The formal sciences can help you classify an otherwise chaotic universe by applying organization and language to complex systems of information.
There is so much information in the universe, and I would venture to say even just in our daily lives. But how do we organize it? For example, how am I creating this web page on the internet for you to read it? And how did you find it when there are so many others to choose from?
To put it simply, the formal sciences provide the means of working in these areas of complex systems of information. The formal sciences consist of accounting, actuarial science, computer science, mathematics, and programming. They provide languages that organize and characterize the systems, allowing us to communicate better with each other and with machines. Such formal languages make it easier to understand and work with complex information especially in systems involving math and logic. Thus, the field is extremely important in areas that apply math and logic, including computers, statistics, and even linguistics.
Having knowledge in the formal sciences allows you to properly describe your findings of the world.
You can then develop inferences about them, further test them, communicate them to others, or implement them in various fields. For instance, I use them to write web pages and determine factors that attract readers to the pages.
The formal sciences information I provide below will help you further understand the branches and meaning of the field.
What Are the Formal Sciences?
There are various types of science, and it’s important to know their differences. Before getting into the fields within formal sciences, I first want to emphasize the differences between pure science and formal science.
Science vs. Formal Science
I would venture to guess that pure science is the most familiar to most readers. It’s what we think of when we think about physics, biology, or chemistry. Pure science encompasses a method of observing and testing the natural world to discover truths about it.
A formal science, on the other hand, is a field that looks at formal systems, or those systems that are founded in logic. Unlike natural sciences wherein scholars study things to better understand them, scientists in the formal sciences design systems to categorize understanding.
This means that the field does not rely on empirical testing or evidence. Rather, it is based on definitions and axioms that deduce statements. Thus, statements in formal sciences are inherently true, also known as being analytic. This makes the formal sciences applicable and useful in all other fields of science.
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.
What Subjects Are Included in the Formal Sciences?
Within this category I go over several disciplines of formal sciences. These include mathematics, theoretical computer science, programming, accounting, and actuarial science. All of these schools of thought rely on the formation of language and systems to categorize their elements for study.
The formal sciences articles, books, and other information I detail here are split into five 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 I believe the formal sciences articles and books here help you master them.
What Does a Degree in the Formal Sciences Entail?
If you are thinking about getting a degree in the formal sciences, I think you should know that you will surely run into certain classes. Like any degree, you will start with a group of core classes that include various subjects.
These subjects will be both related and unrelated to the formal sciences. But the most important ones for the formal sciences are math and logic. So if you have the opportunity to select certain classes in these areas, I suggest you do some research to make sure you choose wisely.
You will then start to take classes that focus more on a specific area of formal sciences. Because the formal sciences help to classify information, you’ll need to learn about the information you’re classifying. For example, if your focus is accounting or actuarial sciences, expect to take business and finance classes. If you focus on computer science or programming, you’ll be learning a lot about computers and technology.
The Formal Sciences of Accounting
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.
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. Accountants, practitioners of the discipline, rely on their industry’s standard to perform analysis of financial information.
As a formal science, the articles I link here will show how accounting relies on formalized language and systems. Colloquially, accounting is the “language of business“. This is because accounting measures economic activities and interprets the information for multiple users.
From the breadth of topics I mentioned above, it surely won’t surprise you that 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.
Understanding it is critical to effectively measuring, processing, and communicating findings on finances of businesses. I aim to link material here that works on teaching this language of business 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.
Highly Rated Books and Courses on Accounting
If you’re new to the world of accounting and want to dip your toes in some warm water, I recommend Accounting Made Simple. It cuts out the technical jargon to ensure you steer clear of any confusion. Instead, you’ll dive straight into clear explanations of important accounting concepts. It’s an optimal text if you’re looking for something that’s not as long or complicated as typical academic texts. It covers the same topics as academic texts, but is shorter, cheaper, and assumes no prior knowledge of accounting.
