and paraphrase. Use abbreviations, such as ft for foot, # for number,def for definition, and RHS for right-hand side. Copy all figures or examples that are presentedduring the lecture. Review and rewrite your notes after class. Do thison the same day, if possible.There are many different methods of note taking and it’salways good to explore new methods. A good time to tryout new note-taking methods is when you rewrite yourclass notes. Be sure to try each new method a few timesbefore deciding which works best for you. Below are threenote-taking methods you can try out. You may even findthat a blend of several methods works best for you.Note-Taking MethodsOutlineAn outline consists of several topic headings, eachfollowed by a series of indented bullet points that includesubtopics, definitions, examples, and other details.Keywords:RatiosNotes:1. Comparison of twoquantities by divisiona2.3.b, a : b, a to bCan reduce4. Common units can cancelSummary: Ratios are used to compare quantitiesand units can cancel.MappingThe mapping method is the most visual of the threemethods. One common way to create a mapping isto write the main idea or topic in the center and drawlines, from the main idea to smaller ideas or subtopics.Additional branches can be created from the subtopicsuntil all of the key ideas and definitions are included.Using a different color for subtopic can help visuallyorganize the topics.Example:Comparison of quantities by divisionCan bereduceda to baba:bThe split page method divides the page vertically into twocolumns with the left column narrower than the rightcolumn. Main topics go in the left column and detailedcomments go in the right column. The bottom of the pageis reserved for a short summary of the material covered.1.Find two other note taking methods anddescribe them.2.Write five additional abbreviations that youcould use while taking notes.Take Me Out to the Ball Game!An activity to demonstrate the use of percents and percent of increase or decrease in real life.The Atlanta Braves baseball team has been one of the most popular baseball teams for fans not only from Georgia, butthroughout the Carolinas and the southeastern United States. The Braves franchise started playing at the Atlanta-FultonCounty Stadium in 1966 and this continued to be their home field for 30 years. In 1996, the Centennial Olympic Stadium thatwas built for the 1996 Summer Olympics was converted to a new ballpark for the Atlanta Braves. The ballpark was namedTurner Field and was opened for play in 1997. In 2017, the braves moved to a new stadium named SunTrust Park.Round all percents to the nearest whole percent.1. The Atlanta-Fulton County Stadium had aseating capacity of 52,769 fans. Turner Field hada seating capacity of 50,096. SunTrust Park has aseating capacity of 41,149.5. Chipper Jones, a popular Braves third baseman,retired in July 2013. He started his career withthe Braves in 1993 at the age of 21.a. Determine the amount of decrease in seatingcapacity between Turner Field and theoriginal Braves stadiuma. In 2001, Chipper had 189 hits in 572at-bats. Calculate Chipper’s batting averagefor the season by dividing the number ofhits by the number of at-bats. Round to3 decimal places.3. When Turner Field opened in 1997, theaverage attendance at an Atlanta Braves gamewas 42,771. In 2016 the average attendancewas 24,950. What is the percent decrease inattendance from 1997 to 2016?QuestionsSplit PageChapter Project2. The Centennial Olympic Stadium hadapproximately 85,000 seats. Some of the seatingwas removed in order to convert it to the TurnerField ballpark. Rounding the number of seats inTurner Field to the nearest thousand, what is theapproximate percent decrease in seating capacityfrom the original Olympic stadium?Main TopicCommon unitscancelOb. Determine the percent decrease in seatingcapacity between SunTrust Park andTurner field.RatiosExample:1. Ratioa. Comparison of two quantities by division.b. Ratio of a to bai.bii. a : biii. a to bc. Can be reducedd. Common units can cancelWIEVETaking notes in class is an important step in understanding new material. While there are several methods for takingnotes, every note-taking method can benefit from these general tips.YLNWEIVApplicationsERNew exercises to assess students’ conceptual understanding of topics and important definitions areincluded in every section.RFO1. Every square is a rectangle but not everyrectangle is a .DEV2e Marketing Booklet.indb 9YLNc. Calculate the percent change in Chipper’sbatting average from 2001 to 2008.d. Does this represent a percent increaseor decrease?a. Calculate the percent change in RBIs from2001 to 2008.4. The highest average attendance for the Braveswas 47,960 in 1993 at the Atlanta-FoultonCounty Stadium. The Lowest average attendancewas 6642 in 1975 at the Atlanta-Foulton CountyStadium. What is the percent increase from thelowest attendance to the highest?Concept Checkb. In 2008, Chipper had 160 hits in 439at-bats. Calculate Chipper’s batting averagefor the season by dividing the number ofhits by the number of at-bats. Round to3 decimal places.6. In 2001, Chipper had 102 RBIs (runs batted in).In 2008, Chipper had only 75 RBIs.Source: baseball-almanac.comSource: baseball-almanac.comSource: espn.go.comb. Does this represent a percent increase ordecrease?OAdditional real-world application problems have beenadded throughout the text to challenge students toapply the concepts taught in the lesson.Extra MaterialAdditional, more advanced topics have been added toprovide students with a text that fully prepares them forfuture college mathematics courses.10/11/2017 10:25:08 AM
