1. O RIGINS OF M ATHEMATICS

2. W HERE DID MATHEMATICS S TART ???? As a math teacher students usually ask “ Who invented Math?” Or “Why was Math invented?” Now we can express the development of mathematics and examples of the process in which the needs of society lead to the development of the math used in a specific time period. Once can stress how the needs of the eras change so does the complexity of the mathematical concepts.

3. T HE BASIS OF COMPUTATION o Who eats first, second, etc? o What comes first, etc? Dominance hierarchy How many? How much? Quantity Ordinals Cardinal s

4. N EEDS FOR MATHMATH Counting Calculations Measurements Lead to development of arithmetic facts and geometry.

5. C OUNTRIES WITH EVIDENCE OF MATH India Egypt Mesopotamia China All having the degree of antiquity, a pioneer in mathematical development, fertile lands, major rivers, strong centralized government and religious life.

6. C OUNTING AND C OMPUTING Question is “ Was counting invented in one location and passed on? Or Did counting arise spontaneously around the world?” Evidence show lots of similarities in the counting and tallying records. The following illustrations are examples of how counting in different artifacts and provide us with an idea of the similarities and possible purposes of the counting concept.

7. Ishango bone, oldest record of sequences of prime numbers or a six month lunar calendar. It is currently located at the Musee d’Histoire Naturelle in Brussels

8. Quipus (sometimes called talking knots ) were recording devices used in the Inca Empire. A quipu usually consisted of colored, spun, and plied thread or strings from llama or alpaca hair, or cotton cords. Used to keep tracks of numerical records and it is said that some told their entire history.

9. Babylonian Tablet

10. Banking System The double tally stick was used by the Bank of England. The amount was cut on a stick and the stick was then cut in half. The bank retained one piece called the foil and the other half was called the stock. It was the receipt issued by the bank. The holder was called a stockholder. When the holder returned the stock it was carefully checked against the foil. The owner would ten be paid. A written certificate was presented which later was referred to as the check.

11. Magic Square a type of permutation and seen throughout mathematical history. Earliest found in China and believed spread to Japan, India and the Middle East. Sangrada Familia church in Barcelona, features a 4×4 magic square. The magic constant of the square is 33, the age of Jesus at the time of the Passion.

12. Counting on fingers was nearly universal among Indian tribes. o The Zuni counted the second ten on their knuckles. o The Bellacoola language shows evidence of subtraction. 16 = one man less four 26= one man and two hands less four

13. S COPE OF A NCIENT M ATHEMATICS Number- ordinal vs. cardinal Base- binary, ternary, decimal, sexagesimal Arithmetic- addition, multiplication, etc Geometry- area and volumes Number Theory- Pythagorean triples, primes, etc Algebra- solution of equation Dividing inheritances, computing logistic needs, allocation of resources, determining volume and area

14. Reference: Allen, D.G. 2002. http://myutbtsc.blackboard.com/bbcswebdav/courses/CD_Math_5305 http://myutbtsc.blackboard.com/bbcswebdav/courses/CD_Math_5305 Ishango bone (n.d.). In Wikipedia. Retrieved August 29, 2011, from http://en.wikipedia.org/wiki/ishango_bone http://en.wikipedia.org/wiki/ishango_bone Zuni. (n.d.) In Wikipedia. Retrieved August 29, 2011 from http://en.wikipedia.org/wiki/zuni_people http://en.wikipedia.org/wiki/zuni_people