Atlas Textbooks Archives - Projeda

Scalars and Vectors

In this chapter, Scalars and Vectors, you will learn the difference between scalar and vector quantities in physics. In addition, you will learn how to identify the magnitude and direction of a vector. Contents Introduction There are many physical quantities […]

Vectors

Vectors (or Vector Quantities) are the combination of two scalars. (Two units, each only with a magnitude only.) Direction and Distance are two common scalars, that combine to form Direction, a vector. In order to describe any type of motion […]

The DOM

Since we have already touched on the formal theory of the DOM — Document Object Model — let’s dive into the Structural Anatomy and Lifecycle of the DOM Tree as it functions in a live browser environment. In our study […]

Identity Property

In a university-level study of the Field Axioms, the Identity Property defines the “existence of neutral elements.” These are the specific values within a set that, when applied to another number through an operation, leave that number unchanged. Every Field […]

Associative Property

In University Algebra and Trig Course, the Associative Property is the axiom that governs the “grouping” of elements within a single operation. While the Commutative Property tells us that order doesn’t matter, the Associative Property tells us that the placement […]

Distributive Property

The Distributive Property is the “bridge” axiom that links the two fundamental operations of a Field: Addition and Multiplication. It is the only axiom that describes how these two distinct operations interact with one another. Formal Definition The Distributive Property […]

Commutative Property

The Commutative Property is defined as a fundamental axiom of a Field, meaning that in mathematics where this property is applied, we can expect an identical result regardless of the sequence in which elements are combined. The “order-independence” of a […]

Real Numbers

Real Numbers (denoted by the symbol $\mathbb{R}$) are presented not just as a collection of points on a line, but as a specific algebraic structure: a Complete Ordered Field. While the Rational Numbers ($\mathbb{Q}$) allow us to perform basic arithmetic, […]

Field Axioms

The Field Axioms provide the definitive structural foundation for the number systems we use in Algebra and Trigonometry. While lower-level math focuses on how to perform calculations, higher-level algebra focuses on why those calculations are valid by defining the properties […]

Vertical Line Test

The Vertical Line Test is the geometric realization of the fundamental definition of a function. As you progress through your STEM track, you will find that the shift from seeing a “drawing” to seeing a “mapping” is critical for higher-level […]