1st Edition

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

By Donald Bindner, Martin Erickson Copyright 2011
    280 Pages 111 B/W Illustrations
    by Chapman & Hall

    280 Pages
    by Chapman & Hall

    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 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

    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 Guide provides a useful service by gathering into one place information that students might otherwise be expected to learn by osmosis.
    MAA Reviews, February 2011