Algebra

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18 videos in this playlist

Mathematical Language
This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
Powers or Indices
A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules…
Logarithms
Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by…
Substitution and Formulae
In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can…
Expanding and Removing Brackets
In this unit we see how to expand an expression containing brackets. By this we mean to rewrite the expression in an equivalent form without any brackets in. Fluency with…
Pascal's Triangle and the Binomial Theorem
A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a…
Factorising Quadratics
An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used…
Transposition of Formulae
It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This unit explains the procedure for doing this.
Linear Equations in One Variable
In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we…
Completing the Square
In this unit we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number…
Completing the Square (max, min)
Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum…
Quadratic Equations
This unit is about the solution of quadratic equations. These take the form ax^2+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square,…
Simultaneous Linear Equations
The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the…
Solving Inequalities
Inequalities are mathematical expressions involving the symbols >, <, >= and <= . To 'solve' an inequality means to find a range, or ranges, of values that an unknown x…
Cubic Equations
All cubic equations have either one real root, or three real roots. In this unit we explore why this is so.
Simplifying Fractions
The ability to simplify fractions and to write them in equivalent forms is an essential mathematical skill required of all engineers and physical scientists. This unit explains how these processes…
Polynomial Division
In order to simplify certain sorts of algebraic fraction we need a process known as polynomial division. This unit describes this process.
Partial Fractions
After reading this text, and/or viewing the video tutorial on this topic, you should be able to: * explain the meaning of the terms 'proper fraction' and 'improper fraction' *…

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The Joy of Higher Algebra
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This lecture shows how to solve quadratic (second-degree) equations from the technique of completing the square and the quadratic formula. The quadratic formula reveals the connection between Fibonacci numbers and the golden ratio.
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Making Use of Linear Equations
Episode 11 of Geometry
Delve deeper into the connections between algebra and geometry by looking at lines and their equations. Use the three basic assumptions from previous lectures to prove that parallel lines have the same slope and to calculate the shortest distance between a point and a line.