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By presenting problem solving in purposeful and meaningful contexts, Mathematical Excursions, 2/e, provides students in the Liberal Arts course with a glimpse into the nature of mathematics and how it is used to understand our world. Highlights of the book include the proven Aufmann Interactive Method and multi-part Excursion exercises that emphasize collaborative learning. An extensive technology program provides instructors and students with a comprehensive set of support tools.
1. Problem Solving
1.1 Inductive and deductive reasoning
1.2 Problem solving with patterns
1.3 Problem-solving strategies
2. Sets
2.1 Basic properties of sets
2.2 Complements, subsets, and venn diagrams
2.3 Set operations
2.4 Applications of sets
2.5 Infinite sets
3. Logic
3.1 Logic statements and quantifiers
3.2 Truth tables, equivalent statements, and tautologies
3.3 The conditional and the biconditional
3.4 The conditional and related statements
3.5 Arguments
3.6 Euler diagrams
4. Numeration Systems and Number Theory
4.1 Early numeration systems
4.2 Place-value systems
4.3 Different base systems
4.4 Arithmetic in different bases
4.5 Prime numbers
4.6 Topics from number theory
5. Applications of Equations
5.1 First-degree equations
5.2 Rate, ratio, and proportion
5.3 Percent
5.4 Second-degree equations
6. Applications of Functions
6.1 Rectangular coordinates and functions
6.2 Properties of linear functions
6.3 Finding linear models
6.4 Quadratic functions
6.5 Exponential functions
6.6 Logarithmic functions
7. Mathematical Systems
7.1 Modular arithmetic
7.2 Applications of modular arithmetic
7.3 Introduction to group theory
8. Geometry
8.1 Basic concepts of Euclidean geometry
8.2 Perimeter and area of plane figures
8.3 Properties of triangles
8.4 Volume and surface area
8.5 Introduction to trigonometry
8.6 Non-Euclidean geometry
8.7 Fractals
9. The Mathematics of Graphs
9.1 Traveling roads and visiting cities
9.2 Efficient routes
9.3 Planarity and Euler's formula
9.4 Map coloring and graphs
10. The Mathematics of Finance
10.1 Simple interest
10.2 Compound interest
10.3 Credit cards and consumer loans
10.4 Stocks, bonds, and mutual funds
10.5 Home ownership
11. Combinatorics and Probability
11.1 The counting principle
11.2 Permutations and combinations
11.3 Probability and odds
11.4 Addition and complement rules
11.5 Conditional probability
11.6 Expectation
12. Statistics
12.1 Measures of central tendency
12.2 Measures of dispersion
12.3 Measures of relative position
12.4 Normal distributions
12.5 Linear regression and correlation
13. Apportionment and Voting
13.1 Introduction to apportionment
13.2 Introduction to voting
13.3 Weighted voting systems
By presenting problem solving in purposeful and meaningful contexts, Mathematical Excursions, 2/e, provides students in the Liberal Arts course with a glimpse into the nature of mathematics and how it is used to understand our world. Highlights of the book include the proven Aufmann Interactive Method and multi-part Excursion exercises that emphasize collaborative learning. An extensive technology program provides instructors and students with a comprehensive set of support tools.
Table of Contents
1. Problem Solving
1.1 Inductive and deductive reasoning
1.2 Problem solving with patterns
1.3 Problem-solving strategies
2. Sets
2.1 Basic properties of sets
2.2 Complements, subsets, and venn diagrams
2.3 Set operations
2.4 Applications of sets
2.5 Infinite sets
3. Logic
3.1 Logic statements and quantifiers
3.2 Truth tables, equivalent statements, and tautologies
3.3 The conditional and the biconditional
3.4 The conditional and related statements
3.5 Arguments
3.6 Euler diagrams
4. Numeration Systems and Number Theory
4.1 Early numeration systems
4.2 Place-value systems
4.3 Different base systems
4.4 Arithmetic in different bases
4.5 Prime numbers
4.6 Topics from number theory
5. Applications of Equations
5.1 First-degree equations
5.2 Rate, ratio, and proportion
5.3 Percent
5.4 Second-degree equations
6. Applications of Functions
6.1 Rectangular coordinates and functions
6.2 Properties of linear functions
6.3 Finding linear models
6.4 Quadratic functions
6.5 Exponential functions
6.6 Logarithmic functions
7. Mathematical Systems
7.1 Modular arithmetic
7.2 Applications of modular arithmetic
7.3 Introduction to group theory
8. Geometry
8.1 Basic concepts of Euclidean geometry
8.2 Perimeter and area of plane figures
8.3 Properties of triangles
8.4 Volume and surface area
8.5 Introduction to trigonometry
8.6 Non-Euclidean geometry
8.7 Fractals
9. The Mathematics of Graphs
9.1 Traveling roads and visiting cities
9.2 Efficient routes
9.3 Planarity and Euler's formula
9.4 Map coloring and graphs
10. The Mathematics of Finance
10.1 Simple interest
10.2 Compound interest
10.3 Credit cards and consumer loans
10.4 Stocks, bonds, and mutual funds
10.5 Home ownership
11. Combinatorics and Probability
11.1 The counting principle
11.2 Permutations and combinations
11.3 Probability and odds
11.4 Addition and complement rules
11.5 Conditional probability
11.6 Expectation
12. Statistics
12.1 Measures of central tendency
12.2 Measures of dispersion
12.3 Measures of relative position
12.4 Normal distributions
12.5 Linear regression and correlation
13. Apportionment and Voting
13.1 Introduction to apportionment
13.2 Introduction to voting
13.3 Weighted voting systems