It is very useful for everyone who is having some doubts and want to use in competitions

2. Content
 What Is Algebra ?
 Why Algebra is important in your life ?
 History of Algebra

3. 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.

4.  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).

5.  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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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.

14. 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.

15.  Like when we are playing games also
we use algebra. Pointing from where to
start and where to end.

17. 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

18. 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

19. 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.

20. 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).

21. 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

22. 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

23. The permutations of Rubik’s Cube have a group
structure; the group is a fundamental concept
within abstract algebra.

24.  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

25. Abhinav S. , Vaibhav S. , Saksham,
Nishit .