Proportions and ratios

A serial dilution is a series of simple dilutions which amplifies the dilution factor quickly. The source of dilution material for each step comes from the diluted material of the previous step.

Serial dilution is used in biology, medicine, and the food industry to reduce the concentration of microorganisms or chemicals, or to measure the alcohol concentration.

Exponential function

Doctors routinely have to consider how long a medicine will stay in a patient’s body.  This will determine how often the patient needs to take their medication and for how long, in order to keep enough medicine in the patient’s body to work effectively, but without overdosing.

The amount of medicine in the body after taking a medication decreases exponentially over time and this is where the exponential function is indispensable.

Parabolas everywhere!

The parabola is a beautiful and elegant curve. The shape of a parabola is useful in a wide range of real world applications: cables on suspension bridges, flight of a projectile, design of mirrors/ torches, satellite dishes, and much more.

One equation – many realms!

It is fascinating how the same mathematical framework can describe phenomena and processes of very different nature, in diverse fields of science and engineering. Here, the same type of a differential equation models the behaviour of suspension in a car, a door damper, buckling of structural beams/columns, current in an electric circuit, a process in a chemical reactor, and many more seemingly unrelated quantities.

No maths – no banking!

The concept of interest rates is perhaps the most frequently used mathematical concept in banking and finance. Interest rate is simply the cost of money over a specific period of time. While the basic idea is simple, the maths can get complicated if the interest rate changes or the sum borrowed is paid back in instalments.

Maths in financial investments

Correlation (where changes in one variable tend to follow changes in another variable) is a very important mathematical concept in portfolio management and risk management. By reducing the correlation between returns from different funds or stocks (in other words choosing to invest in funds or stocks that do not follow the same patterns as each other in terms of the return on investment), investors can reduce the risk of losses from investments. 

Maths meets Computer Science

Machine learning is the scientific study of algorithms and statistical models that computer systems use to effectively perform a specific task without using explicit instructions, relying on patterns and inference instead. The big four maths disciplines that make up machine learning are linear algebra, probability theory, calculus, and statistics.

Cryptography is the science of using mathematics to encrypt or decrypt data. Cryptography allows you to store sensitive information or transmit it across insecure networks safely. Modern cryptography is heavily based on mathematical theory.

Graph theory & Computer Science

In mathematics, graphs are a way to formally represent a network, which is a collection of linked objects. In computer science, graphs are used to represent networks of communication, links structures of websites, data organization, computational devices, the flow of computation and more.