All about mathematics

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All about mathematics

  1. 1. All About Mathematics Created by N@NDEESH L@XETTY Xc20
  2. 2. What is the difference between a mathematician and a philosopher? The mathematician only needs a pencil, paper, and trash bin for his work. . . the philosopher can do without the trash bin.
  3. 3. <ul><li>-History of Math </li></ul><ul><li>Levels of Math </li></ul><ul><li>Famous Mathematicians </li></ul><ul><li>-Mathematics Video </li></ul><ul><li>Fun Page - Resources </li></ul><ul><li>Concept Map </li></ul>Menu
  4. 4. History of Math In 50,000 B.C. there was the first evidence of counting, which was the same time of the Neanderthal man. Here’s irony; in 180 BC the 360 degree circle was defined. Just thirty years before the 360 degree circle, the Great Wall of China began construction. Then in 140 BC, the first Trigonometry was discovered followed by two forms of Algebra in 830 AD by Al-Khowarizmi and in 1572 AD by Bombelli (the more popular choice in text books). A few centuries later, we run out of things to discover, so we improvise; which is what Matiyasevich does in 1970 by proving that Hilbert’s Tenth Problem is unsolvable. Six years later the Four Color Conjecture is verified by computer. The key codes that we use every day to clock in at work, at our ATM, to secure our house, etc. was introduced in 1977 by three Mathematicians; Adelman, Rivest and Shamir. In 1994 Wiles proves Fermat’s Last Theorem . And lastly, in 2000, mathematical challenges of the 21 st century here was announced. Quit
  5. 5. Mathematics have come a great length. What people do not realize is that mathematics are used everywhere; GPS, cellular phones, computers, the weather, our television cable guide, sound waves (use a sinusoidal wave or sine wave), clocks, speed limits, shopping, balancing our checkbooks, etc. Math is used everywhere. Another thought; if trigonometry was discovered first, why is it we take Algebra before Trigonometry? Or how did they do Trigonometry without knowing Algebra first? Hmm. A couple of fun facts: 111111111 12345679 x 9 = 111111111 x 111111111 and 12345678987654321 12345679 x 8 = 98765432 Quit Click to view video on History of Math
  6. 6. Levels of Math Kindergarten – whole numbers and counting 1 st – addition, subtraction, measurements 2 nd – place value, base – 10 system, addition, subtraction, measurement 3 rd – addition, subtraction, place value, multiplication, division, fractions, geometry 4 th – multi-digit multiplication, fractions, decimals, mixed numbers, area 5 th – multi-digit division, adding and subtracting of fractions and decimals, triangles, quadrilaterals, and algebra Quit
  7. 7. 6th – multiplication and division of fractions and decimals, ratios, rates and percents, 2-3 dimensional figures 7th – rational numbers, linear equations, proportionality and similarity, surface area and volume, probability and data 8th – linear functions and equations, geometry, analysis of data sets 9th - 12th – Algebra 1, Geometry, Algebra 2, Trigonometry, Statistics, and Calculus Click here to view teacher certification exam in 1874 Quit
  8. 8. Famous Mathematicians René Descartes (1596 – 1650) – (x,y) coordinates. Blaise Pascal (1623-1662) – Pascal triangle, Pascal’s Theorem, created the first digital calculator. Eukleides (Euclid) c. 330 - 275 B.C.E - Euclidean geometry, “The Elements”. Pierre de Fermat 1601 – 1665 – Father of Calculus, lawyer, Probability Theory Quit
  9. 9. Unsolved Math Problems 1. Are there infinitely many primes of the form n^2+1? 2. Is every integer larger than 454 the sum of seven or fewer positive cubes? 3. Start with any positive integer. Halve it if it is even; triple it and add 1 if it is odd. If you keep repeating this procedure, must you eventually reach the number 1? For example, starting with the number 6, we get: 6, 3, 10, 5, 16, 8, 4, 2, 1. 4. Let f(n) be the maximum possible number of edges in a graph on n vertices in which no two cycles have the same length. Determine f(n). 5. Prove: If G is a simple graph on n vertices and the number of edges of G is greater than n(k-1)/2 , then G contains every tree with k edges http://math.whatcom.ctc.edu/content/Links.phtml?cat=60&c=0 Quit
  10. 10. Fun Page Online Worksheet Printouts: http://www.clcmn.edu/kschulte/mathworksheets.html Games: http://www.math.com/students/puzzles/puzzleapps.html http://sudoku.math.com/ http://cte.jhu.edu/techacademy/web/2000/heal/siteslist.htm http://www.visualmathlearning.com/Games/shortest_route.html Math Jokes: http://www.math.ualberta.ca/~runde/jokes.html Quit
  11. 11. http://en.wikipedia.org/wiki/Hilbert's_tenth_problem http://www.aft.org/pubs-reports/american_educator/issues/fall2005/Ball05SB1.pdf http://www.k12.wa.us/Curriculuminstruct/Mathematics/RevisedStandards/FullWAK-highschool.pdf http://www.math.com/students/puzzles/puzzleapps.html http://www.math.ualberta.ca/~runde/jokes.html http://cte.jhu.edu/techacademy/web/2000/heal/siteslist.htm Continued on next page. . . Resources Quit
  12. 12. http://www.mathplayground.com/mathvideos.html http://www.math.wichita.edu/~richardson/timeline.html# http://www.clcmn.edu/kschulte/mathworksheets.html http://www.visualmathlearning.com/Games/shortest_route.html http://www.mathematicianspictures.com/Mathematicians/ http://www.math.fau.edu/locke/Unsolved.htm http://math.whatcom.ctc.edu/content/Links.phtml?cat=60&c=0 http://www.youtube.com/watch?v=wo-6xLUVLTQ http://www.youtube.com/watch?v=3hOrqDIFT2w Quit
  13. 13. Return to Previous Slide Quit
  14. 14. <ul><li>Mativasevich exhibits a system of 10 simultaneous first and second degree equations which provide a Diophantine definition of the set of pairs ( a , b ) such that </li></ul><ul><ul><li>          where     is the n th Fibonacci number. </li></ul></ul><ul><li>This proves J.R. and thus completes the proof that all recursively enumerable sets are Diophantine, and that therefore Hilbert's tenth problem is unsolvable. </li></ul>Hilbert’s Tenth Problem Quit Return to History of Math
  15. 15. <ul><li>Fermat's Last Theorem is the name of the statement in </li></ul><ul><li>number theory that: </li></ul><ul><ul><li>It is impossible to separate any power higher than the second into two like powers, or, more precisely: </li></ul></ul><ul><ul><li>If an integer n is greater than 2, then the equation a   n  +  b   n  =  c   n has no solutions in non-zero integers a , b , and c . </li></ul></ul>Fermat's Last Theorem Quit Return to History of Math
  16. 16. The four color theorem (also known as the four color map theorem) states that given any plane separated into regions, such as a political map of the states of a country, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color. Note that there must be 4+n (where n < 0 and must consist of whole numbers) regions. (added by Jessica Gokey) The Four Color Theorem Click here to view printout activity of the Four Color Theorem Quit Return to History of Math
  17. 17. Quit Return to History of Math
  18. 18. Object of Four Color Theorem Printout: Pick any four colored pencils, crayons, or markers. Using all four colors, color each region without the same color touch twice. Example: Do not let red touch red, green touch green, blue touch blue, or yellow touch yellow. This is a fun activity and can be created in many different shapes. Enjoy! Return to Printout
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