STEEMIT MATH CLASS | LESSON 1 - INTRODUCING ALGEBRA.

Hello Everyone, you are welcome to Steemit Math Class with @whileponderin. Mathematics has been one of the most misunderstood and feared subjects by student all over the world. This unfortunate situation can be traced to the lack of the right approach by most maths teachers. Some, unintentionally make the education process so tough and confusing that they end up scaring the students away.

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This series, termed Steemit Math Class aims at developing a global solution to this problem by running a refresher-course that will cover all the maths topics we have learnt in high school and the first two years in tertiary institution. Considering that several science courses are based on some topics we call "math's building blocks" I will be handle those topics first, as they will be the blocks upon which we will handle the complex ones.

This week, we will be discussing about Algebra.

ALGEBRA

Algebra is a very broad topic in Mathematics. It is the branch of mathematics which represents every mathematical problem as a mathematical expression.

Example 1:

Take for instance, you are given a word problem, that says "Jane went to the market and bought 10 oranges. On her way home, she met her neighbor, Linda, who gifted her 3 more oranges. How many oranges does Linda have in total?".

Now, the branch of mathematics that decodes this problem, and transcribe it such that it now has mathematical operators such as addition, substraction, division, multiplication signs, and so forth, as well as constants and variables is called Algebra.

For the problem mentioned above, Algebra transcribes it to:

10 oranges + 3 Oranges

Assuming we decide to represent Oranges with a variable "a", then the expression becomes:

10a + 3a

Notice that I have not added an equality sign. The difference between Expressions and Equations is the equality sign "=". Therefore, the above expression can be solved by converting it to an equation.

10a + 3a = 13a.

Remember that "a" stands for Oranges, therefore the solution to Example 1 is 13 Oranges.

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Characteristics Of Algebra Equation

Apart from word problems, Algebra can be applied to other branches of mathematics such as Trigonometry, Calculus, coordinate geometry e.t.c. In all, you must always remember than an algebraic equation must have three things.

1. Constant(s): A constant is a number that doesn't change, e.g 1, 2, 3, e.t.c.

2. Variable(s): As the name implies, these variables can assume any value depending on the situation. The are not numbers, rather they are normally represented by letters of the alphabet e.g a, b, c, x, y, e.t.c.

3. Mathematical Operation signs: You must see a plus, or (and) minus, or division, or multiplication, as well as an equation sign.

Example 2: For instance, given an algebraic equation

3x - 6 = 12.

In the equation above,

3, 6 and 12 are constants (as they can't change).

x is a variable and can adapt to any value depending on the situation. i.e it can be 1, 2, 3 etc. we can't tell for sure yet.

Finally, an Equation sign (=) which makes the algebraic problem an equation.

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Difference between Constant and Coefficient.

All coefficients are constant, but not all constant are coefficient. Coefficient are basically those constants found in the front of a variable. Take for instance in the equation given below:

3x - 6 = 12

Although 3, 6 and 12 are constants (as they don't change), only 3 is a coefficient, as it is the only one found in front of a variable (in this case "x"). x is the variable in this equation because we don't know it's value, therefore the constant (3) in front of it is referred to as it's coefficient.

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Classification of Algebra

Algebra are of different levels and complexities. Depending on the complexity, Algebra can be classified into various branches as shown below.

1. Pre-algebra: This branch of algebra involves the transformation process, of turning a word problem to an algebraic expression.

2. Elementary Algebra: In this part of algebra, you are expected to solve the algebraic expression. It is in this branch that the algebraic expression is converted to an algebraic equation for solving. Now, depending on the powers/index of the variable that makes up the algebraic equation, the equation can be a linear equations, or a quadratic equations, or simply polynomials.

Example 3: An algebraic equation of this format: 2x + 3 = 4 or 5x + 7y + 9 = 0 are linear equations. They are linear because the highest power or index of the two variables "x and y" in the equation is 1.

Example 4: If the algebraic equation is of this format: 5x^2 + 6x + c = 0, where x is a variable, and the highest power of the variable x in the whole equation is just "2", then the algebraic equation is called a Quadratic Equation.

Example 5: If on the other hand, the highest power in the algebraic equation is greater than 2, (i.e 3 and above) then the algebraic equation is called a polynomial.

x^n + 4x^(n-1)+ 5x^(n-2)+ .....7= 0.

Where n > 2.

Note, when n = 3, it is called a cubic equation.

1. Abstract Algebra: This branch of algebra basically makes use of the ring and group theories, and talks about abstract concepts like groups, ring e.t.c.

2. Universal Algebra: Under this category, we have all the other forms of algebraic problems such as calculus, Trigonometry and coordinate geometry.

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Some topics we will be discussing under Algebra

Some topics we will be discussing under Algebra includes,

1. Solving Algebraic Equation:- In this section, we will discuss how to solve for the variables found in the Linear, Quadratic and Polynomial Equations.

2. Sequences and Series:- Another Interesting topic, Sequence is a set of numbers that have a common mathematical relationship amongst them. This means that you can derive one from the other. Series on the other hand is a sum of the terms in a sequence. Series can be finite and infinite. While the progression can be arithmetic or geometric. We will discuss this more in the Sequence and series class.

3. Exponents and Logarithm: Exponents are most times used to simplify algebra, whil the inverse function to exponents in Algebra is Logarithm.

4. Sets: The main purpose of a set is to organize related Objects into a group, and to achieve this, algebra is needed.

But before we go into that, its vital that you remember these basic Rules and Properties of Algebra.

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Rules / Properties of Algebra

Below are some of the rules of Algebra you should bear in mind. Where x, y and z are all variables.

1. Commutative Property (Addition): x + y = y + x

2. Commutative Property (Multiplication): x × y = y × z

3. Associative Property (Addition): x + (y + z) = (x + y) + z

4. Associative Property (Multiplication): x × (y × z) = (x × y) × z

5. Distributive Property: x × (y + z) = (x × y) + (x × z), or it can be, x × (y - z) = (x × y) - (x × z)

6. Reciprocal: The reciprocal of x = 1/x

7. Additive Identity Property: x + 0 = 0 + x = x

8. Multiplicative Identity Property: x × 1 = 1 × x = x

9. Additive Inverse: x + (-x) = 0

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IN SUMMARY

In this post, we have been able, to introduce, Algebra, define algebraic expression and Equation as well as the branches of Algebra. We also listed out the Rules and Properties of algebra as well as several section in the mathematics where Algebra can be applied. In the coming sub-lessons, we will be discussing each of these sections one after the other. So, stay tuned to this blog. To check your progress for this lesson, try out these activities.

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ACTIVITY

1. What's the difference between Algebraic Expression and Algebraic Equation?

2. What's the difference between a coefficent and a constant?

3. In the equation "2x +3 = 0." Which of the values is a coefficient?

4. A man bought 8 pens and 5 note books. He spent a total of $10 in the process. Represent this as an Algebraic Expression and as an Algebraic Equation.

INTERESTING SCIENCE FACT: Did You know that...

A sneeze travels at 161 kilometres (100 miles) per hour.

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I hope you found this class informative. This was sponsored by Recipe Checklist and Wealth Rector, See you next time

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