Survey of Mathematics with Applications, A: Expanded Sixth Edition

by Angel, Allen R.; Porter, Stuart R.

• ISBN13: 9780201703085
• ISBN10: 0201703084
• Edition: 6th
• Format: Hardcover
• Copyright: 2001-01-01
• Publisher: Addison Wesley

Summary

This expanded sixth edition of the Angel/Porter text contains two additional chapters, "Graph Theory" and "Voting and Apportionment". This best-selling text balances solid mathematical coverage with a comprehensive overview of mathematical ideas as they relate to varied disciplines. This text provides an appreciation of mathematics, highlighting mathematical history, applications of mathematics to the arts and sciences across cultures and introduces students to the uses of technology in mathematics. It is an ideal book for students who require a general overview of mathematics, especially those majoring in the liberal arts, elementary education, the social sciences, business, nursing and allied health fields.

Table of Contents

Critical Thinking Skills	1	(37)
Inductive Reasoning	2	(6)
Estimation	8	(10)
Problem Solving	18	(20)
Chapter Summary	32	(1)
Review Exercises	32	(3)
Chapter Test	35	(1)
Group Projects	36	(2)
Sets	38	(44)
Set Concepts	39	(6)
Subsets	45	(6)
Venn Diagrams and Set Operations	51	(8)
Venn Diagrams with Three Sets and Verification of Equality of Sets	59	(8)
Applications of Sets	67	(7)
Infinite Sets	74	(8)
Chapter Summary	77	(1)
Review Exercises	78	(1)
Chapter Test	79	(1)
Group Projects	80	(2)
Logic	82	(65)
Statements and Logical Connectives	83	(12)
Truth Tables for Negation, Conjunction, and Disjunction	95	(11)
Truth Tables for the Conditional and Biconditional	106	(8)
Equivalent Statements	114	(13)
Symbolic Arguments	127	(8)
Euler Diagrams and Syllogistic Arguments	135	(12)
Chapter Summary	141	(1)
Review Exercises	142	(2)
Chapter Test	144	(1)
Group Projects	145	(2)
Systems of Numeration	147	(35)
Additive, Multiplicative, and Ciphered Systems of Numeration	148	(6)
Place-Value or Positional-Value Numeration Systems	154	(6)
Other Bases	160	(5)
Computation in Other Bases	165	(9)
Early Computational Methods	174	(8)
Chapter Summary	178	(1)
Review Exercises	178	(2)
Chapter Test	180	(1)
Group Projects	180	(2)
Number Theory and the Real Number System	182	(74)
Number Theory	183	(10)
The Integers	193	(8)
The Rational Numbers	201	(13)
The Irrational Numbers and the Real Number System	214	(7)
Real Numbers and Their Properties	221	(6)
Rules of Exponents and Scientific Notation	227	(10)
Arithmetic and Geometric Sequences	237	(8)
Fibonacci Sequence	245	(11)
Chapter Summary	251	(1)
Review Exercises	252	(2)
Chapter Test	254	(1)
Group Projects	255	(1)
Algebra, Graphs, and Functions	256	(89)
Order of Operations	257	(4)
Linear Equations in One Variable	261	(12)
Formulas	273	(8)
Applications of Linear Equations in One Variable	281	(5)
Variation	286	(8)
Linear Inequalities	294	(6)
Graphing Linear Equations	300	(14)
Linear Inequalities in Two Variables	314	(2)
Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula	316	(9)
Functions and Their Graphs	325	(20)
Chapter Summary	339	(1)
Review Exercises	339	(3)
Chapter Test	342	(1)
Group Projects	343	(2)
Systems of Linear Equations and Inequalities	345	(48)
Systems of Linear Equations	346	(8)
Solving Systems of Equations by the Substitution and Addition Methods	354	(10)
Matrices	364	(10)
Solving Systems of Equations by Using Matrices	374	(6)
Systems of Linear Inequalities	380	(3)
Linear Programming	383	(10)
Chapter Summary	389	(1)
Review Exercises	390	(1)
Chapter Test	391	(1)
Group Projects	392	(1)
The Metric System	393	(37)
Basic Terms and Conversions within the Metric System	394	(7)
Length, Area, and Volume	401	(9)
Mass and Temperature	410	(7)
Dimensional Analysis and Conversions to and from the Metric System	417	(13)
Chapter Summary	426	(1)
Review Exercises	426	(2)
Chapter Test	428	(1)
Group Projects	429	(1)
Geometry	430	(59)
Points, Lines, Planes, and Angles	431	(10)
Polygons	441	(9)
Perimeter and Area	450	(10)
Volume	460	(11)
The Mobius Strip, Klein Bottle, and Maps	471	(6)
Non-Euclidean Geometry and Fractal Geometry	477	(12)
Chapter Summary	484	(1)
Review Exercises	484	(2)
Chapter Test	486	(1)
Group Projects	487	(2)
Mathematical Systems	489	(28)
Groups	490	(6)
Finite Mathematical Systems	496	(10)
Modular Arithmetic	506	(11)
Chapter Summary	513	(1)
Review Exercises	513	(1)
Chapter Test	514	(1)
Group Projects	515	(2)
Consumer Mathematics	517	(58)
Percent	518	(9)
Personal Loans and Simple Interest	527	(10)
Compound Interest	537	(8)
Installment Buying	545	(13)
Buying a House with a Mortgage	558	(17)
Chapter Summary	569	(1)
Review Exercises	570	(2)
Chapter Test	572	(2)
Group Projects	574	(1)
Probability	575	(87)
The Nature of Probability	576	(8)
Theoretical Probability	584	(8)
Odds	592	(5)
Expected Value (Expectation)	597	(8)
Tree Diagrams	605	(7)
Or and And Problems	612	(11)
Conditional Probability	623	(5)
The Counting Principle and Permutations	628	(10)
Combinations	638	(5)
Solving Probability Problems by Using Combinations	643	(6)
Binomial Probability Formula	649	(13)
Chapter Summary	656	(1)
Review Exercises	656	(4)
Chapter Test	660	(1)
Group Projects	661	(1)
Statistics	662	(69)
Sampling Techniques	663	(5)
The Misuses of Statistics	668	(4)
Frequency Distributions	672	(5)
Statistical Graphs	677	(9)
Measures of Central Tendency	686	(8)
Measures of Dispersion	694	(7)
The Normal Curve	701	(12)
Linear Correlation and Regression	713	(18)
Chapter Summary	726	(1)
Review Exercises	726	(3)
Chapter Test	729	(1)
Group Projects	730	(1)
Graph Theory	731	(47)
Graphs, Paths, and Circuits	732	(8)
Euler Paths and Euler Circuits	740	(12)
Hamilton Paths and Hamilton Circuits	752	(10)
Trees	762	(16)
Chapter Summary	772	(1)
Review Exercises	773	(3)
Chapter Test	776	(1)
Group Projects	777	(1)
Voting and Apportionment	778
Voting Systems	779
Flaws of Voting	795
Apportionment Methods	808
Flaws of the Apportionment Methods	824
Chapter Summary	831
Review Exercises	832
Chapter Test	836
Group Project	837
Answers	A-1
Credits	C-1
Index	I-1