Thinking Mathematically

by Blitzer, Robert

• ISBN13: 9780139488450
• ISBN10: 0139488456
• Format: Hardcover
• Copyright: 2000-01-01
• Publisher: Pearson College Div

Summary

This highly anticipated first edition achieves the difficult balance between coverage and motivation while helping students develop strong problem-solving skills. Blitzer's examples, problems and applications foster both an appreciation and understanding of mathematics encouraging students to take the math a step further into their everyday lives. Blitzer's use of current data and examples drawn from real life are used to develop key mathematical concepts, as well as reduce math anxiety in students.

Table of Contents

About the Author	x
To the Student	xi
To the Instructor	xii
Acknowledgments	xiii
Applications Index	xxi
Problem Solving and Critical Thinking	2	(30)
Inductive and Deductive Reasoning	4	(7)
Estimation and Graphs	11	(8)
Problem Solving	19	(13)
Summary	28	(1)
Review Exercises	28	(2)
Chapter 1 Test	30	(2)
Set Theory	32	(42)
Basic Set Concepts	34	(9)
Venn Diagrams and Subsets	43	(10)
Venn Diagrams and Set Operations	53	(5)
Set Operations and Venn Diagrams with Three Sets	58	(7)
Surveys and Cardinal Numbers	65	(9)
Summary	71	(1)
Review Exercises	72	(1)
Chapter 2 Test	73	(1)
Logic	74	(72)
Statements, Negations, and Quantified Statements	76	(6)
Compound Statements and Connectives	82	(9)
Truth Tables for Negation, Conjunction, and Disjunction	91	(12)
Truth Tables for the Conditional and Biconditional	103	(10)
Equivalent Statements, Conditional Statements, and De Morgan's Laws	113	(10)
Arguments and Truth Tables	123	(10)
Arguments and Euler Diagrams	133	(13)
Summary	141	(2)
Review Exercises	143	(1)
Chapter 3 Test	144	(2)
Number Representation and Calculation	146	(30)
Our Hindu-Arabic System and Early Positional Systems	148	(7)
Number Bases in Positional Systems	155	(6)
Computation in Positional Systems	161	(6)
Looking Back at Early Numeration Systems	167	(9)
Summary	172	(1)
Review Exercises	173	(2)
Chapter 4 Test	175	(1)
Number Theory and the Real Number System	176	(66)
Number Theory: Prime and Composite Numbers	178	(9)
The Integers; Order of Operations	187	(10)
The Rational Numbers	197	(9)
The Irrational Numbers	206	(8)
Real Numbers and Their Properties	214	(6)
Exponents and Scientific Notation	220	(9)
Arithmetic and Geometric Sequences	229	(13)
Summary	237	(2)
Review Exercises	239	(2)
Chapter 5 Test	241	(1)
Algebra: Equations and Inequalities	242	(64)
Algebraic Expressions and Formulas	244	(9)
Solving Linear Equations	253	(11)
Applications of Linear Equations	264	(8)
Ratio, Proportion, and Variation	272	(11)
Solving Linear Inequalities	283	(7)
Solving Quadratic Equations	290	(16)
Summary	302	(1)
Review Exercises	303	(2)
Chapter 6 Test	305	(1)
Algebra: Graphs, Functions, and Linear Systems	306	(64)
Graphing and Functions	308	(11)
Linear Functions and Their Graphs	319	(8)
Quadratic Functions and Their Graphs	327	(10)
Exponential Functions	337	(5)
Systems of Linear Equations	342	(13)
Linear Inequalities in Two Variables	355	(5)
Linear Programming	360	(10)
Summary	366	(1)
Review Exercises	367	(2)
Chapter 7 Test	369	(1)
Consumer Mathematics and Financial Management	370	(54)
Percent	372	(9)
Interest	381	(9)
Installment Buying	390	(11)
The Cost of Home Ownership	401	(8)
Investing in Stocks, Bonds, and Mutual Funds	409	(15)
Summary	419	(1)
Review Exercises	420	(3)
Chapter 8 Test	423	(1)
Measurement	424	(28)
Measuring Length; The Metric System	426	(9)
Measuring Area and Volume	435	(8)
Measuring Weight and Temperature	443	(9)
Summary	449	(1)
Review Exercises	450	(1)
Chapter 9 Test	451	(1)
Geometry	452	(70)
Points, Lines, Planes, and Angles	454	(8)
Triangles	462	(9)
Polygons, Quadrilaterals, and Perimeter	471	(6)
Area and Circumference	477	(9)
Volume	486	(7)
Right Triangle Trigonometry	493	(11)
Beyond Euclidean Geometry	504	(18)
Summary	514	(1)
Review Exercises	515	(5)
Chapter 10 Test	520	(2)
Counting Methods and Probability Theory	522	(68)
The Fundamental Counting Principle	524	(6)
Permutations	530	(7)
Combinations	537	(6)
Fundamentals of Probability	543	(8)
Probability with the Fundamental Counting Principle, Permutations, and Combinations	551	(6)
Events Involving Not and Or; Odds	557	(11)
Events Involving And; Conditional Probability	568	(9)
Expected Value	577	(13)
Summary	584	(1)
Review Exercises	585	(4)
Chapter 11 Test	589	(1)
Statistics	590	(72)
Sampling, Frequency Distributions, and Graphs	592	(13)
Measures of Central Tendency	605	(13)
Measures of Dispersion	618	(8)
The Normal Distribution	626	(16)
Scatter Plots, Correlation, and Regression Lines	642	(20)
Summary	655	(1)
Review Exercises	656	(4)
Chapter 12 Test	660	(2)
Mathematical Systems	662	(23)
Mathematical Systems	664	(9)
Rotational Symmetry, Groups, and Clock Arithmetic	673	(12)
Summary	683	(1)
Review Exercises	683	(2)
Chapter 13 Test	685
Answers to Selected Exercises	AA1
Subject Index	I-1
Photo Credits	P-1