Numbers and Sequences in Mathematics  Revised
Gain an understanding of how numbers are arranged, stored, displayed and used in Mathematics.
Description
An understanding of Numbers is the essential and fundamental foundation of mathematics, along with the sequences in which they are arranged, stored and displayed are vital to your understanding and ability in Mathematics.
The course starts of be discussing large decimal numbers been written in the standard form or scientific notation. Teaching you how to convert form decimal format to the standard form and back again. You will learn about working with indices or powers, when they are negative, fractional, equal to 0, and how to multiply and divide numbers with indices.
Next you will be thought about patterns with imaginary numbers detailing what imaginary numbers are following on by an explanation of what is rational and irrational numbers. Then you are introduced to the mathematical concept of proof by contradiction, how to find cubed roots, along with how to change the base of a logarithm and work out a logarithmic equation.
The second half of module two will introduce you to the limit of sequences in mathematics, taking you through and example. After which you will learn about an arithmetic series and a geometric series and the formula for both of them. You will learn about deriving an amortisation formula from a geometric series, and about four different circumstances proof by induction can be applied.
In the last module you will learn about what complex numbers are and how to manipulating and used the in mathematics. You will learn about what an Argand diagram is and what the modulus is, along with the meaning of I and imaginary numbers. You will learn how to convert complex numbers to the polar form and multiply and divide in the polar form. Lastly you will learn about proving De Moivre’s Theore, solving equations that have complex numbers, and find complex and cubed roots.
Start Course NowModules
Numbers Part 1

Numbers Part 1  Learning Outcomes

Large Numbers in Standard Form

Changing Decimals to Standard Form

Changing Large Numbers from Standard Form

Changing Small Numbers from Standard Form

Adding and Multiplying Simple Powers

Working with Indices

Negative Indices

Fractional Indices, Numerator of 1

Index Power Equal to 0

Positive Fractional Indices All Types

Negative Fractional Indices

Writing Index Numbers as a Power of 2

Quadratic Number Patterns

Numbers Part 1  Lesson Summary
Numbers Part 2

Numbers Part 2  Learning Outcomes

Patterns with Imaginary Numbers

Rational or Irrational

Proof by Contradiction – Root 2 is Irrational

Finding the Cube Roots of 8

Changing the Base of a Logarithm

Logarithmic Equations

Limit of Sequences

Arithmetic Series

Geometric Series

Infinite Geometric Series  Part 1

Infinite Geometric Series  Part 2

Deriving Amortisation Formula from Geometric Series

Proof by Induction – The Sum of the First N Natural Numbers

Proof by Induction Applied to a Geometric Series

Further Proof by Induction – Multiples of 3

Further Proof by Induction – Factorials and Powers

Numbers Part 2  Lesson Summary
Complex Numbers

Complex Numbers  Learning Outcomes

Manipulating Complex Numbers and The Complex Conjugate

The Argand Diagram and Modulus

The Meaning of i

Patterns with Imaginary Numbers

Writing Complex Numbers in Polar Form

Multiplying and Dividing in Polar Form (Proof)

Multiplying and Dividing in Polar Form (Example)

Proof of De Moivre’s Theorem

Complex Numbers When Solving Quadratic Equations

Cubic Equations with Complex Roots

Finding the Cube Roots of 8

Complex Numbers  Lesson Summary
Course assessment
Learning Outcomes
Having completed this course students will be able to:
 Identify how to write large numbers in the standard form or scientific notation
 Discuss how to you multiply and add power of numbers(indices)
 Define a quadratic number pattern, calculate and equation for a quadratic number pattern
 Define what imaginary numbers, rational and irrational numbers are.
 Discuss proof by contradiction
 Identify how to change the base of a logarithm
 Discuss the concept of a limit in mathematics
 Define what both an Arithmetic series and a Geometric series are
 Recognize how to derive the amortisation formula from a geometric series
 Recognize how to manipulate complex numbers and the algebra of complex numbers
 Recognize how to write complex numbers in polar form
 Identify how to multiply and divide complex number in the polar form
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
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