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A Student's Guide to the Study, Practice, and Tools of Modern MathematicsBy Donald Bindner
M00002113
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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.
Table of Contents
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
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.
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Author(s)
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.
Reviews
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
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