Trigonometric identities come in handy whenever trigonometric functions are involved in an equation or an expression. These identities are true for every value of variables occurring on both sides of an equation. Geometrically, they involve certain trigonometric functions (such as sine, cosine, and tangent) of one or more angles. Sine, cosine and tangent are known…

Here you will learn everything about Whole Numbers in arithmetic, starting from natural numbers and ending with operations on Whole Numbers. Also, see: Dedekind’s Theory of Real Numbers Natural numbers Natural numbers are regular numbers that we use to count objects or indicate the serial number of an object. For example, you can count the…

To define Supremum and Infimum in real analysis, we will have to define upper and lower bounds first. Upper and Lower Bounds A set $ A \subset \mathbb{R}$ of real numbers is bounded from above if there exists a real number $ a \in \mathbb{R}$ , called an upper bound of A, such that $…

What is a Function? A function is a relation such that no two distinct members have the same first coordinate in its graph. $ f$ is a function iff Notation for functions A function is usually defined as ordered-pairs, and $ \text{ordered pair } (x,y) \in \text{function } f$ so that $ xfy$ is (was)…

Set

What is a Set in Mathematics? A set is a well-defined collection of distinct objects. The theory of Set (now called the Set Theory), as a mathematical discipline, rose up with George Cantor, a German mathematician, when he was working on some problems in Trigonometric series and series of real numbers after he recognized the…

In geometry, we deal with different geometrical figures, and with the help of these geometrical figures, we can visualize the concept of the circumcenter. The circumcenter is the center of a special type of circle which is called the circumcircle. A circumcircle is a circle that passes through all the vertices of a polygon, most…

"What are Significant Figures?", "What are they used for?", "What is their significance?" Students often ask these questions because why would you want to identify significant numbers, if you can do mathematical calculations without them, right? Where the idea of using significant figures might come off as unnecessary, it is a crucial concept that you…

Finding the zero of a function is one of the most frequently encountered problems in basic and advanced algebra classes. These entities are the values of x where f(x) is equal to zero. As you progress and improve your solving skills for the zeroes of functions, you will encounter problems of varying complexity. You regularly…

Formulas are the most important part of mathematics and as we all know one is the backbone of the latter. Considering there are thousands of mathematical formulas to help people develop analytical approach and solve problems easily — there are some that go beyond. Some formulas aren’t just timesaving but those also do wonders. In…

Introduction In earlier parts we discussed the basics of integral equations and how they can be derived from ordinary differential equations. We also solved a linear integral equation using the trial method in the second part. Now we are in a situation from where the main job of solving Integral Equations can be started. But before we go…

Are you getting started with Functional Analysis? If you are, you must be looking for some of the most important definitions in Functional Analysis. In this article, I have summarized those. Functional Analysis Functional analysis is the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and…