Numbers and Sequences in Mathematics | Alison

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Numbers and Sequences in Mathematics - Revised

Gain an understanding of how numbers are arranged, stored, displayed and used in Mathematics.

Series and Sequences
Free Course
This free online mathematics course will teach you about numbers and their sequences. Numbers, the foundation of mathematics, can be simple or complex. This course will cover important mathematical topics about numbers, from writing them in scientific notation and multiplying powers, to imaginary numbers and irrational numbers. Start this free online course today and give your mathematical skills a solid boost in no time at all.
  • Duration

    3-4 Hours
  • Certification

  • Responsive

  • Publisher

  • Accreditation






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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.

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Numbers Part 1

Numbers Part 2

Complex Numbers

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


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