General History
 Number Systems
 Babylonian had a place value system which used base 60, like our seconds and minutes. The numbers are written smallest to the right, just like what we normally do, but with a space between the place values.
 Egyptian had a symbolic system, it had a symbol for each place value and number, so for 30 they would write their 10 3 times.
The numbers are written smallest to the left, the opposite of the HinduArabic and Babylonian.
A good book on the history of mathematics of the Ancient Egyptians is Mathematics in the Time of the Pharaohs by Richard J. Gillings.  HinduArabic is they number system most commonly used in the world today. It is a place value system using base 10, also called a decimal system. The symbols that can go in each place value are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
 Mayan had a vertical place value system which used base 20. The smallest value on the bottom.
 Other Bases are commonly used today, such as base 12 when working with inches and feet. However, more common are the ones used with computers, binary (base 2), octal (base 8), and hexidecimal (base 16).
Any number can be a base, we just have to tell what base we are working in, if different than base 10. For example, if we write the number 576, we assume it is base 10, but it could be base 8. When there is a chance for confusion, we write the base as a subscript, that is 576_{8}.  Place Value for most modern base systems we write our numbers with the largest place value to the left and smallest to the right.
 Decimal System, we use the powers of 10 for our place values. We can write them easily in numbers. However to get used to other bases, the more formal mathematical notation using exponents is helpful.
 Other Bases, we use powers of our other bases for the place values, but we don't have nice words for them. The numbers in the base would be the same. Just like we do not have a single symbol for 10, we don't have one for our other bases, so if working in base 5, we would use 0, 1, 2, 3, 4. 5 would be written at 10 since that would be 5^{1}.
 Arithmetic in Other Bases
 This is very similar to clock arithmetic, or modulo arithmetic. For example when we start at 9AM, and say we are meeting someone in 4 hours, we don't say 13AM, we say 1PM.
 Adding & Subtracting: When we reach 'our base' we put a 1 in the next higher power column, and keep going.
 Multiplication & Division: Having a 'times table' to reference is best when starting out.
 Symbols used in Math & their meaning (PDF ~ partial list)
 Math Shorthand (To be added)
 Common Symbols for constants (To be added)
 Symbols from a particular topic are with that topic
 Illustrated Mathematics Dictionary https://www.mathsisfun.com/definitions/
 Mathwords http://www.mathwords.com/
 Number Words and Number Symbols by Karl Menninger
 Some good book on the History of Mathematics
 History of Mathematics by Victor Katz
 The Historical Roots of Elementary Mathematics by Bunt, Jones, & Bedient
 Math through the Ages by Berlinghoff & Gouvêa
 History of Mathematics by Boyer
 Sherlock Holmes in Babylon by Anderson, Katz, & Wilson
 Mathematics of the Incas by Ascher & Ascher
 Additional information on these topics can be found on the following sites, as well as many others:
 Canadian Society for the History and Philosophy of Mathematics http://www.cshpm.org
 History of Mathematics http://archives.math.utk.edu/topics/history.html
 HOMSIGMAA  History of Mathematics SIGMAA http://homsigmaa.org/
 Math History http://web.stcloudstate.edu/wbbranson/MathHistory.html
 Mathematics History http://library.thinkquest.org/22584/
 Teaching with Original Historical Sources in Mathematics http://www.math.nmsu.edu/~history/
 The following sites have information about Binary, Hexidecimal, and other helpful information when working with computers. There are many other good ones.
 http://www.w3schools.com
 http://www.w3schools.com/charsets/default.asp
 http://www.asciicode.com/
 https://mothereff.in/binaryascii
 http://www.colorhexa.com
3 
2 
1 
0 
1 
2 
3 


words 
thousands 
hundreds 
tens 
ones 
tenths 
hundredths 
thousandths 
numbers 
1000 
100 
10 
1 
0.1 
0.01 
0.001 
Powers of 10 
10^{3} 
10^{2} 
10^{1} 
10^{0} 
10^{1} 
10^{2} 
10^{3} 
3 
2 
1 
0 
1 
2 
3 


numbers 
1000 
100 
10 
1 
0.1 
0.01 
0.001 
Base 2 
2^{3} (in base 10, 2^{3} = 8) 
2^{2} 
2^{1} 
2^{0} 
2^{1} 
2^{2} 
2^{3} 
Base 8 
8^{3} (in base 10, 8^{3} = 512) 
8^{2} 
8^{1} 
8^{0} 
8^{1} 
8^{2} 
8^{3} 