# Introduction to Mathematical Literacy

Author(s): Martin Braun

Edition: 2

Pages: 408

## \$52.27

ISBN 9781524941246

Details Electronic Delivery EBOOK 180 days

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

Single-Peaked Preference Rankings

1.4 Approval Voting

1.5 The Search for an Ideal Voting System

Writing Exercises

Projects

Key Terms

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

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

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

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

Index

Martin Braun

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

Single-Peaked Preference Rankings

1.4 Approval Voting

1.5 The Search for an Ideal Voting System

Writing Exercises

Projects

Key Terms

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

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

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

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