Formal Sciences Inner Life of the Mind

Formal Sciences (The Definitive Guide For Students and Professionals)

Formal Sciences on Direct Knowledge

The formal sciences classify the otherwise chaotic universe through a principled methodology. This structure allows scientists to describe their findings of the world and develop inferences about them. Formal sciences is one of five main sections of material on Direct Knowledge. Other sections including applied sciences, humanities, natural sciences, and social sciences are also available to help build knowledge and skills in all areas. The formal sciences articles and books here on Direct Knowledge will help you understand the branches and meaning of formal sciences.

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Defining 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 of formal sciences. 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, the category of formal sciences articles and books contains the five further categories of accounting, actuarial science, computer science, math, and programming. There is one common trait joining these categories as part of the formal sciences: Each studies formal language that describes formal systems. Math, statistics, general logic, and other similar fields all need a formal language for us to work in and understand them. The formal sciences give us those languages, and the formal sciences articles and books here help you master them.

Computers and Formal Science

In many ways, computers have become a lifeline for formalizing processes used to observe and study all kinds of phenomena. They have made life in the 20th and 21st centuries much easier. With them, long and complicated calculations and tracking data can now be done automatically. In this way, computers are an intrinsic part of the study of natural sciences and the field of applied sciences. However, what goes into making computers and their programs are themselves formal sciences. The formal sciences articles and books here will help you understand this process and how to get involved in it yourself.


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, the articles here will show how accounting 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 another's 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 models to create tables for analysis of different situations. This typically results in a chart used to determine premiums or costs for different institutions.

Actuaries themselves go through a lot of intense training and obtain certification through several in-depth professional exams. But computers also 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.

Formal Sciences Php Programming Html Coding Cyberspace Concept

Computer Science

A fairly modern formal science in terms of its development of formal languages and systems, computer science is a quickly growing field. You can find articles on the history of this applied sciences on Direct Knowledge to get a better idea of how it all started. Put simply, the field 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, computer science is a readily available field in many nations across hundreds of universities. A career in the field is also quite lucrative. You can take a look at what it's like to work in the field by reading formal sciences articles on outstanding computer scientists. You'll see that 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 boom 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 web pages 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 to read articles on. You can learn a great deal from articles and then apply that knowledge in school and work in many areas. This is because 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.

Formal Sciences Senior women as math lecturer in university lecture hall

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.

In the applied sciences articles here on Direct Knowledge, you'll learn about history such as how calculation, counting, and measurement emerged from contemplative studies in mathematics. In using abstraction and logic, the field provided the foundation for numerous scientific discoveries. You'll also see how 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. If applied mathematics is more your speed, you may want to also check out articles in the applied sciences category as well as those in the formal sciences.

Formal Sciences Books - Math teacher drawing fuction graph on a blackboard during math class shallow DOF, color toned image

Using the Formal Science of Math in the Field

While mathematics is a type of formal science in its own right, there are various 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.

Behind the Cover of Formal Sciences Books

Unlike books in the natural sciences, the books in formal sciences won’t focus on studying the natural world to better understand it. Rather, these books study systems designed to categorize certain areas. They help scientists in other areas by giving them better ways to describe findings or develop inferences about them.


For example, accounting is often referred to as the “language of business”. Understanding it is critical to effectively measuring, processing, and communicating findings on finances of businesses. The financial accounting books on Direct Knowledge work on teaching this language and how to apply it in the field. Books such as Financial Accounting and Principles of Financial Accounting even include practice problems to reinforce the knowledge. Some books are designed specifically for beginners or students in college. Others are perfectly suited for experienced professionals just looking to learn something new or even brush up on the fundamentals.

Actuarial Science

Similar to accounting, actuarial science relies on the language of math and statistics. It also often focuses on the field of finance, but can play important roles in other areas such as insurance, natural hazards, and pensions. Formal sciences books in the area of actuarial science focus on minimizing risk through understanding a range of topics such as probability theory and economics. Risk Management for Enterprises and Individuals is somewhat of a one-size-fits-all when it comes to avoiding risk. It’s great for professionals with big decisions to make that affect many other people. But it can also serve as a great introduction to the topic for people who are new to it.

Computer Science

You won’t find a lot of really old formal sciences books in this category as computer science is relatively new. But that doesn’t stop it from being immensely popular and prolific. Computers are the way of the future (and the present), so understanding how to use them is critical for many. The field looks at developing programs that represent the interactions between processes and data by using algorithms. These processes allow us to make incredible computations and create intricate digital masterpieces. An Introduction to Web Development and Programming will give you an idea of how computer languages help create things like web pages and computer applications. Books such as this one introduce various tools to beginners. These tools let them follow along one step at a time in practicing their own web development.


Anyone looking to get into computer science will also surely need to check out formal sciences books specifically on programming. This category provides various books on individual programming languages. Each language has its own benefits and quirks, so it’s always good to have at least a few under your belt. Some of the most popular languages are Python, Java, JavaScript, and R. Books such as Think Python can give anyone a good introduction to the topic with hands-on exercises and challenges. Think Java offers the same opportunities for Java, and Eloquent JavaScript is there to help make sure you don’t get the two very different languages confused. There are also books that focus on the parts of languages that commonly cause problems for new students. Linear Regression Using R looks at data modeling in R and the specific tricks that can help you grasp the language.

These formal sciences books help students grasp the fundamentals of computer science to prepare them for more challenging concepts. They start with the math and algorithms that make the language run, so the student can then use the language. More advanced use of these concepts leads students to creating their own applications.


Potentially the most fundamental formal science, math plays a crucial role in all of the others listed here. It has been around for millennia in many cultures, modern and ancient. Some of the math we use today comes from these ancient cultures. But much of the math we used today has come from great refinement over time, especially in the past few centuries.

Math gives us various formal languages that help us identify and use patterns. The formal language it uses is made of numbers and symbols. These numbers and symbols allow for representing abstract concepts and logic itself. But getting to such abstract ideas can be tough if you don’t understand the language. Like any language, it can be tough to learn and require a large time commitment. But the formal sciences books here are often designed to help students struggling with the sometimes complicated concepts. They focus on certain tough areas and reinforce the ideas with practice problems, diagrams, and examples.

The series of Calculus 1, 2, and 3, provide a thorough guide through the topic. And, these books follow the common structure of college classes, making them great supplements for either school or independent study. Other math topics include Proofs, Intro to Number Theory, and Intro to Linear Algebra. Through them, you’ll learn the fundamentals of math as well as some of the ways they apply to practical situations.

An Informal Way to Learn Formal Sciences

The formal sciences articles and books here on Direct Knowledge give you a way to learn these topics in the way that’s best for you. The online format allows easy access anytime, anywhere. And, the practice problems and examples found in many of the books give you the chance to put your knowledge to the test, but all at your own pace.

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