music

# elementary algebra

## summary

Elementary algebra is the mathematical field of study of the properties of operations on the real number system and complex number system and the relations between real and complex numbers which involve a finite number of additions and muliplications. These can be extended to solutions of equations that may require an infinite number of additions and multiplications.

## free computer programming text book project

table of contents
If you like the idea of this project,
then please donate some money.
more information on donating

### stub section

This subchapter is a stub section. It will be filled in with instructional material later. For now it serves the purpose of a place holder for the order of instruction.

Professors are invited to give feedback on both the proposed contents and the propsed order of this text book. Send commentary to Milo, PO Box 1361, Tustin, California, 92781, USA.

# elementary algebra

Elementary algebra is the mathematical field of study of the properties of operations on the real number system and complex number system and the relations between real and complex numbers which involve a finite number of additions and muliplications. These can be extended to solutions of equations that may require an infinite number of additions and multiplications.

The ancient Greeks attributed the development of algebra to the ancient Egytpians. There is archaeological evidence to show that the Babylonians independently developed algebra (algorithmic methods for solving linear equations, quadratic equations, and indeterminate linear equations) and some scholars argue that the Egyptians learned algebra from the Babylonians. At this time the Greeks, Egyptians, and Chinese were primarily using geomtric solutions.

The ancient Greeks made significant advances using geometric algebra, that is solving number problems using geometric processes. These processes involved classical construction (straight edge and compass) and the sides of geometric objects. German mathematician Johann Carl Friedrich Gauss demonstrated in Disquisitioned arithmeticae in a discussion of the problem of constructing regular polygons that there was a one to one correspondence between classical geometric construction and repeated use of four rational operations and square root extraction.

Hero or Heron of Alexandria (1st Century C.E.) combined the methods of the Egyptians and the Babylonians to make advances in algebra. Alexandrian mathematician Diophantus (3rd Century C.E.) wrote a series of books entitled Arithmetic dealing with the solution of algebraic equations. Note that the Library of Alexandria combined both the Greek and Egyptian cultures and religions in the worship of Serapis and Isis.

Indian mathematician and astronomer Brahmaupta (7th Century C.E.) wrote Brahmasphutasiddhanta, which is often considered to be the foundational work of modern algebra. In this work Brahmaupta first introduced a complete arithmetic solution to quadratic equations (including both zero and negative solutions).

The Hindu advances in algebra were introduced to Europe by the Islamic mathematician Muhammad ibn Musa Al-Khawarizmi (8th Century C.E.), who studied mathematics in India. Al-Khowarizmi (variant spelling) wrote Book on Addition and Subtraction after the Method of the Indians, in which he argued in favor of the use of Hindu-Arabic numerals, and The Compendious Book on Calculation by Completion and Balancing, which established algebra as a separate branch of mathematics from arithmetic and geometry. The Enlgish words “algorithm” and “algorism” are corruptions of Al-Khawarizmi’s name. The Arabic word al-jabr means “restitution”, a reference to the transposition of subtracted terms to the other side of an equation or the cancellation of like terms on opposite sides of the equation.

# free music player coding example

Coding example: I am making heavily documented and explained open source code for a method to play music for free — almost any song, no subscription fees, no download costs, no advertisements, all completely legal. This is done by building a front-end to YouTube (which checks the copyright permissions for you).

View music player in action: www.musicinpublic.com/.

Create your own copy from the original source code/ (presented for learning programming).

## view text bookHTML file

Because I no longer have the computer and software to make PDFs, the book is available as an HTML file, which you can convert into a PDF.

 previous page next page
 Tweets by @osdata

## free computer programming text book project

Building a free downloadable text book on computer programming for university, college, community college, and high school classes in computer programming.

If you like the idea of this project,
then please donate some money.

send donations to:
Milo
PO Box 1361
Tustin, California 92781

Supporting the entire project:

If you have a business or organization that can support the entire cost of this project, please contact Pr Ntr Kmt (my church)

more information on donating

Some or all of the material on this web page appears in the
free downloadable college text book on computer programming.

This web site handcrafted on Macintosh computers using Tom Bender’s Tex-Edit Plus and served using FreeBSD .

†UNIX used as a generic term unless specifically used as a trademark (such as in the phrase “UNIX certified”). UNIX is a registered trademark in the United States and other countries, licensed exclusively through X/Open Company Ltd.

Names and logos of various OSs are trademarks of their respective owners.

Copyright © 2010 Milo

Created: September 13, 2010

Last Updated: September 14, 2010