Numbers and Sequences in Mathematics

An understanding of whole numbers is the essential and fundamental foundation of mathematics, and, along with the infinite sequence in which they are arranged, stored, and displayed, are vital to your understanding and ability in Mathematics.

The course starts off by discussing how large decimal numbers are written in the standard form or in scientific notation. You will learn how to convert from decimal format to the standard form and back again. You will also learn about working with indices or powers when they are negative, fractional, equal to 0, a set of natural numbers, and how to multiply and divide numbers with indices.

Next, you will be tought about patterns with imaginary numbers, what imaginary numbers are, and the definitions of rational, irrational, and prime 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 an 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 under which, proof by induction can be applied.

In the last module, you will learn about what complex numbers are and how to manipulating and use them in mathematics. You will learn about what an Argand diagram is and what the modulus is, along with the meaning of I, counting numbers, and imaginary numbers. You will learn how to convert complex numbers to the polar form and multiply and divide them in the polar form. Lastly, you will learn about proving De Moivre's Theorem, solving equations that have complex numbers, and find complex and cubed roots.