Class notes on Basic Mathematics (Algebra), ISBN: 9781351965804
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Course
Engineering and Mathematics
Institution
Engineering And Mathematics
Book
Higher Engineering Mathematics
We focus on algebra expression, factorization, division, multiplication, addition and subtraction of algebra. Almost all topics of algebra are covered here.
HIGHER ENGINEERING MATHEMATICS 5TH EDITION JOHN BIRD SAMPLE OF WORKED SOLUTIONS TO EXERCISES
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Mathematics
Chapter 1: Algebraic expressions
Basic Mathematics
, Mathematics
Chapter 1: Algebraic expressions
The word Mathematics derives from the Greek µαϑηµα meaning
”knowledge, study, learning”. Mathematics involves the study of
quantity (number theory, measure theory), structure (algebra),
space (geometry) and change (analysis).
The origins of counting can be traced back 50000 years to the
neolithic age. The most ancient mathematical texts available are
from Mesopotamia and Egypt - Plimpton 322 (Babylonian c. 1900
BC), the Rhind Mathematical Papyrus (Egyptian c. 2000–1800
BC) and the Moscow Mathematical Papyrus (Egyptian c. 1890
BC). All of these texts mention the so-called Pythagorean triples
and so, by inference, the Pythagorean theorem, seems to be the
most ancient and widespread mathematical development after
basic arithmetic and geometry.
, Mathematics
Chapter 1: Algebraic expressions
The study of mathematics as a ”demonstrative discipline” begins
in the 6th century BC with the Pythagoreans, who coined the term
”mathematics”. Greek mathematics greatly refined the methods
(especially through the introduction of deductive reasoning and
mathematical rigour in proofs, laying the foundations for the
mathematics we know.
This is not the time and place to expand on the history of
mathematics. It has continued to for thousands of years. With the
arrival of computers, all kinds of mathematical techniques that
used to be of merely theoretical importance have acquired and
continue to acquire new and surprising applications. This is why
there is the catchphrase ”Mathematics - solving tomorrow’s
problems yesterday”.
An algebraic expression is a meaningful mathematical term
containing numbers, variables and the ordinary operations of
arithmetic.
Examples of algebraic expressions
2
3x, x = 2 + x1 , a − b2 √
4 , x − 7.
In this chapter, our aim is to learn how to manipulate and
transform algebraic expressions. This comes under the heading
”simplifying”, where an algebraic expression is simplified when it is
replaced it by an equivalent one that is shorter or easier to work
with.
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