Welcome

Mathematics means different things to different people. Students and teachers study mathematics to learn it. Others learn mathematics because for them the study of mathematics is itself interesting. In all cases though people use mathematics as a tool to solve practical problems. The purpose of this site is to act as a resource for this purpose.

For students and teachers this usually means learning mathematics and then applying the ideas to solving problems from the textbook. This is useful for two reasons. This process helps in understanding the mathematical concepts and, in giving mathematics something to do, it comes to be seen as a useful practical tool for getting at results that otherwise would be difficult if not impossible to obtain.

This site is about learning and applying mathematics as a tool for understanding the world and for solving practical problems. Practical problems include those of the teacher who has a main problem of first teaching mathematics, which is by nature abstract and logical, and then showing the student how it can be used. This latter problem of providing insight and practice for relevance of mathematics is the more difficult of the two. Typically the practical problem of the student is twofold. The student as a practical matter is concerned with passing the course and getting the best grade possible. Ideally this occurs as a result of the student demonstrating in various ways a level of mastery that justifies the grade. This is the modern education paradigm and it must be a cooperative process in order for the student and teacher to succeed.

In this case success means that the student acquires the intended knowledge and understanding and that it has some relevance. Relevance in this context often means being able to use the acquired knowledge and understanding for something useful to the student. This issue of the relevance of mathematics is not limited to teachers and students in the quest of education. At some point everyone uses mathematics as a tool to achieve some purpose.

There is a contemporary debate amongst educators now about the negative effects of the reliance of students on hand-held calculators. Some schools have gone so far as to prohibit their use. The claim is that the use of these devices by students results in deficiencies of one form or another. The allegations against the calculator run the gamut. Now of course there are also powerful computer software with capabilities that dwarf those of the calculator typically used by students.

This debate in a sense is not a new one. Historically it is the reverse of the struggle between the professional abacists and the algorists. History teaches that the algorists gained the upper hand and schools now teach their arithmetic using the Indo—Arabic decimal place value system of numeration with the once mysterious zero along with the conventional algorithms for computations using these symbols. The abacus has been relegated to a toy for the infant’s bedroom.

What should have been learned from this history that has now been forgotten is that what we view as natural and essential in terms of what it means to be computationally competent is a relatively recent invention. Algorism has come to be accepted as defining what is minimally acceptable know-how.

 When I was a high school and university student slide rules were our calculators. Textbooks had appendices with tables of mathematical data. These were our calculators. No one questioned their usefulness or necessity. It was just too much work and required too much precious time to compute these data using pencil-and-paper algorithms. No one wasted any time debating about whether this was a good thing or not.

Of course there is no substitute for having an understanding of the basics required for success in any endeavor, whether it is mathematics, flying an airplane, or wind surfing. However, there is also no point in laboring under the yoke of the obvious once the principles are understood if there is a better way to accomplish the task at hand. The effort required for doing what is well- understood and routine can be used for more important tasks. This site is intended to promote the use of available tools for teaching, learning, and using mathematics.

The observation of this quotation has been made using other words by different people over the years. If there is a problem with the use of calculators or any other tools related to mathematics, then the culprit is not the tool. It is how it is being used. No skilled craftsman or artisan blames his tools. Neither are they a substitute for the essential know-how.

This site features the XMathBox which is a virtual machine file that may used with virtual machine software such as VirtualBox™ by Sun Microsystems. Click on the Software tab above for complete information. This math tool box provides the user with a complete Xubuntu Linux virtual machine featuring a full set of tools for learning mathematics, visualization, and problem solving. XMathBox is available to users having GNU/Linux, Apple Mac OS X™, or Microsoft Windows™ operating systems by merely installing VirtualBox™ host software and configuring the virtual machine. The XMathBox project is not approved, sponsored, or affiliated with Xubuntu™, Ubuntu™ or its related projects.

For Microsoft Windows™ users the recommended mathematics tool is the Euler Math ToolBox, a creation of Professor R. Grothmann from the University of Eichstätt, near Munich Germany. 

The resources featured by this site focus on what is both useful and freely available. There are proprietary and commercial resources available with considerable capabilities and features. However, the quality and availability of open-source software and documents are such that these must be considered as valuable resources. These resources are in the categories of documents, software, application files and links to resources. Resources in these categories are accessed through the tabs at the top of this page.

Of course people are also a resource in this sense. You can contribute to this site by becoming a member. Members may create documents, provide comments, and upload files for others to use. With these privileges comes responsibility. Read the site Acceptable Use Policy before registering as a user. Registering as a user implies your agreement to comply with the terms of this Acceptable Use Policy.

Email any questions or comments to me by clicking on the Site Administrator link that follows. I hope you find these resources useful.

David E. Miller
Site Administrator