# Welcome to Al Lehnen's Web Site

I am a former mathematics instructor at Madison Area Technical College in Madison, Wisconsin USA:  1701 Wright Street, Madison, WI 53704 ; Email alehnen@madisoncollege.edu or aplehnen@execpc.com

The graphic above was generated as a parametric surface using the Java Program CalcPlot3D, authored by Professor Paul Seeburger of  Monroe Community College in Brighton, New York.

# Schedule in Retirement

• Monday
• 7:30 - 5:00         : Whatever
• Tuesday
• 7:30 - 5:00         : Whatever
• Wednesday
• 7:30 - 5:00         : Whatever
• Thursday
• 7:30 - 5:00         : Whatever
• Friday
• 7:30 - 5:00         : Whatever

 The Axioms of Humility: A. Just because I don't understand an idea, doesn’t mean that it is wrong. B. Just because I do understand an idea, doesn’t mean that it is right.

 Fall 2022 WisMATYC Presentation: A Court of Inquiry Bernoulli Numbers and Bernoulli Polynomials:  A Survey of Basic Properties and Some Applications Math Club Presentation: Friday 10/02/2020 The Stereographic Projection of Circles on the Riemann Sphere Fall 2019 WisMATYC Presentation: The Intersection of a Cylinder with a Plane Winplot Links Links to Math Websites including Online Tutorials A Detailed Description of an Algorithm that uses Cardano's Method to Solve Cubic Equations with Real Coefficients Solving the Cubic Equation an Excel file using Cardano's Method to find all roots of any cubic equation with real coefficients. Integration by the Method of Substitution Checking Indefinite Integrals by Numerical Quadrature The Sum of the Alternating Harmonic Series Derivation of the Taylor Series Examples of the Gradient Trig Lemmas The Arithmetic, Geometric and Harmonic Means Notes on the Weierstrass Funcion that's Everywhere Continuous, Nowhere Differentiable The animated gif below shows the shape of the cycloid solution to the Brachistochrone problem animated on the ratio of the horizontal displacement to the vertical displacement of the falling object. Also shown (in red) is the trajectory of the least time parabola. The graphs were generated in WinPlot. In of January 2021 Madison College removed the files from the facutly server that had I maintained before my retirement. I have set up fifteen online folders of files for the following sixteen courses. Calculus 1 Calculus 2 Calculus 3 College Algebra College Math Elementary Algebra with Applications Intermediate Algebra Introduction to Engineering Statistics Linear Algebra Machine Tool Math 1 Machine Tool Math 2 Math Analysis Technical Math 1 and Technical Math 2 Trigonometry Vocational Math In addition, the following files can be downloaded as individual PDF's Notes on Logic and Set Theory Text Book for Introduction to College Math (804-107) Text Book for Vocational Math (804-379)

Older Conference Presentations:
 The Number of Symmetric Permutation Matrices : Presented at the Fall 2013 WisMATYC Conference at Waukesha County Technical College Some Different Perspectives on Linear Least Squares: Presented at the Fall 2012 WisMATYC Conference at UW Manitowoc Singular Values and Elliptic Orbits of First Oder Linear Differential Systems in 2D: Presented at the MAA Wisconsin 2012 Spring Conference at Milwaukee School of Engineering Some Elementary Results Discovered Preparing to Teach Linear Algebra: Presented at the Fall 2010 WisMATYC Conference at UW Marathon County The Logistic Equation with a Harvesting Term: Presented at the Fall 2009 WisMATYC Conference at MATC A Deranged Experiment by Euler and Bernoulli: Presented at the Fall 2008 WisMATYC Conference at UW Sheboygan County The Brachistochrone: A Timely Consideration: Presented in July 2008 at the MAA MathFest in Madison Roofing Applications of Trigonometry: Presented at the Fall 2007 WisMATYC Conference at Fox Valley Technical College Using Linear Algebra to Generate Trig Identities: A Revision Co-Authored with Eric Luck of the Original Presentation Made at The Spring 2006 Meeting of Wisconsin Section of the MAA ay UW White Water The Golden Triangle and the Mathematical Black Magic of the Pentagram A Play in Four Acts: Presented at the Fall 2006 WisMATYC Conference at UW Marshfield Moments of the Distance from the Force Center in a Two-Body Kepler Orbit (Or "Just How Far Away is the Sun Anyway?"): Presented at the MAA Wisconsin 2004 Spring Conference at UW Platteville The Sphere Game in N Dimensions : A Presentation Made at The Spring 2002 Meeting of the Wisconsin Section of the MAA The Sphere Game in 3 Dimensions The Use of Rational Function Factors in Approximating e: A Presentation Made at The Spring 2001 Meeting of Wisconsin Section of the MAA