R For College Mathematics and Statistics: 1st Edition (Hardback) book cover

R For College Mathematics and Statistics

1st Edition

By Thomas Pfaff

Chapman and Hall/CRC

326 pages | 99 B/W Illus.

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Hardback: 9780367196851
pub: 2019-05-08
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This book encourages the use of R in the college mathematics classroom. Intructors no longer have to be limtited to ``nice'' functions in calculus classes. They can require reports and homework with graphs. They can do simulations and experiments. R can be useful for student projects, for creating graphics for teaching, as well as for scholarly work. This book presents ways R can enhance teaching mathematics.

R has the potential to help students learn mathematics due to the need for precision, understanding of symbols and functions, and the logical nature of code. Moreover, we can provide students the opportunity for experimenting with concepts in any mathematics course.

Table of Contents

1 Getting Started

1.1 Importing Data into R

2 Graphing

2.1 Graphing Functions

2.2 Scatter Plots

2.3 Dot, Pie, and Bar Charts

2.4 Boxplot with a Stripchart

2.5 Histogram

2.6 Exercises

3 Sequences, Series, and Limits

3.1 Sequences and Series

3.2 Limits Recursive Sequences

3.3 Exercises

4 Defining Functions: TBD

5 Polynomials: Unedited

5.1 Basic Polynomial Operations

5.2 The LCM and GCD of Polynomials

5.3 Illustrating Roots of a Degree Three Polynomials

5.4 Creating Pascal’s Triangle with Polynomial Coefficients

5.5 Calculus with Polynomials

5.6 Taylor Polynomial to Sin(x)

5.7 Legendre Polynomials

5.8 Exercises

6 Calculating Derivatives

6.1 Symbolic Differentiation

6.2 Finding Max, Min, and Inflection Points Example

6.3 Graphing a Function and It’s Derivative.

6.4 Graphing a Function with Tangent Lines Example

6.5 Shading the Normal Density Curve Outside the Inflection Points Example.

6.6 Exercises

7 Riemann Sums and Integration

7.1 Riemann Boxes

7.2 Numerical Integration

7.2.1 Numerical Integration of Iterated Integrals

7.3 Area Between two Curves

7.4 Graphing an Antiderivative

7.5 Exercises

8 Graphing 3D:TBD

9 Volumes of Rotation:TBD

10 Curve Fitting:TBD

11 Simulation: unedited

11.1 A Coin Flip Simulation

11.2 An Elevator Problem

11.3 A Monty Hall Problem

11.4 Chuck-A-Luck

11.5 The Buffon Needle Problem

11.6 The Deadly Board Game

11.7 Exercises

12 The Central Limit Theorem and Z-test

12.1 A Central Limit Theorem Simulation

12.2 Z Test and Interval for One Mean

12.3 Z Test and Interval for Two Means

12.4 Exercises

13 The T–Test

13.1 T Test and Intervals for One and Two Means

13.1.1 Paired T-test

13.2 Confidence Interval Theory Examples

13.3 Exercises

14 Testing Proportions

14.1 Tests and intervals for One and Two Proportions

14.2 Theory of Hypothesis Testing Examples

14.3 Exercises

15 Linear Regression

15.1 Multiple Linear Regression

15.2 Exercise

16 Nonparametric Statistical Tests: TBD

17 Miscellaneous Statistical Tests: in progress, no text, unedited

17.1 Testing Standard Deviations

17.2 One-way ANOVA

17.3 Contingency Tables

17.4 Goodness of Fit

17.5 Exercises

18 Matrices

18.1 Eigenvalues, Eigenvectors and other Operations

18.2 Row Operations

18.3 Exercises

19 Differential Equations: TBD

20 Some Discrete Mathematics: unedited

20.1 Binomial Coefficients, Pascal’s Triangle, and a Little Number Theory

20.2 Set Theory

20.2.1 Venn Diagrams

20.2.2 Power Set, Cartesian Product, and Intervals

20.2.3 A Cantor Set Example

20.3 Graph Theory

20.3.1 Creating and Displaying Graphs

20.3.2 Random Graphs

20.3.3 Some Graph Invariants

20.4 Exercises

A A For Loop or Sapply() 230


About the Author

Tom Pfaff is a professor of Mathematics at Ithaca College and served as the all college Honors Program director for three years. He was the PI on three-year NSF grant Multidisciplinary Sustainability Modules: Integrating STEM Courses. The scope of his publications range from traditional mathematics to applied mathematics, including the SABR newsletter, and sustainability to essays about higher education. His blog sustainbilitymath.org provides resources to incorporate sustainability ideas into mathematics courses and he is currently interested in using R for student projects in all courses. When he is not at work, he is spending time with family, gradening, and being physically active. He has competed as a rower, runner, short track speed skater, and an inline skater and I is now on a quest to hike the 46 peaks of the Adirondacks (19 completed as of 7/7/18).

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