# Formal Sciences Articles

## Programming

Programming Articles In this category, you’ll find information about what is becoming a critical part of modern society: computer programming. So much technology relies on programming to function, making it a skill in high demand. Even elementary schools are beginning to teach the fundamentals of programming to kids! For the rest of us, it helps …

## Mathematics

Mathematics Articles Surprisingly, mathematics has no widely accepted definition. It has been defined in various ways for centuries, such as the science of quantity, logic, or intuition. A few main schools of thought exist today about how to formally define it, but let’s leave that for more in-depth mathematics articles. In a nutshell, you can …

## Computer Science

Computer Science Articles Computer science is the study of the processes that occur in computers where data transforms into programs that we can use. Through these programs, we can utilize information in digital form for communicating with each other, making calculations, and more. This field is particularly useful today given the huge increase in computer …

## Actuarial Science

Actuarial Science Articles Actuarial science is a formal mathematical discipline that uses primarily statistics to determine risk. Risk is important in long term financial industries such as insurance and pensions. In these areas, money is set aside for so long that any number of things could happen to it. Actuaries use a variety of mathematical …

## Accounting

Accounting Articles Accounting, also known as accountancy or financial reporting, is the management of economic information for entities such as businesses and corporations. This includes measuring, calculating, and communicating financial and non-financial information to keep track of how the organization is doing economically. The organization itself uses this information to optimize performance, but other entities …

## Outstanding Actuarial Scientists (10 Great Careers)

When you think about finance, you probably think about the stock market, banks or C-suite executives. However, there is a large part of the sector, particularly in the realm of insurance, that offers six-figure salaries and controls a lot of what consumers pay for financial services. Outstanding actuarial scientists use statistics to provide data on …

## Current Events in Accounting (5 Need-to-Knows)

To those out of the loop, accounting sounds boring and dry. For professionals, it’s an industry and field booming with opportunity. Numbers aren’t everyone’s favorite, and many struggle with math, let alone accounting processes. Accounting is the process of managing numbers in a variety of settings. Every sort of business or establishment needs an accountant. …

## Current Events in Mathematics (5 Need to Knows)

Current events in mathematics point to a growing field with a diversifying range of utilities and practices. The history of mathematics is an interesting dive into the past, present and future. It’s long been one of the most studied disciplines. In fact, it’s older than most other fields of study in general. To be fair, …

## Current Events in Programming (5 Must Reads)

To those who don’t “speak” the language, programming seems incomprehensible. If you’ve ever taken a course on HTML or Java, however, you know it’s all about the formula. Programming is a key component to our increasingly digital lives. In fact, without programming, we wouldn’t have a lot of the online resources we use today. Programming …

## Confluent Relations (using Reduction Relations)

We discuss confluent relations; in particular, we prove Newman’s Lemma: that local confluence, confluence, the Church-Rosser property, and the unique normal forms property are all equivalent for a well-founded relation. We also give a generalization of Newman’s lemma based on the Buchberger-Winkler’s Property. Reduction Relations Let $\longrightarrow$ be a relation on $X.$ If there exists  …

## Well-Founded Relations (and Well-Founded Induction)

Well-Founded induction is a generalization of mathematical induction. Well-Founded Induction Definition. Let $\longrightarrow$ be a relation on $X.$ 1) If $A\subseteq X$ and $a\in A,$ then $a$ is called a $\longrightarrow$-minimal element of $A$ if  there does not exist $b\in A$ such that $a\longrightarrow b.$ 2) If each nonempty subset of $X$ has a $\longrightarrow$-minimal …

## Partial Order Relations (Mappings on Ordered Sets)

We discuss many properties of ordered sets including Noetherian ordered sets and order ideals. We also detail monotone mappings and isomorphisms between ordered sets. Ordered Sets Throughout we assume $(X,\geq)$ is an ordered set.  By this we mean that $X$ is a set and that $\geq$ is binary relation on $X$ that is reflexive, antisymmetric, …

## Equivalence Relations (Properties and Closures)

Equivalence Relations We discuss the reflexive, symmetric, and transitive properties and their closures. The relationship between a partition of a set and an equivalence relation on a set is detailed. We then give the two most important examples of equivalence relations. Reflexive, Symmetric, and Transitive Relations Definition. Let $X$ be a set. A relation $R$ …

## Binary Relations (Types and Properties)

Let $X$ be a set and let $X\times X=\{(a,b): a,b \in X\}.$ A (binary) relation $R$ is a subset of $X\times X$. If $(a,b)\in R$, then we say $a$ is related to $b$ by $R$. It is possible to have both $(a,b)\in R$ and $(a,b’)\in R$ where $b’\neq b$; that is any element in $X$ could be related to …

## Composition of Functions and Inverse Functions

Composition Theorem. Let $f:X\to Y$ be a function. If $g:Y\to Z$ and $g\circ f$ is injective, then $f$ is injective. Proof. Let $x_1, x_2\in X$. Then $$f(x_1)=f(x_2) \Longrightarrow (g\circ f)(x_1)=(g\circ f)(x_2) \Longrightarrow x_1=x_2$$ shows that $f$ is injective. Theorem. Let $f:X\to Y$ be a function.  If $g:Y\to Z$ and $g\circ f$ is surjective, …

## Set Theory (Basic Theorems with Many Examples)

We discuss the basics of elementary set theory including set operations such as unions, intersections, complements, and Cartesian products. We also demonstrate how to work with families of sets. For a brief discussion of the reviews of (elementary) Halmos’ Naive Set Theory read this. A solid understanding of propositional and predicate logic is strongly recommended. To …

## Strength in Numbers (Book Review)

The book Strength in Numbers: An In-Depth Look at Actuarial Science for Math Enthusiasts by Chloe Hung, lays out the steps from being a math enthusiast to working as an actuary. We give a brief review of the book and thoughts from a credentialed actuary. In her short book Strength in Numbers: An In-Depth Look …

## Actuarial Science History (What Do Actuaries Do?)

The history of actuarial science has its roots in ancient times, when insurance was used to manage shipping risk. Today, actuarial science encompasses many fields such as probability theory, finance, and statistics. Actuaries work in the insurance and other industries to measure and manage financial risk. What is an Actuary? You may have seen actuary …

## 63 Actuarial Science Journals & Magazines (What Are the Differences?)

A list of about 60 actuarial science journals that actuaries may be interested in. These journals can be classified as either actuarial, insurance, or finance journals. Most of these journals are peer-reviewed and some of these journals are open access.  Actuary Magazine (The) Annals of Actuarial Science Applied Mathematical Finance ASTIN Bulletin Australian Actuarial Journal Australian Journal …

## 40 Actuarial Societies and Organizations (Which Is Right for You?)

Here is a comprehensive list of actuarial societies and organizations. Actuaries are remarkable professionals who generate solutions for complex financial issues. They regularly communicate their work to coworkers who are often uninformed of the necessary mathematics and training needed to answer their inquiries and formulate their analyses. For these reasons, actuaries are in high-demand. Through …

## The Importance of Actuarial Science as a Profession

Actuarial science is concerned with risk analysis and evaluation of possible risk mitigation strategies to cushion business from the risk associated with uncertainties in life. Actuarial science knowledge is useful in the assessment of risk. Insurance providers in the property, health and casualty sectors need experienced actuaries to determine insurance policy costs concerning the risks …

Scroll to Top