If you have a specific interest in investing or small businesses, then one of the other two books I include here would be helpful. Warren Buffett Accounting focuses on the accounting of investing for beginners in the field based on the wildly successful investor Warren Buffet. Reviewers of the book even say that it is actually fun to read (I will admit that perhaps that is a bit rare for accounting books). It also has benefits outside of the text itself, namely an online forum filled with other investors and the authors themselves.
I also recommend Accounting for the Numberphobic if you’re involved in small business. It highlights the importance of proper accounting in growing your business while using simple terminology and methods.
Branching away from books, I am going to include some Udemy links to what I think are useful courses. The less passive nature of a course means you’ll be actively learning and applying knowledge, thus helping it stick. A good place to start is with the basics in Accounting & Financial Statement Analysis. Then you can move on to something with more material like Introduction to Finance, Accounting, Modeling and Valuation. Or if you prefer to get it all in one fell swoop, check out Accounting: From Beginner to Advanced.
Actuarial sciences aim to assess risk through the application of mathematical and statistical, methods. Many industries use this knowledge to ensure stability, particularly for financial purposes. However, insurance is one of the most common fields in this area. After all, nearly everyone has some type of insurance on themselves or their family.
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. These models help to create tables for analysis of different situations. This typically results in a chart used to determine premiums or costs for different institutions.
Training and Requirements
Actuaries themselves go through intense training and obtain certification through several in-depth professional exams. But computers also now play a role in making their jobs faster, so I would recommend getting comfortable with them.
Interestingly, this profession is a leader in both need and ingress of young actuaries with these types of new skills. 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.
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 I am confident it can also serve as a great introduction to the topic for people who are new to it.
Highly Rated Books and Courses on Actuarial Sciences
If you want something that will really hook you into a story, Against the Gods provides a uniquely engaging introduction to the topic of actuarial sciences. Reviews call it “fascinating” and “incredibly readable” due to its unique topics. In it, you’ll learn about the history of risk management and prediction in the context of compelling stories of the past.
On the less thrilling side, A Practical Guide to Risk Management focuses more on the critical tools that aid organizations in their financial strategies. It looks at both quantitative tools of the actuarial sciences as well as human tools such as wisdom and sound judgment. But if that text is a bit too advanced for you, then I recommend Financial Risk Management for Dummies. Not that you’re a dummy, but I firmly believe there’s no shame in admitting you’re not an expert yet! The award-winning author of this book ensures that the material is clear, easy-to-follow, and useful. You’ll find information on topics like financial risk, stop losses, hedge bets, set limits, and control drawdowns.
You’ll also find some of this introductory material in online courses. For beginners, I suggest both What does and actuary actually do? and Actuarial Science for Non-Actuaries. They will help you get familiar with the basics. Then, there are various courses like Actuarial Statistics to help you with more advanced concepts in the field.
The Importance of Computer Science in the Formal Sciences
In many ways, computers have become a lifeline for formalizing processes used to observe and study all kinds of phenomena.
I certainly rely on them for my work, as do many others. They have also 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 I provide here will help you understand this process and how to get involved in it yourself.
A fairly modern formal science in terms of its development of formal languages and systems, computer science is a quickly growing field. I link to articles on the history of this applied sciences here to help you 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 evolved, there are several fields within this branch of science. I will briefly outline these fields here: first, there is the theory itself, then computer systems and design, computer applications, and software development. Each of these areas consists of its own languages and utilizes or develops its own systems to ensure accuracy of effect.
Degrees, Careers, and More
I want to note that computer science is a readily available field in many nations across hundreds of universities. Additionally, I think you might appreciate that 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, I think it is safe to predict the 21st century will see a boom in training computer science professionals.
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.
Highly Rated Books and Courses on Computer Science
I know that getting a job in computer science can be tricky, especially when it comes to the demanding interviews. Interviewers will frequently ask tough questions or require on-the-spot coding using nothing but whiteboards. If you’ve never dealt with that kind of pressure before, you might feel overwhelmed. But Cracking the Coding Interview takes knowledge from the interviewer herself about these stressful interview requirements.
