Thinking Mathematically

by Blitzer, Robert F.

Edition:

3rd

ISBN13:

9780131432437

ISBN10:

0131432435

Format:

Hardcover

Pub. Date:

1/1/2005

Publisher(s):

Prentice Hall

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Summary

This general survey of mathematical topics helps a diverse audience, with different backgrounds and career plans, to understand mathematics. Blitzer provides the applications and technology readers need to gain an appreciation of mathematics in everyday life. Demonstrates how mathematics can be applied to readers'lives in interesting, enjoyable, and meaningful ways. Features abundant, step-by-step, annotated Examplesthat provide a problem-solving approach to reach the solution; annotations are conversational in tone, explaining key steps and ideas as the problem is solved. Begins each section with a compelling vignette highlighting an everyday scenario, posing a question about it, and exploring how the chapter section subject can be applied to answer the question. A highly readable reference for anyone who needs to brush up their mathematics skills.

Problem Solving and Critical Thinking
Inductive and Deductive Reasoning
Estimation, Graphs, and Mathematical Models
Problem Solving
Set Theory
Basic Set Concepts
Subsets
Venn Diagrams and Set Operations
Set Operations and Venn Diagrams with Three Sets
Survey Problems
Logic
Statements, Negations, and Quantified Statements
Compound Statements and Connectives
Truth Tables for Negation, Conjunction, and Disjunction
Truth Tables for the Conditional and the Biconditional
Equivalent Statements, Variations of Conditional Statements, and DeMorganrsquo;s Laws
Arguments and Truth Tables
Arguments and Euler Diagrams
Number Representation and Calculation
Our Hindu-Arabic System and Early Positional Systems
Number Bases in Positional Systems
Computation in Positional Systems
Looking Back at Early Numeration Systems
Number Theory and the Real Number System
Number Theory: Prime and Composite Numbers
The Integers; Order of Operations
The Rational Numbers
The Irrational Numbers
Real Numbers and Their Properties
Exponents and Scientific Notation
Arithmetic and Geometric Sequences
Algebra: Equations and Inequalities
Algebraic Expressions and Formulas
Linear Equations in One Variable
Applications of Linear Equations
Ratio, Proportion, and Variation
Linear Inequalities in One Variable
Quadratic Equations
Algebra: Graphs, Functions, and Linear Systems
Graphing and Functions
Linear Functions and Their Graphs
Systems of Linear Equations in Two Variables
Linear Inequalities in Two Variables
Linear Programming
Approximating Reality with Nonlinear Models
Consumer Mathematics and Financial Management
Percent, Sales Tax, and Income Tax
Simple Interest
Compound Interest
Annuities, Stocks, and Bonds
Installment Buying
Amortization and the Cost of Home Ownership
Measurement
Measuring Length; The Metric System
Measuring Area and Volume
Measuring Weight and Temperature
Geometry
Points, Lines, Planes, and Angles
Triangles
Polygons, Perimeter, and Tessellations
Area and Circumstances
Volume
Right Triangle Trigonometry
Beyond Euclidean Geometry
Counting Methods and Probability Theory
The Fundamental Counting Principle
Permutations
Combinations
Fundamentals of Probability
Probability with the Fundamental Counting Principle, Permutations, and Combinations
Events Involving Not and Or ; Odds
Events Involving And ; Conditional Probability
Expected Value
Statistics
Sampling, Frequency Distributions, and Graphs
Measures of Central Tenden
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