NERCOMP • Amherst College • 22 Feb 2000

Mathematica for New Users:

The Second Day

Murray Eisenberg
Mathematics and Statistics Department
University of Massachusetts, Amherst
http://www.math.umass.edu/~murray

Abstract

How best to introduce Mathematica to new users can be perplexing: standard introductory treatments often range so widely through the daunting number of features, or touch upon so many areas of application, as to be unsuitable.  This talk presents two somewhat circumscribed introductions—Hero's method for estimating square roots and rigid motions of the plane—that we have used with college math students; these topics have minimal mathematical prerequisites.  Whereas the presentation may be pedagogically suggestive for experienced users, it can also serve as an introduction to those attendees who are themselves new to Mathematica.

Introduction

The problem

• Mathematica textbooks & on-line tutorials too general
• Exception: self-contained Mathematica courseware (e.g.m Math Everywhere)

A solution

• The zeroth day—demo in lecture, not lab

Middle A

• The first day—getting started
• The second day—explore a relevant topic

⚠ These notebooks for presentation—not tutorial use!

The first day

Mechanics

• starting and exiting Mathematica
• notebook files
• windows
• mousing around
• printing

Entering input and producing output

1 + 1

%  +  5

N[Pi,  100]

Cells and groups

• cell selection
• opening/closing grouped cells

• starting and exiting Mathematica
• notebook files
• windows
• mousing around
• printing

Cut - and - paste

The "bread and butter"—numerics, symbolics, and graphics

Table[Sin[2. ^-k]/2^-k,  {k,  1,  9}]

Expand[(a  +  2)^20]

D[Exp[2  x] Sin[5 x],  x]

Integrate[x/(x^2  +  2  x  +  2),  x]

Plot[Exp[-(1/2) (x^2)],  {x,  -3,  3}];

Entering StandardForm expressions: typesetting!

E^(-theta) Sin[(2  Pi/440) theta]

(E^(-θ)) Sin[((2  π)/440) θ]

(∫_0^∞) (1/(Sqrt[2 π])) (E^(-(1/2) (x^2))) \[DifferentialD]x

Getting information and using the Help Browser

?Integrate

Do something wonderful with Mathematica

Surfaces

The second day

Hero's method

• Audience:  calculus; numerical analysis; faculty workshop; introduction for computer professionals
• Mathematically elementary
• Can expand and extend to go further and deeper into Mathematica
• Leads to further math: Newton's method; dynamical systems

Hero' s method

Rigid motions of the plane

• Audience:  linear algebra, multivariable calculus
• Appealing graphical content
• Good motivator for problems

Rigid Motions

Conclusion

• Tailor the introduction to the course and audience: choose relevant topics
• Employ graphics and symbolics along with numerics

About the author

Since 1960 Murray Eisenberg has taught at the University of Massachusetts, Amherst, where he is Professor of Mathematics and Statistics and directs his department's undergraduate computer lab.  His research interests are in the topology of dynamical systems, but in recent years he has concentrated upon studying cognitive and pedagogical issues of using computer programming to teach mathematics.  He has published articles on topological dynamics and topology, the APL programming language and its offshoot the J programming language, and the use of computing in teaching math.  He is the author of three undergraduate texts—on axiomatic set theory,topology,and mathematical rigor and proof.
Murray has been using computers to teach mathematics for some twenty years.  Since version 2.2,he has been using Mathematica to teach calculus, linear algebra, multivariate analysis, differential equations, and numerical analysis.  Recently he has conducted workshops on Mathematica for area science faculty.  At regional and international conferences he spoken about use of the Mathematica software package in undergraduate math.