Astrophysics is a branch of astronomy that involves the application of principles of physics and chemistry to explain the birth, life and death of stars, planets, galaxies, nebulae and other objects in the universe. It provides an understanding of the physical properties and dynamic behaviour of celestial bodies and phenomena, including relativity, quantum mechanics, stellar dynamics and evolution, and the big bang theory.
The Big Bang Theory is a scientific model that describes how the universe expanded from an extremely high-density and high-temperature state. It provides a comprehensive explanation covering various cosmic phenomena.
Compression refers to the process by which information or data is reduced in volume but can ultimately be reproduced in its original, full form. It can be applied in various fields like mathematics, physics, computer science, and engineering. The goal of compression is to reduce the redundancy in stored or communicated data, thus saving on storage space or data transmission capabilities.
Cosmology is the scientific study of the universe's origin, its structure, evolution, and eventual fate. This branch of astronomy involves theories of quantum mechanics, general relativity and emission data to construct a comprehensive explanation of the cosmos.
Cryptography is the science of encoding and decoding messages to keep these messages secure. It is an essential method for protecting information in computer systems.
Differential Equations are mathematical equations involving a function and its derivatives. They describe the relationship between a function and its rates of change and play a vital role in fields as diverse as physics, engineering, and biology.
Discrete math is a branch of mathematics that deals with distinct, often finite, sets. It includes a wide variety of topics such as logic, set theory, combinatorics, graph theory, and algorithms. Discrete math is foundational for computer science and information theory.
Fourier analysis studies how functions, signals, or data can be represented as sums or integrals of sinusoids. It provides tools like Fourier series and Fourier transforms to move between time/space and frequency domains, revealing periodic structure, spectral content, and enabling operations such as filtering, compression, and solving differential equations.
Fractions and decimals are two ways to represent parts of a whole and precise quantities between whole numbers. Fractions use a numerator and denominator to show how many parts of a partitioned whole are taken, while decimals use place value to the right of the decimal point (tenths, hundredths, thousandths, etc.). Understanding how to compare, convert between, and operate with fractions and decimals is foundational for arithmetic, percentages, ratios, measurement, and algebra.
Number operations are the foundational actions we perform on numbers—addition, subtraction, multiplication, and division. They allow us to combine, compare, and transform quantities. Mastering their meanings, properties (like commutative and distributive), and order of operations equips learners to work confidently across whole numbers, integers, fractions, decimals, and beyond.
Operators are rules or mappings that take one or more inputs from a set (often a vector space or a space of functions) and produce an output in a set, frequently the same set. They generalize familiar actions like addition, multiplication, differentiation, and matrix transformation. Studying operators involves understanding their domains and codomains, algebraic and analytic properties (such as linearity, boundedness, and invertibility), and how they compose, represent, and act on structures. Operators are foundational across algebra, analysis, and applied mathematics, linking ideas like eigenvalues, spectra, and transforms.
Physics is a branch of science that studies matter, its motion and behavior through space and time, and the related entities of energy and force. It is fundamental to understanding the natural world, and forms the foundation for other scientific disciplines including chemistry, biology, and astronomy.
Rational numbers are numbers that can be expressed as the ratio of two integers, where the denominator is not zero.