1st Edition

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

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**A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics** provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to *Mathematica*^{®} and Maple**™** to MATLAB^{®} and R. Along with a color insert, the text includes exercises and challenges to stimulate creativity and improve problem solving abilities.

The first section of the book covers issues pertaining to studying mathematics. The authors explain how to write mathematical proofs and papers, how to perform mathematical research, and how to give mathematical presentations.

The second section focuses on the use of mathematical tools for mathematical typesetting, generating data, finding patterns, and much more. The text describes how to compose a LaTeX file, give a presentation using Beamer, create mathematical diagrams, use computer algebra systems, and display ideas on a web page. The authors cover both popular commercial software programs and free and open source software, such as Linux and R.

Showing how to use technology to understand mathematics, this guide supports students on their way to becoming professional mathematicians. For beginning mathematics students, it helps them study for tests and write papers. As time progresses, the book aids them in performing advanced activities, such as computer programming, typesetting, and research.

**THE STUDY AND PRACTICE OF MODERN MATHEMATICSIntroduction **

**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 MATHEMATICSIntroduction**

**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**

*Exercises appear at the end of each chapter.*

### Biography

**Donald Bindner** is an assistant professor of mathematics at Truman State University. He is an advocate of free software.

**Martin Erickson** is a professor of mathematics at Truman State University. He has written several mathematics books, including *Pearls of Discrete Mathematics* (CRC Press, 2010) and *Introduction to Number Theory* (CRC Press, 2008) with Anthony Vazzana.

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

—MAA Reviews, February 2011