Foundations for College Mathematics 3e
Publisher: Red Bank Publishing
Published: 2011
Place of publication: Marysville, OH
Format: Hardcover
Number of pages: 746
ISBN-13: 9780981753645
Description: Learning Algebra II (Intermediate Algebra) is made simpler by using pedagogical and curricular techniques based on basic brain function and the mathematical notion of function behaviors and function representation. Long-term memory, recall, and understanding of the algebra are accomplished through neural responses to the use of daily connections, early use of visualizations, meaning added through contextual situations, and pattern-building to a generalization.
Table of contents: title: CHAPTER ONE; title: NUMBERS; title: 1.0	Introduction and Numbers	1; title: 1.1	Properties of Numbers, Equality, and Inequality	5; title: 1.2	Data Analysis	20; title: Basic Brain Function – A Beginning	26; title: 1.3	Describing Sets of Numbers with Interval Notation	27; title: Basic Brain Function – Connections	38; title: 1.4	Notation for Big and Little Numbers	39; title: Chapter Test	47; title: CHAPTER TWO; title: REPRESENTATION AND BEHAVIOR OF FUNCTIONS; title: 2.0	Introduction	49; title: Basic Brain Function – Can Algebra be Simple?	52; title: 2.1	Data Relationships Represented Numerically and Graphically	53; title: 2.2	Data Relationships Represented Symbolically	61; title: Basic Brain Function – What’s with the Prefrontal Lobes Stuff?	74; title: 2.3	Geometric Behaviors of Data Relationships	75; title: Basic Brain Function – Visualizations I	90; title: 2.4	Functions Represented Graphically	91; title: Chapter Test	100; title: CHAPTER THREE; title: COMMON BEHAVIORS OF FUNCTIONS; title: 3.0	Introduction to Geometric Behaviors of Functions	101; title: 3.1	An Introduction to the Analysis of the Linear Function  	102; title: 3.2	An Introduction to the Analysis of the Quadratic Function  	115; title: 3.3	An Introduction to the Analysis of the Absolute Value Function  	128; title: Basic Brain Function – Generalizing	138; title: 3.4	An Introduction to the Analysis of the Square Root Function  	139; title: 3.5	An Introduction to the Analysis of the Exponential Function  	149; title: Chapter Test	155; title: CHAPTER FOUR; title: FUNCTIONS: NOTATION AND OPERATIONS; title: 4.0	Introduction	156; title: 4.1	Definition of a Function, Again	158; title: 4.2	Addition and Subtraction of Polynomial Functions	171; title: 4.3	Multiplication of Polynomial Functions	180; title: Basic Brain Function – Visualizations II	193; title: 4.4	Factoring: Common Factors, Grouping, and Difference of Squares	194; title: 4.5	Factoring the Trinomial	205; title: Basic Brain Function – Unconscious Processing	214; title: 4.6	Function Operations from a Graphical Perspective	215; title: Chapter Test	224; title: CHAPTER FIVE; title: ADVANCED ANALYSIS OF THE LINEAR FUNCTION; title: 5.0	Introduction and Review of the Function  	225; title: 5.1	Rate of Change, Initial Condition, and the Zero --; title: Slope and Intercepts of the Linear Function	228; title: Basic Brain Function – Distributed Learning	239; title: 5.2	Slope-Intercept Method of Graphing	240; title: 5.3	Point-Slope Form:  	245; title: 5.4	The Linear Function as a Mathematical Model	256; title: Chapter Test	267; title: CHAPTER SIX; title: EQUATIONS AND INEQUALITIES; title: 6.0	Introduction	269; title: 6.1	Solving Equations Containing the Linear Function	271; title: Basic Brain Function – Connections Revisited	284; title: 6.2	Solving Inequalities Containing the Linear Function	285; title: 6.3	Solving Inequalities and Equations Containing the Absolute Value