xPrefaceDevelopmental Mathematics: Content HighlightsAdditional FeaturesMath at WorkMargin ExercisesEach chapter begins with a brief discussion related to aconcept developed in the coming material and includesquestions students will solve later in the chapter tosolidify their knowledge and understanding.Each example has a corresponding margin exerciseto test students’ understanding of what was taught inthe example.YLN1. Solve: 3x 4 7ObjectivesAnswersThe objectives provide students with a clear andconcise list of the main concepts and methods taught ineach section, enabling students to focus their time andeffort on the most important topics. Objectives havecorresponding labels located in the section text wherethe topic is introduced for ease of reference.1. x 1RRObjectivesA. Multiply fractions.FOB. Reduce fractions to lowestterms.WIEVEExamplesExamples are denoted with titled headers indicating theproblem-solving skill being presented. Each sectioncontains carefully explained examples with appropriatetables, diagrams, and graphs. Examples are presentedin an easy-to-understand, step‑by‑step fashion andannotated with notes for additional clarification.Solution6 8 6 8 48 7 5 7 5 35Notes boxes in the margin point out important information that will help deepen student understanding ofthe topics. Often these are helpful hints about subtledetails in the definitions that many students do notnotice upon first glance.Greek mathematician Euclid isoften referred to as the ‘Father ofGeometry’ for his revolutionaryideas and influential textbookcalled Elements that he wrotearound the year 300 BC.A First objectiveExample 1 Multiplying Fractions6 8Multiply: 7 5ONotesC. Multiply and reduce fractionsto lowest terms.RFONotesWEIVDefinition BoxesYLNOERStraightforward definitions are presented in highlyvisible boxes for easy reference.AlgebraThe branch of mathematics that deals withgeneral statements of relations, utilizing lettersand other symbols to represent specific setsof numbers, values, vectors, and so on, in thedescription of such relations.DEFINITIONNow work margin exercise 1.DEV2e Marketing Booklet.indb 1010/11/2017 10:25:10 AM
Developmental Mathematics: Content HighlightsxiPrefaceCommon ErrorsWriting and ThinkingThese hard-to-miss boxes highlight common mistakesand how to avoid them.This feature gives students an opportunity to independently explore and expand on concepts presented in thechapter. These questions foster a better understandingof the concepts learned within each section.AttentionCollaborative LearningDon’t forget to carry the 1!CalculatorsFor visual learners, key strokes and screenshots areprovided when appropriate for visual reference. Wealso provide step‑by‑step instructions for using asimple four‑function calculator for more basic operations, as well as a TI-84 Plus for graphing skills.RRǞǞ CALCULATORSPerforming a task with a calculatorFOWIEEach chapter contains an index highlighting themain concepts within the chapter. This summarygives complete definitions and concise steps
Introduction to Algebra 8.1 The Real Number Line and Absolute Value 8.2 Addition with Real Numbers 8.3 Subtraction with Real Numbers 8.4 Multiplication and Division with Real Numbers 8.5 Order of Operations with Real Numbers 8.6 Properties of Real Numbers 8.7 Simplifying and Evaluating Algebraic Expressions 8.8 Translating English Phrases
Hawkes Learning System Lessons: The Hawkes lessons are how you will learn the material for this course. These lessons play the role of lecture and homework in a face-to-face class. There are 31 total lessons to complete on Hawkes as well as two online webtests to complete on Hawkes. Your two lowest Hawkes lessons will be dropped.
Hawkes graphs Paul Embrechts, Matthias Kirchnery RiskLab, Department of Mathematics, ETH Zurich, R amistrasse 101, 8092 Zurich, Switzerland This version: January 23, 2017 Abstract This paper introduces the Hawkes skeleton and the Hawkes graph. These objects summa-rize the branching structure of a multivariate Hawkes point process in a compact .
also discuss stability for Hawkes processes from a regeneration point of view. We will give a constructive proof of a random time such that the incremented Hawkes process is a Hawkes process in itself independent of the past. Standard Markov chain techniques allow us to prove various asymptotic results for the Hawkes process. Finally, we end by .
multi-dimensional Hawkes processes is proposed in [Hall and Willett, 2014], which approximates continuous Hawkes processes in a discrete manner. Multi-dimensional Hawkes processes have achieved promising results in many chal-lenging tasks. However, most of the existing works fo-cus on learning triggering patterns of sequences while few
mance for learning multiple point processes when incorporating their relational information. 2 BACKGROUND We briefly review Neural Hawkes Process [21] and Transformer [29] in this section. Neural Hawkes Process generalizes the classical Hawkes pro-cess by parameterizing its intensity function with recurrent neural networks. Specifically, ( ) Õ
3.2 Multi-dimensional Hawkes Processes In order to model social influence, one-dimensional Hawkes process discussed above needs to be extended to the multi-dimensional case. Specifically, we have U Hawkes processes that are coupled with each other: each of the Hawkes processes corresponds to an in-dividual and the influence between .
2.2. Hawkes Processes Though Poisson processes have many nice properties, they cannot capture interactions between events. For this we turn to a more general model known as Hawkes pro-cesses (Hawkes,1971). A Hawkes process consists of K point processes and gives rise to sets of marked events fs n;c ngN 1, where c n2f1;:::;Kgspecifies the process
2.2 Hawkes Processes Hawkes processes [13] have been widely used to capture self-exciting and mutual-exciting behavior between entities. A few ap-plications are predicting earthquakes, modeling!nancial markets and crime modeling [12, 16, 20]. pted to model information propagation on networks[24 .
