Search free study notes

…tiny particles to massive galaxies, using observations and mathematical models. It helps us understand natural phenomena and build new technologies. You'll learn to apply fundamen…

…alled "operational" because they used to be used to perform mathematical operations in analog computers. You don't need to know the transistors and resistors making up an op-amp. W…

…er those actions. It allows you to describe these movements mathematically. A point on a 2D plane is uniquely identified by an ordered pair of numbers, $(x, y)$, where $x$ is the h…

…ognize, classify, and combine them. Think of polynomials as mathematical "words" made from "letters" (variables) and "numbers" (coefficients) joined by addition, subtraction, and m…

Linear equations in one variable are mathematical statements where you're finding the value that makes both sides equal. They follow the pattern ax + b = c, where you isolate x thr…

…mework. This review solidifies your foundation for advanced mathematics. Linear equations are the building blocks of mathematical relationships. Everything connects: slopes become…

Cryptography is about securing communication and data using mathematical techniques, primarily focusing on confidentiality, integrity, and authenticity. It uses algorithms with key…

…ants), variables (letters representing unknown values), and mathematical operations (addition, subtraction, multiplication, division). Unlike equations, expressions don't have an e…

…s. Mastering these methods will allow you to tackle complex mathematical models in engineering. Think of integration as the ultimate sum: you're adding up an infinite number of inf…

…e and a direction. We use vectors to represent these forces mathematically, allowing us to accurately describe and combine them. Understanding how forces act and how to represent t…

…J is a descendant of APL, known for its expressiveness and mathematical notation. It's often called a "tacit" or "point-free" language because you frequently operate on data witho…

…n't know yet. They're like placeholders. An expression is a mathematical phrase that can contain numbers, variables, and operations (like addition or subtraction). It doesn't have…

…py. When you enlarge a shape, you create a new shape that's mathematically similar to the original. This means that: All corresponding angles stay exactly the same. All correspondi…

…ion tests your numerical ability and how well you can solve mathematical problems. It covers topics like: Number System: Understanding different types of numbers (prime, even, odd)…

…hese ancient puzzles still spark debate and have influenced mathematics and philosophy for centuries. Imagine trying to reach a wall. Before you can reach it, you must first cover…

…different types of functions, and applying these to various mathematical problems. This topic forms the backbone for much of advanced mathematics, so a strong grasp here is essenti…

…t just gives the instructions. An algebraic expression is a mathematical phrase that can contain numbers, variables (like 'x' or 'y'), and operation signs (+, -, ×, ÷). Unlike an e…

…apes using numbers. It lets you translate visual ideas into mathematical equations and vice versa. Understanding this fundamental concept opens the door to analyzing graphs and sol…

…late. Your job is to translate those words into the correct mathematical operation. Photo by Katerina Holmes on Pexels You'll typically use HCF when a problem involves: Dividing th…

…describe and predict these actions precisely. Physics uses mathematical models to describe the rules governing the universe. In mechanics, we're particularly interested in how for…