Function	294; title: 6.4	Formulas and Direct Variation	309; title: Chapter Test	321; title: Basic Brain Function – Learning	322; title: CHAPTER SEVEN; title: ADVANCED ANALYSIS OF THE EXPONENTIAL FUNCTION; title: 7.0	Introduction	323; title: 7.1	The Exponential Function	325; title: 7.2	Simplifying Symbols in Exponential Functions	342; title: 7.3	Equations and Inequalities Containing the Exponential Function	352; title: Basic Brain Function – Enriched Environment	360; title: 7.4	The Exponential Function as a Mathematical Model	361; title: Chapter Test	372; title: CHAPTER EIGHT; title: ANALYSIS OF THE RATIONAL FUNCTION; title: 8.0	Introduction	373; title: 8.1	Rational Functions	375; title: 8.2	The Fundamental Property of Rational Functions	390; title: 8.3	Multiplication and Division of Rational Functions	398; title: 8.4	Addition and Subtraction of Rational Functions and Simplification; title: of Complex Rational Functions	405; title: 8.5	Solving Equations and Inequalities Containing the Rational Function and; title: Inverse Variation	419; title: Chapter Test	434; title: CHAPTER NINE; title: ADVANCED ANALYSIS OF THE SQUARE ROOT FUNCTION; title: 9.0	Introduction	435; title: 9.1	The Square Root Function	437; title: 9.2	Properties of Irrational Expressions	449; title: 9.3	Operations with Irrational Expressions	458; title: 9.4	Fractional Exponents	466; title: 9.5	Solving Equations Containing the Square Root Function	472; title: 9.6	The Square Root Function as a Mathematical Model	483; title: Basic Brain Function – Graphing Technology	492; title: Chapter Test	493; title: CHAPTER TEN; title: ADVANCED ANALYSIS OF THE QUADRATIC FUNCTION; title: 10.0	Introduction	494; title: 10.1	The Quadratic Function	496; title: Basic Brain Function – Attention	508; title: 10.2	Solving Quadratic Equations of the Form (ax + b)(cx + d) = 0	509; title: 10.3	Solving Quadratic Equations by the Completing-the-Square Method	514; title: 10.4	Solving Quadratic Equations with the Quadratic Formula	522; title: 10.5	The Quadratic Function as a Mathematical Model	533; title: Chapter Test	540; title: CHAPTER ELEVEN; title: BASIC GEOMETRY; title: 11.0	Introduction	541; title: 11.1	The Distance and Midpoint Formulas	542; title: 11.2	Triangles	552; title: 11.3	Parallelograms	562; title: 11.4	Circles	568; title: Chapter Test	577; title: CHAPTER TWELVE; title: BASIC TRIGONOMETRY; title: 12.0	Introduction	578; title: 12.1	Conversions between Degrees and Radians	580; title: 12.2	Trigonometric Definitions	590; title: 12.3	Solving Right Triangles	601; title: 12.4	Trigonometric Functions as Mathematical Models	609; title: Basic Brain Function – Practice Practice Practice	615; title: Chapter Test	616; title: CHAPTER THIRTEEN; title: SYSTEMS OF EQUATIONS AND INEQUALITIES; title: 13.0	Introduction to Systems of Equations	617; title: Basic Brain Function – The Role of Dopamine	618; title: 13.1	Solving Systems Graphically	619; title: 13.2	Solving Systems by the Addition and Substitution Methods	629; title: 13.3	Solving Systems Using Cramer's Rule and Matrices	639; title: 13.4	Modeling with Systems of Equations	656; title: Chapter Test	670; title: CHAPTER FOURTEEN; title: INTRODUCTION TO THE ANALYSIS OF THE LOGARITHMIC FUNCTION; title: 14.0	Introduction	671; title: 14.1	The Logarithmic Function	673; title: 14.2	Properties of Logarithms	685; title: 14.3	Solving Logarithmic and Exponential Equations	697; title: Basic Brain Function – Meaning and Understanding	704; title: 14.4	The Logarithmic Function as a Mathematical Model	705; title: Chapter Test	718; title: Answers to selected odd exercises	I; title: Index		XIX