It can be difficult to start to study new subjects that is related directly or indirectly to mathematics. The accurate statements given in a logical and more formal sequence sometimes hinders understanding. This does not mean to say that logical deduction should not play a major role. An alternative way to start a study is to supply more statements that are more intuitive, yet not to undermine the logical "flavor" of the subject. In fact remarks of a more technical nature should be labeled as such.
By intuitive, it is meant a bridging of familiar, sometimes almost trivial, daily events with a branch of mathematics. Hopefully this will provide an understandable preparation for the topic in mathematics to be discussed. The work here is not scholarly, not impressive with new and astounding discoveries. There are many good technical works to cover that aspect. Many text books also cover more completely the branches of mathematics. If the present work can enlighten the reader and motivate him to study mathematics further then the main goal for creating this work has been accomplished.
The content of all the volumes is intended for teachers ("you cannot lead anyone farther than you have gone yourself")and high school students of mathematics, perhaps members of a math club. It attempts to show them a mixture of classical and modern trends of mathematical thinking in a very intuitive way. Some of the material was used during some NSF summer institutes for teachers of mathematics and science. SInce then it has been updated, supplemented and made more "intuitive." Hopefully, some of the ideas may be used directly in the classroom. Everything is written in a format suitable for location on a website on the internet, on a CD or in some computer, with access using a browser. Windows Explorer in Windows operating systems Vista (32-bit) and Windows 7 were used in the creation of the volumes.
Given below is a list of links to the various branches of mathematics. Each branch is included in a volume and contains a preface, the main text, the usual exercises, answers to some of the exercises, sometimes computer programs for computational situations. There is also additional material that provides more explanation. If the reader already understands some topic in the main text, then he need not find further explanation in the additional material. All this can be accessed by clicking on the indicated links. The computer is not used as an electronic page turner, but allows somewhat random access to relevant material - the reader customizes somewhat the presentation of the material being studied.
The reader may leave all volumes and return to Windows by clicking on the X in the upper right corner (possibly more than one such X).
An enormous amount of work is involved in this writing. The work is incomplete, and more will be added later. But everything is offered free of charge. It is requested that it remain free and accessable to everyone.
The discussions are stored in different volumes. Click to select the volume:
Volume A Logical Thinking and Sets
Volume B Number Systems*
Volume C Relations, Functions and Groups
Volume D Vectors
Volume E Matrices and Geometry*
Volume F Graph Theory*
Appendix
Parts of Math to be Discussed in the Future
In each volume are one or more chapters (folders) and an index file. Click on one of the above links to go to an index file which contains links to the chapters. Each chapter contains the main text file containing the central discussions. In various places of the text file are links to a file of added material, to a file of exercises and in some cases, a file containing computer programs. The additional material contains more explanations of topics in the main text, and may contain discussions of more difficult material. The reader may ignore them for a quicker study of the main text (not recommended). The chapters are divided into sections. Both chapters and sections have headings.
* The applications of some material in Volumes B,E and F demand extensive computation. To reduce, if not eliminate, the tedium of much arithmetic and algebra, computer programs have been written (using the C language). Clicking on the link Computer (name) will display a page with a list of executable programs. Selecting and clicking on the program with the given "name" activates the computer to produce output which saves the reader much time and work by hand to obtain that output.