## Current Events in Mathematics

Mathematics is the study of numbers and their practicality in solving mysteries of the world. Current events in this subject help to uncover the true meaning of the study. Many who dislike math don’t truly understand what it accomplishes or aims to discover. By focusing on current events, students and professionals alike help to show why math is such a force in society.

## Notes on Diffy Qs: Differential Equations for Engineers

Do you see differential equations and think dreadful equations? This doesn’t have to be. Notes on Diffy Qs is an engineer’s guide to differential equations. The book is suited for engineering students taking their first course on “diffy Qs.” Differential

## Linear Regression Using R: An Introduction

Stuck writing linear regressions? Fret not. Linear Regression Using R: An Introduction to Data Modeling will take you back to basics. It is a textbook for beginners that explains how to work in this particular computer language. It takes a

## Outstanding Mathematicians (10 Phenomenal Careers)

Furthering math may seem like a daunting task to many; however, for these educators and researchers, that is literally the best part of the job. From solving theorems and proofs to putting math into real-life practice, mathematicians are important members

## Outstanding Computer Scientists (10 Unique Careers)

As vital members of the modern tech-based world, computer scientists design the programs and software we rely on daily. Perhaps you open Facebook once or twice daily. Maybe you use Google for research. Even if you simply own a computer-based

## Current Events in Computer Science

Computer science is an expanding field of study that involves several technological considerations. There are so many studies and research projects contributing to daily life each day. From work on supercomputers to mobile phones, find out how current events in computer science impact the world each day. Plus, explore the subject further in a meaningful way.

## What are the Formal Sciences?

Scholars discuss the formal sciences regularly in research, but too few people know the simple meaning of this branch of academia. Explore the fields of study in this subject and find out which disciplines fall under this umbrella. Also, explore why these branches hold great importance to society. What are the Formal Sciences?

## About Mathematics and Why It Is Essential

Mathematics uses numbers as a language to explore some of the world’s most complex theories and problems. Children in school associate math with difficulty or confusion. With proper study, the subject can become an exciting way to view the world. Read all about the topic and its many branches.

## Math Topics (A Condensed Guide to Mathematics)

No matter who you are, youâ€™ve probably had some math classes in your life. After all, math is an important subject not only for success in technical subject areas, but also for giving your mind a workout and making it

## Applied Mathematics Journals (Explained For You)

Applied mathematics bears many connections to various other fields within academic and professional life. Consequently, itâ€™s important to stay up-to-speed on the most recent theoretical and practical developments. Advancements in applied mathematics can affect everything from pharmaceutical research and development

## Implicit Differentiation (and Logarithmic Differentiation)

The procedure of implicit differentiation is outlined and many examples are given. Proofs of the derivative formulas for the inverse trigonometric functions are provided and several examples of using them are given. Also detailed is the logarithmic differentiation procedure which

## Calculus (Start Here) – Enter the World of Calculus

Welcome, calculus enthusiasts, and enthusiasts-to-be! This page is your introduction to the world of calculus. You may be studying it for the first time, or maybe for the first time since high school. You may be using it in your

## Chinese Remainder Theorem

This definitive guide covers proofs, examples, algorithms, applications, and history of the Chinese Remainder Theorem. It also includes links to additional resources such as online articles, courses, books, and tutors to help students learn from a variety of sources. Professionals can also use these resources to increase their knowledge of the field or help structure courses for their students.

## Propositional Logic (Truth Tables and Their Usage)

By a mathematical statement (or statement, or proposition) we mean  a declarative sentence that can be classified as either true or false, but not both. For example, the sentences $$1+3=4, \quad 1+3=5, \quad \text{July is not a month}$$ can be accepted

## Double Integrals and the Volume Under a Surface

The Volume Under a Surface Consider the rectangle given by $$R=[a,b]\times[c,d]=\{(x,y)\mid a\leq x\leq b, c\leq x\leq d\}.$$ We wish to construct a (regular) partition of $R.$ To do so, let  a=x_0 < x_1 < x_2 < \cdots <

## Differentiation Rules (with Examples)

Computing the limit of the difference quotient can be tedious and require ingenuity; fortunately for a large number of common functions there is a better way to compute the derivative. In this section, we detail the power rule and the

## Polynomial Congruences with Hensel’s Lifting Theorem

The idea behind solving polynomial congruence equations is that we can reduce a congruence equation to an equivalent system of congruence equations using prime factorization. We then 1) solve each equation modulo a prime number (by brute force), 2) use

## Euler’s Totient Function and Euler’s Theorem

We prove several properties of Euler’s Totient Function and give many examples. We also discuss solving functional equations and reduced residue systems. One of Euler’s most important theorems is then demonstrated and proven. Introduction to Euler’s Totient Function Definition. For

## Congruence Theorems (and Their Proofs)

We discuss congruence theorems on the integers by proving several elementary lemmas. Modular arithmetic and least positive residues is also discussed. Introduction to Congruence Theorems A modern treatment of congruences was introduced by Carl Friedrich Gauss. Congruence, or modular arithmetic,

## Inner Products and Orthonormal Bases

Recall that the norm of $x\in \mathbb{R}^n$ defined by $\left|\left |x\right|\right | = \sqrt{x_1^2+x_2^2}$ is not linear. To injective linearity into the discussion we introduce the dot product: for $x,y\in \mathbb{R}^n$ the dot product of $x$ and $y$ is defined

## Diagonalization of a Matrix (with Examples)

An $n\times n$ matrix $A$ is called diagonalizable if $A$ is similar to some diagonal matrix $D.$ If the matrix of a linear transformation $T$ with respect to some basis is diagonal then we call $T$ diagonalizable. Diagonalization Theorem Theorem.

## Limits (Calculus Starts with Limits)

Limits are used to study the behavior of quantities under a process of change. For example, limits can be used to describe the behavior of a function on its domain. Here we study one-sided limits and two-sided limits with emphasis

## Fundamental Theorem of Calculus

We being by reviewing the Intermediate Value Theorem and the Extreme Value Theorem both of which are needed later when studying the Fundamental Theorem of Calculus. The Mean Value Theorem for Integrals and the first and second forms of the

## Derivative Definition (The Derivative as a Function)

We begin with the definition of the derivative as a limit of a difference quotient. We then give several examples of how to find the derivative of a function using this definition. Finding an equation of the tangent line is