Formal Sciences

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Green's Theorem
Formal Sciences

Green’s Theorem

Green’s Theorem for Simple Connected Regions Theorem. (Green’s Theorem) Let $R$ be a simply connected region with a piecewise smooth boundary curve $C$ oriented counterclockwise

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Formal Sciences

A field that looks at formal systems, or those that are founded in logic and hold principles for understanding, is considered a formal science. Unlike natural sciences, wherein scholars study things to better understanding them, scientists in these fields design systems to categorize understanding. In other words, they formalize the otherwise chaotic universe through a principled methodology.

The formal sciences develop formal languages for logical, mathematical and theoretical systems. As such, they exhibit key traits as tools that aid other fields of scholarship, such as the natural and social sciences, through the provision of structure. This structure allows scientists to better describe their findings of the world and develop inferences about them.

Within this category are several disciplines. These include mathematics, theoretical computer science, theoretical linguistics, and theories for games, systems and decisions. All of these schools of thought rely on the formation of language and systems to categorize their elements for study.

At Direct Knowledge, we consider accounting, actuarial sciences, computer science, mathematics and programming within this category. Each of these fields holds clear academic and professional value in need of exploration.

Computers and Formal Science

In many ways, computers have become a lifeline for formalizing processes. They have made life in the 20th and 21st centuries much easier. However, what goes into making computers and their programs are themselves formal sciences.

Computer Science

A fairly modern formal science in terms of its development of formal languages and systems, computer science is a quickly growing field. It develops programs that represent how processes and data interact through the use of algorithms. These algorithms are capable of manipulating, storing and showing digital material. As such, the computations required to develop these algorithms are reliant on computers and computer-based programs.

Computer scientists not only study the theories involved in designing computers and programs but also the actual development and design of various software systems. Because of the extraordinary pace at which computers have been developed and evolved, there are several fields within this branch of science. Briefly, there is the theory itself, computer systems and design (e.g., computer engineering), computer applications (e.g., graphics and artificial intelligence), and software development. Each of these areas consists of their own languages and utilize (or develop) their own systems to ensure accuracy of effect.

Of note, studying computer science is a readily available field in many nations across hundreds of universities. A career in the field is also quite lucrative. All types of industries rely on computers and people who understand how they work. Moreover, numerous sectors are contingent on the use and development of programs to make them more lucrative. As such, it is safe to predict the 21st century will see a boon in training computer science professionals.


Programming builds upon computer science through the creation of computer applications and software. Within the field, programmers design elements, like webpages or usable applications, that rely on various “computer” languages. However, these languages are executed with a general purpose in mind. Their central goal is to provide the written content for programs and software in a wide variety of application domains. Thus, it provides users a means through which to communicate a set of instructions to the computer. Most of us know this as “code.”

As a formal science, programming is one of the most practical. Programs rely on formalized languages that are used within a formal system. As such, the codes are more or less universal and highly applicable and attainable. Nonetheless, working within the field requires a great deal of study and practice. Basic programming courses can take an entire semester to teach students how to instruct a computer to read “hello world” through a specific code.

Because of its clear link to computer science, programming is a quickly growing field. The emphasis on designing applications that intertwine with human-interface and artificial intelligence technologies identify it as a premier industry for growth.

Mathematics as a Formal Science

Believed to have emerged in several ancient cultures simultaneously, the study of mathematics is broad and foundational in numerous societies. In short, this formal science devised several formalized languages in systems to identify and utilize patterns that can resolve conjectures. Through discussion of and discovery within topics like change, quantity, space and structure, mathematicians model concrete, or real, phenomena to offer insight into “why” and “how.” This data also enables predictions about said phenomena, making the science highly applicable in other fields, like natural science.

Calculation, counting and measurement emerged from contemplative studies in mathematics. In using abstraction and logic, the field provided the foundation for numerous scientific discoveries. Mathematics is essential to studies within several other fields, principally engineering, finance, medicine, and the natural and social sciences. For any field using quantifying studies, mathematics is necessary.

Of note, this field is broken down into two key areas of study: applied and pure mathematics. Applied math is more recent in its evolution and is used as an application of mathematical principles. Statistics and game theory are examples of this category. Pure mathematics, on the other hand, engages simply in doing math to further the discipline. Those who participate in this field simply wish to discover more about math concepts themselves without necessarily feeling complied to apply it elsewhere.

Using the Formal Science of Math in the Field

While mathematics is its own type of formal science in its own right, there are ways in which it is applied. These systems create formal systems relying on the language of math, at least initially, to explain other phenomena. Particularly within economics, finance, business and insurance, math plays a large role in developing these other branches.


Accounting is the science of financial information and economics. It measures, processes and communicates findings on finances, and it is usually most relevant within the world of business. However, as a field, it is useful to both personal and large-scale financiers alike in order to quantify profits and losses and make predictions related to economic health.

As a formal science, it relies on formalized language and systems. Colloquially, accounting is the “language of business” because it measures economic activities and interprets the information for multiple users. There are a variety of systems within the field. Accountants, practitioners of the discipline, rely on their industry’s standard to perform analysis of financial information.

Within the field, there are several professions. Whether operating to review finances, manage budgets, predict economic upswings and downturns, devise accounting systems, audit financiers or simply “keep the books”, professionals in accounting are trained in the language and systems of their trade. As such, scholarship in the academic arena is widespread and varies greatly between nations and organizational classifications. Nonetheless, because of the clear-cut formalities within the science as a whole, scholars are able to build from one anothers’ findings to further the field.

Actuarial Sciences

Insurance workers are perhaps the most easily recognizable actuaries because their field is premier within this category. Actuarial sciences aim to assess risk through the application of mathematical, namely statistical, methods. Numerous industries use this knowledge to ensure stability, particularly for financial purposes. However, insurance is one of the most common fields as nearly everyone has some type of insurance for him or herself.

From a disciplinary approach, this formal science incorporates the use of interrelated finance-oriented subjects. These include probability theory, statistics, economics and computer sciences. Through the application of these theories and practices, actuarial sciences develop and rely on deterministic models to create tables for analysis of different situations. This typically results in a chart used to determine premiums, or costs, for different institutions.

While actuaries themselves go through a lot of intense training and obtain certification through several in-depth professional exams, computers now play a role in making their jobs faster. Interestingly, this profession is a leader in both need and ingress of young actuaries. Of note, the incorporation of computer science into the field is fairly recent (since about the 1980s). As a budding element within the field, it is critical to follow developments that enhance the effectiveness and accuracy of actuarial science.

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