R For College Mathematics and Statistics

Thomas J. 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.

Getting Started



Importing Data into R

Functions and Their Graphs



A Piecewise-Defined Function. A Step Function. Polar Coordinates. Parametric Equations. Geometric Definition of a Parabola. Functions that Return a Function. Phythagorean Triples and a Checkerboard Plot.

Graphing



Graphing Functions. Scatter Plots. Dot, Pie, and Bar Charts. A look for loops. Boxplot with a Stripchart. Histogram.

Polynomials



Basic Polynomial Operations. The LCM and GCD of Polynomials. Illustrating Roots of a Degree–Three Polynomial. Creating Pascal’s Triangle with Polynomial Coefficients. Calculus with Polynomials. Taylor Polynomial of Sin(x). Legendre Polynomials.



Sequences, Series, and Limits



Sequences and Series. The Derivative as a Limit. Recursive Sequences.



Calculating Derivatives



Symbolic Differentiation. Finding Maximum, Minimum, and Inflection Points. Graphing a Function and Its Derivative. Graphing a Function with Tangent Lines. Shading the Normal Density Curve Outside the Inflection Points.



Riemann Sums and Integration



Riemann Boxes. Numerical Integration. Numerical Integration of Iterated Integrals. Area Between two Curves. Graphing an Antiderivative.



Planes, Surfaces, Rotations, and Solids



Interactive: Surface Plots. Interactive: Rotations around the x-axis. Interactive: Geometric Solids.



Curve Fitting



Exponential Fit. Polynomial Fit. Log Fit. Logistic Fit. Power Fit.



Simulation



A Coin Flip Simulation. An Elevator Problem. A Monty Hall Problem. Chuck-A-Luck. The Buffon Needle Problem. The Deadly Board Game.



The Central Limit Theorem and Z-test



A Central Limit Theorem Simulation. Z Test and Interval for One Mean. Z Test and Interval for Two Means.



The T-Test



T Test and Intervals for One and Two Means. Paired T-Test. Illustrating the Meaning of a Confidence Interval Simulation.



Testing Proportions



Tests and intervals for One and Two Proportions. Illustrating the Meaning of α Simulation.



Linear Regression



Multiple Linear Regression.



Nonparametric Statistical Tests



Wilcoxon Signed Rank Test for a Single Population. Wilcoxon Rank Sum Test for Independent Groups. Wilcoxon Signed Rank Test for Dependent Data. Spearman’s Rank Correlation Coefficient. Kruskal-Wallis one-way analysis of variance.



Miscellaneous Statistical Tests



One-way ANOVA. Stacking Data. Chi-Square Tests. Testing Standard Deviations.



Matrices



Eigenvalues, Eigenvectors and other Operations. Row Operations.



Differential Equations



Newton’s Law of Cooling. The Logistic Equation. Predator-Prey Mode.



Some Discrete Mathematics



Binomial Coefficients, Pascal’s Triangle, and a Little Number Theory. Set Theory. Venn Diagrams. Power Set, Cartesian Product, and Intervals. A Cantor Set Example. Graph Theory. Creating and Displaying Graphs. Random Graphs. Some Graph Invariants.