A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics

Donald Bindner and Martin Erickson

Publisher:

Chapman & Hall/CRC

Publication Date:

2011

Number of Pages:

260

Format:

Paperback

Series:

Discrete Mathematics and Its Applications

Price:

39.95

ISBN:

9781439846063

Category:

Textbook

MAA Review
Table of Contents

[Reviewed by

John D. Cook

, on

02/10/2011

]

Mathematics students, particularly graduate students, need to learn a variety of tools, often with little guidance. Somewhere along the way they learn LaTeX and become familiar with packages such as Mathematica, MATLAB, R, etc. Donald Bindner and Martin Erickson have written a book to introduce mathematics students to these tools: A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics.

The first 20% of the book is general advice on studying mathematics. The latter 80% of the book is devoted to software. The book says little about the study and practice of modern mathematics but much more about its tools.

A Student’s Guide surveys many software packages in 200 pages and so the space devoted to each is necessarily limited. However, each section ends with references for further reading. Also, some packages, such as LaTeX, appropriately receive more attention than others. Since LaTeX is the de facto standard for mathematical typesetting, it does not need to share space with rivals.

No computational package has the same dominance that LaTeX has in typesetting, and so the authors survey several packages with overlapping functionality: Mathematica, Maple, Maxima, MATLAB, Octave, and R. (SAGE, which is both very powerful and free, is not mentioned.) The authors discuss creating graphics with these packages and also survey more packages for specifically for graphics: PSTricks, PostScript, gnuplot, Graphviz, Geometer’s Sketchpad, and GeoGerba.

The broad scope of the book is an advantage for someone wanting to survey the possibilities. Some readers, however, might prefer a book that discusses fewer options but goes into more depth or one that gives more advice on which tools to use for which tasks.

The coverage of some topics is so brief as to provide little value. For example, in the chapter How to choose a programming language, the languages Perl, Ruby, and Python share half a page. The chapter did not mention that Python is far more common in scientific computing than the other two languages, nor did it mention Python’s SciPy and matplotlib libraries.

A Student’s Guide provides a useful service by gathering into one place information that students might otherwise be expected to learn by osmosis.

John D. Cook is a research statistician at M. D. Anderson Cancer Center and blogs daily at The Endeavour.

THE STUDY AND PRACTICE OF MODERN MATHEMATICS
Introduction

How to Learn Mathematics
Why Learn Mathematics?
Studying Mathematics
Homework Assignments and Problem Solving
Tests
Inspiration

How to Write Mathematics
What Is the Goal of Mathematical Writing?
General Principles of Mathematical Writing
Writing Mathematical Sentences
Avoiding Errors
Writing Mathematical Solutions and Proofs
Writing Longer Mathematical Works
The Revision Process

How to Research Mathematics
What Is Mathematical Research?
Finding a Research Topic
General Advice
Taking Basic Steps
Fixing Common Problems
Using Resources
Practicing Good Mathematical Judgment

How to Present Mathematics
Why Give a Presentation of Mathematics?
Preparing Your Talk
Do’s and Don’ts
Using Technology
Answering Questions
Publishing Your Research

Looking Ahead: Taking Professional Steps

What Is It Like Being a Mathematician?

Guide to Web Resources

A Mathematical Scavenger Hunt
Mathematicians
Mathematical Concepts
Mathematical Challenges
Mathematical Culture
Mathematical Fun

THE TOOLS OF MODERN MATHEMATICS
Introduction

Getting Started with LaTeX
What Is TeX?
What Is LaTeX?
How to Create LaTeX Files
How to Create and Typeset a Simple LaTeX Document
How to Add Basic Information to Your Document
How to Do Elementary Mathematical Typesetting
How to Do Advanced Mathematical Typesetting
How to Use Graphics
How to Learn More

Getting Started with PSTricks
What Is PSTricks?
How to Make Simple Pictures
How to Plot Functions
How to Make Pictures with Nodes
How to Learn More

Getting Started with Beamer
What Is Beamer?
How to Think in Terms of Frames
How to Set up a Beamer Document
How to Enhance a Beamer Presentation
How to Learn More

Getting Started with Mathematica, Maple, and Maxima
What Is a Computer Algebra System (CAS)?
How to Use a CAS as a Calculator
How to Compute Functions
How to Make Graphs
How to Do Simple Programming
How to Learn More

Getting Started with MATLAB and Octave
What Are MATLAB and Octave?
How to Explore Linear Algebra
How to Plot a Curve in Two Dimensions
How to Plot a Surface in Three Dimensions
How to Manipulate the Appearance of Plots
Other Considerations
How to Learn More

Getting Started with R
What Is R?
How to Use R as a Calculator
How to Explore and Describe Data
How to Explore Relationships
How to Test Hypotheses
How to Generate Table Values and Simulate Data
How to Make a Plot Ready to Print
How to Learn More

Getting Started with HTML
What Is HTML?
How to Create a Simple Web Page
How to Add Images to Your Web Pages
How to Add Links to Your Web Pages
How to Design Your Web Pages
How to Organize Your Web Pages
How to Learn More

Getting Started with Geometer’s Sketchpad and GeoGebra
What Are Geometer’s Sketchpad and GeoGebra?
How to Use Geometer’s Sketchpad
How to Use GeoGebra
How to Do More Elaborate Sketches in Geometer’s Sketchpad
How to Do More Elaborate Sketches in GeoGebra
How to Export Images from Geometer’s Sketchpad and GeoGebra
How to Learn More

Getting Started with PostScript
What Is PostScript?
How to Use the Stack
How to Make Simple Pictures
How to Add Text to Pictures
How to Use Programming Constructs
How to Add Color to Pictures
More Examples
How to Learn More

Getting Started with Computer Programming Languages
Why Program?
How to Choose a Language
How to Learn More

Getting Started with Free and Open Source Software
What Is Free and Open Source Software?
Why Use Free and Open Source Software?
What Is Linux?
How to Install Linux
Where to Get Linux Applications
How Is Linux Familiar?
How Is Linux Different?
How to Learn More

Putting It All Together

Bibliography

Index

Tags:

Transition to Advanced Mathematics