Formal Sciences Articles

Programming Articles - Coding Program With Encryption Symbols


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 …

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Mathematics Articles - Scientist Adding Microscopy To Brain Study App


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 …

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Accounting Articles - Business concept. Business people discussing the charts and graphs showing the results of their successful teamwork

Accounting (Articles, Books, and Careers)

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 use the …

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Outstanding Actuarial Scientists

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 …

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Current Events in Accounting

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. …

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Confluence Relations

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  …

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Well-Founded Relations

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 …

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Equivalence Relations

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 $R$ …

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One-to-One Functions and Onto Functions

One-to-One Functions and Onto Functions

One-to-one and Onto Functions Injective Functions Definition. Let $X$ and $Y$ be sets. A function $f:X\to Y$ is called injective if  $$ \forall x_1,x_2\in X, f(x_1)=f(x_2)\implies x_1=x_2. $$ Theorem. Let $f:X\to Y$ be a function.  If $f$ is injective and $A\subseteq X$, then $f|_A$ is injective. Proof. Let $x_1, x_2\in A$.  Then  $$ f|_A(x_1)=f|_A(x_2)  \Longrightarrow …

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Set theory

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 …

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Strength in Numbers

Strength in Numbers (Book Review)

This review of the short book Strength in Numbers: An In-Depth Look at Actuarial Science for Math Enthusiasts by Chloe Hung summarizes the book and provides thoughts by a credentialed actuary. Learn what actuarial science is, what actuaries do, and why it all matters. Those interested in math or actuarial science will find something interesting in this book.

Actuarial Science History

Actuarial Science History (What Do Actuaries Do?)

The actuarial profession typically ranks high on lists of high-paying job. But what is an actuary, and what is actuarial science? This article provides a brief history of actuarial science and an introduction to the work of actuaries. From ancient shipping routes to modern securities trading, learn how actuarial science helps measure and manage risk.

Actuarial Science Journals

Actuarial Science Journals & Magazines (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 …

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Actuarial Societies and Organizations

Actuarial Societies and Organizations (Explained)

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 …

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Actuarial Science as a Profession

Actuarial Science as a Profession (Importance)

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 as a profession 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 …

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