Introduction to Mathematical Literacy
Edition: 2
Copyright: 2017
Pages: 408
Edition: 2
Copyright: 2017
Pages: 408
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Introduction to Mathematical Literacy is intended primarily for non- STEM majors (i.e. non-science majors), though STEM majors can also benefit greatly from reading it. It is divided, essentially, into two parts. Chapters 1 and 2 form one unit and Chapters 3 –7 form a second unit. Chapter 1 deals with elections which have more than 2 candidates. How many different ways are there to decide the winner, and which method is the fairest of them all?
You’ll be very surprised at the answer to this question! Chapter 2 deals with the problem of apportionment. Chapters 3 –7 comprise a simple and basic unit that teaches us how to deal with data sets. Just as the famous American Express commercial, in touting the American Express card, beseeches you to “not leave home without it”, so too, in this technological age, you cannot leave College without knowing this material.
Chapter 1 Voting Methods
1.1 Plurality and Runoff Methods
Runoff Elections
Preference Rankings
1.2 Borda’s Method: A Scoring System
1.3 Head-to-Head Comparisons
Single-Peaked Preference Rankings
1.4 Approval Voting
1.5 The Search for an Ideal Voting System
Writing Exercises
Projects
Key Terms
Suggested Readings
Chapter 2 Apportionment: Sharing What
Cannot Be Divided Arbitrarily
2.1 Quota Methods
Hamilton’s Method
Lowndes’ Method
2.2 Early Divisor Methods
Jefferson’s Method
Webster’s Method
2.3 Apportionment in Today’s House of Representatives
The Hill–Huntington Method
Other Apportionment Methods
2.4 The Search for an Ideal Apportionment Method
Writing Exercises
Projects
Key Terms
Review Test
Suggested Readings
Chapter 3 INTRODUCTION
3.1 Overview of Course (Basic Concepts)
Population
Sample
Random Sample
Internal and External Validity
3.2 Why We Sample
Sampling to Determine μ
Sampling to Determine P
Excel Excitement
Summary
Exercises
Chapter 4 ORGANIZING AND ANALY ZING DATA
4.1 Graphical Representations
Histogram
Population Histograms
Frequency Polygon
Circle Graph
4.2 Measures of Central Tendency (Ungrouped Data)
Arithmetic Mean
Median
Mode
Comparison of the Mean, Median, and Mode
4.3 Measures of Dispersion or Spread (Ungrouped Data)
Range
Standard Deviation
4.4 Estimating Population Characteristics
4.5 Measures of Central Tendency and Dispersion/Spread
(Grouped Data)
Mean
Standard Deviation
Modal Class
4.6 z Scores and the Use of the Standard Deviation
Two Important Findings
4.7 Additional Descriptive Topics
Pictogram
Stem-and-Leaf Display
Box-and-Whisker Plot
Quartiles
Percentiles
4.8 Writing Research Reports
Background Statement
Design and Procedures of the Study
Results
Analysis and Discussion
Conclusions and Recommendations
Excel Excitement
Summary
Exercises
Research Reports
Chapter 5 Probability
5.1 Probability Defined: Empirically
Subjective Probability
5.2 Probability Defined: Classically
Two Fundamental Properties
And and OR Statements
Practice Exercises
Use of Mathematical Formulas in Simple Experiments
5.3 More Complex Experiments: Tree Diagram
5.4 More Complex Experiments: Multiplication Rules
Dependent and Independent Events
Counting Principle
5.5 Early Gambling Experiments Leading to Discovery of the
Normal Curve
5.6 Additional Probability Topics
Mean and Standard Deviation of a Discrete Probability Distribution
Expected Value
Permutations and Combinations
Summary
Exercises
Chapter 6 Normal Distribution
6.0 Origins of the Concept
6.1 Idealized Normal Curve
Characteristics of the Normal Curve
Use of the Normal Curve Table
6.2 Applications: Idealized Normal Curve
6.3 Working Backward with the Normal Curve Table
Applications
6.4 Binomial Distribution: An Introduction to Sampling
Sampling from a Two-Category Population
Normal Curve Approximation to the Binomial Sampling Distribution
Terminology
6.5 Binomial Sampling Distribution: Applications
Importance of Random Selection
Importance of a Large Population
Excel Excitement
Summary
Exercises
Endnotes
Chapter 7 CENTRAL LIMIT THEOREM
7.1 Central Limit Theorem
7.2 Applying the Central Limit Theorem
Random Selection
7.3 How n and σ Affect sx
How σ Affects sx
How n Affects sx
7.4 Central Limit Theorem Applied to Nonnormal Populations
Excel Excitement
Summary
Excel
Exercises
Endnotes
Answer key
Index
Introduction to Mathematical Literacy is intended primarily for non- STEM majors (i.e. non-science majors), though STEM majors can also benefit greatly from reading it. It is divided, essentially, into two parts. Chapters 1 and 2 form one unit and Chapters 3 –7 form a second unit. Chapter 1 deals with elections which have more than 2 candidates. How many different ways are there to decide the winner, and which method is the fairest of them all?
