R For College Mathematics and Statistics

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).