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Application of algebra

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Application of algebra

  1. 1. Content  What Is Algebra ?  Why Algebra is important in your life ?  History of Algebra
  2. 2. What is Algebra ?  Algebra is one of the broad parts of mathematics, together with number theory , geometry and analysis.  As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields.  Elementary algebra is essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics.
  3. 3.  The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra.  Much early work in algebra, as the origin of its name suggests, was done in the Near East, by such mathematicians as Omar Khayyam (1050-1123).
  4. 4.  The word algebra is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an "algebra", and the word is used, for example, in the phrases linear algebra and algebraic topology .  A mathematician who does research in algebra is called an algebraist.
  5. 5. Why Algebra is important in your life ?  Mathematics is one of the first things you learn in life. Even as a baby you learn to count. Starting from that tiny age you will start to learn how to use building blocks how to count and then move on to drawing objects and figures. All of these things are important preparation to doing algebra.
  6. 6. The key to opportunity  These are the years of small beginnings until the day comes that you have to be able to do something as intricate as algebra. Algebra is the key that will unlock the door before you. Having the ability to do algebra will help you excel into the field that you want to specialize in. We live in a world where only the best succeed.
  7. 7. Prerequisite for advanced training  Most employers expect their employees to be able to do the fundamentals of algebra. If you want to do any advanced training you will have to be able to be fluent in the concept of letters and symbols used to represent quantities.
  8. 8. Science  When doing any form of science, whether just a project or a lifetime career choice, you will have to be able to do and understand how to use and apply algebra.
  9. 9. Every day life  Formulas are a part of our lives. Whether we drive a car and need to calculate the distance, or need to work out the volume in a milk container, algebraic formulas are used everyday without you even realizing it.
  10. 10. Data entry  What about the entering of any data. Your use of algebraic expressions and the use of equations will be like a corner stone when working with data entry. When working on the computer with spreadsheets you will need algebraic skills to enter, design and plan.
  11. 11. Interest Rates  How much can you earn on an annual basis with the correct interest rate. How will you know which company gives the best if you can't work out the graphs and understand the percentages. In today's life a good investment is imperative.
  12. 12. Algebra in day-to-day life  You use algebra all the time in real life. It might not happen to involve numbers, but the skills are still there. Say you get home from school one day and you can't find your key. How would you get into your house? You'd probably do some version of turning the problem around, maybe check the windows to see if you could get in that way, and maybe retrace your steps to see if you dropped your keys somewhere. Eventually, something would work out, and you'd figure out a way to get into your house.
  13. 13. Uses of algebra  Most of us use algebra every day - simple problems that we "do in our heads". For instance, say you have $20 and you go to the store. The store is having a "buy one and get one at half price" sale. How do you figure out what you can buy? There's an equation for that. Or, "how tall is that building?" If you know how far away it is, and the height of any one thing you have at hand, there's an equation for that.
  14. 14.  Like when we are playing games also we use algebra. Pointing from where to start and where to end.
  15. 15. Egyptian Algebra  Earliest finding from the Rhind Papyrus – written approx. 1650 B.C.  Solve algebra problems equivalent to linear equations and 1 unknown  Algebra was rhetorical – use of no symbols  Problems were stated and solved verbally  Cairo Papyrus (300 B.C.) – solve systems of 2 degree equations
  16. 16. Babylonian Algebra  Babylonians were more advanced than Egyptians  Like Egyptians, algebra was also rhetorical  Could solve quadratic equations  Method of solving problems was rhetorical, taught through examples  No explanations to findings were given  Recognized on positive rational numbers
  17. 17. Greek Algebra  The Greeks originally learned algebra from Egypt as indicated in their writings of the 6th century BCE. Later they learned Mesopotamian geometric algebra from the Persians. They studied number theory, beginning with Pythagoras (ca 500 BCE), continuing with Euclid (ca 300 BCE) and Nicomachus (ca 100 CE). The culmination of Greek algebra is the work of Diophantus in the 3rd century CE.
  18. 18. Syncopated Algebra  200 CE-1500 CE  Started with Diophantus who used syncopated algebra in his Arithmetica (250 CE) and lasted until 17th Century BCE.  However, in most parts of the world other than Greece and India, rhetorical algebra persisted for a longer period (in W. Europe until 15th Century CE).
  19. 19. Aryabhata & Brahmagupta  1st century CE from India  Developed a syncopated algebra  Ya stood for the main unknown and their words for colors stood for other unknowns
  20. 20. Abstract Algebra  In the 19th century algebra was no longer restricted to ordinary number systems. Algebra expanded to the study of algebraic structures such as:  Groups  Rings  Fields  Modules  Vector spaces
  21. 21. The permutations of Rubik’s Cube have a group structure; the group is a fundamental concept within abstract algebra.
  22. 22.  19th century  British mathematicians explored vectors, matrices, transformations, etc.  Galois (French, 1811-1832)  Developed the concept of a group (set of operations with a single operation which satisfies three axioms)  Cayley (British, 1821-1895)  Developed the algebra of matrices  Gibbs (American, 1839-1903)  Developed vectors in three dimensional space
  23. 23. Abhinav S. , Vaibhav S. , Saksham, Nishit .

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