You’ll be very surprised at the answer to this question! Chapter 2 deals with the problem of apportionment. Chapters 3 –7 comprise a simple and basic unit that teaches us how to deal with data sets. Just as the famous American Express commercial, in touting the American Express card, beseeches you to “not leave home without it”, so too, in this technological age, you cannot leave College without knowing this material.
Chapter 1 Voting Methods
1.1 Plurality and Runoff Methods
Runoff Elections
Preference Rankings
1.2 Borda’s Method: A Scoring System
1.3 Head-to-Head Comparisons
Single-Peaked Preference Rankings
1.4 Approval Voting
1.5 The Search for an Ideal Voting System
Writing Exercises
Projects
Key Terms
Suggested Readings
Chapter 2 Apportionment: Sharing What
Cannot Be Divided Arbitrarily
2.1 Quota Methods
Hamilton’s Method
Lowndes’ Method
2.2 Early Divisor Methods
Jefferson’s Method
Webster’s Method
2.3 Apportionment in Today’s House of Representatives
The Hill–Huntington Method
Other Apportionment Methods
2.4 The Search for an Ideal Apportionment Method
Writing Exercises
Projects
Key Terms
Review Test
Suggested Readings
Chapter 3 INTRODUCTION
3.1 Overview of Course (Basic Concepts)
Population
Sample
Random Sample
Internal and External Validity
3.2 Why We Sample
Sampling to Determine μ
Sampling to Determine P
Excel Excitement
Summary
Exercises
Chapter 4 ORGANIZING AND ANALY ZING DATA
4.1 Graphical Representations
Histogram
Population Histograms
Frequency Polygon
Circle Graph
4.2 Measures of Central Tendency (Ungrouped Data)
Arithmetic Mean
Median
Mode
Comparison of the Mean, Median, and Mode
4.3 Measures of Dispersion or Spread (Ungrouped Data)
Range
Standard Deviation
4.4 Estimating Population Characteristics
4.5 Measures of Central Tendency and Dispersion/Spread
(Grouped Data)
Mean
Standard Deviation
Modal Class
4.6 z Scores and the Use of the Standard Deviation
Two Important Findings
4.7 Additional Descriptive Topics
Pictogram
Stem-and-Leaf Display
Box-and-Whisker Plot
Quartiles
Percentiles
4.8 Writing Research Reports
Background Statement
Design and Procedures of the Study
Results
Analysis and Discussion
Conclusions and Recommendations
Excel Excitement
Summary
Exercises
Research Reports
Chapter 5 Probability
5.1 Probability Defined: Empirically
Subjective Probability
5.2 Probability Defined: Classically
Two Fundamental Properties
And and OR Statements
Practice Exercises
Use of Mathematical Formulas in Simple Experiments
5.3 More Complex Experiments: Tree Diagram
5.4 More Complex Experiments: Multiplication Rules
Dependent and Independent Events
Counting Principle
5.5 Early Gambling Experiments Leading to Discovery of the
Normal Curve
5.6 Additional Probability Topics
Mean and Standard Deviation of a Discrete Probability Distribution
Expected Value
Permutations and Combinations
Summary
Exercises
Chapter 6 Normal Distribution
6.0 Origins of the Concept
6.1 Idealized Normal Curve
Characteristics of the Normal Curve
Use of the Normal Curve Table
6.2 Applications: Idealized Normal Curve
6.3 Working Backward with the Normal Curve Table
Applications
6.4 Binomial Distribution: An Introduction to Sampling
Sampling from a Two-Category Population
Normal Curve Approximation to the Binomial Sampling Distribution
Terminology
6.5 Binomial Sampling Distribution: Applications
Importance of Random Selection
Importance of a Large Population
Excel Excitement
Summary
Exercises
Endnotes
Chapter 7 CENTRAL LIMIT THEOREM
7.1 Central Limit Theorem
7.2 Applying the Central Limit Theorem
Random Selection
7.3 How n and σ Affect sx
How σ Affects sx
How n Affects sx
7.4 Central Limit Theorem Applied to Nonnormal Populations
Excel Excitement
Summary
Excel
Exercises
Endnotes
Answer key
Index