The book thoroughly covers 189 different questions and scenarios you might run into in the meeting room so that you’ll be prepared for anything. There’s also an online course called The Coding Interview Bootcamp, if that’s more your style.
If you’re not quite ready for a full-on interview, I would suggest starting with Computer Science Distilled. It goes over essential topics you would learn in a classroom, but without as much academic mumbo jumbo. In it, you’ll learn the basics of discrete math, algorithms, data structures, and programming languages.
Apart from pure career and academic advice, I also wanted to include something more relatable and personal. Algorithms to Live By draws connections between computers and characteristics that we think of as very human. It will help you understand computers and maybe even yourself a bit better.
And if you would prefer a more technical look at said algorithms, I have a couple courses to show you. Both Data Structures & Algorithms and Data Structure and Algorithms Analysis – Job Interview provide a thorough look at the subject. And the latter puts it in the context of a software engineer interview.
Speaking of Computers: The Formal Science of Programming
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 I link to here 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 weeks 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.
Additional Sources to Learn Programming
Anyone looking to get into computer science will also surely need to check out formal sciences books specifically on programming. I provide various books in this category on individual programming languages. Each language has its own benefits and quirks, so I think it’s always good to have at least a few under your belt.
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 create their own applications.
Highly Rated Books and Courses on Programming
You don’t have to be a master programmer of twenty different languages to make useful code. I selected Automate the Boring Stuff with Python because it shows that even beginners can use simple techniques without any experience to perform useful tasks. Searching for text, changing folders, downloading content, and other tasks will become a breeze once you read this book. And there is also a course in addition to the book! I suggest looking into both to see which fits your learning style.
Speaking of Python, you might be surprised when it comes to how much you can do with it. It’s a fairly simple and easy language to learn, but that doesn’t stop it from being powerful. I included Python Tricks The Book here to help you learn about all the hidden secrets of Python that can help you take your abilities to the next level.
But, of course, Python isn’t the only language out there. To be a truly skilled programmer does mean having experience with multiple languages. I recommend The Complete Software Developer’s Career Guide to help you learn whatever language that interests you and to turn your skills into a career. Two very useful languages that I recommend are C and C++. You can get started in either of them using the Udemy courses C Programming for Beginners and Beginning C++ Programming.
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 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 I provide here, 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. I will also cover 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.
I work hard to be thorough in all areas, but mathematics in particular has a special place in my heart. This is because I have a degree in the subject and taught college-level classes for years. It might make me a bit biased, but you can be confident that I know what I’m talking about!
Divisions of Math
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, I recommend checking out articles in the applied sciences category as well as those in the formal sciences.
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.
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 and articles I provide here are 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, that I wrote myself 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.
Highly Rated Books and Courses on Mathematics
Mathematics doesn’t have to be all about serious theories, proofs, and algorithms. What If? by the creator of the Webcomic XKCD highlights the fun and silly applications of math that I think can capture the imagination of people who might not have had interest in math before. It poses hypothetical questions in any area imaginable and shows how math can accurately answer them, no matter how absurd the proposition. Through math, you’ll learn about fire tornadoes, jetpacks, and speed-of-light baseball pitches.
The second book I include on this list also effortlessly hooks the reader’s interest. Fermat’s Enigma details a layered story behind the pursuit of the proof of Fermat’s Last Theorem. The elusive proof puzzled the smartest minds of the time for hundreds of years. But don’t worry about keeping up with the math itself in this one. It’s more about the story of discovery, and is written so that you don’t need to understand the numbers.
Similarly, Prime Obsession will introduce you to another of one of the most elusive proofs in history. It, too, includes many passages of what I consider a fascinating history of the Riemann Hypothesis. However, these stories also alternate with more in-depth analysis of mathematical properties ideas (which I personally also think is fascinating!).
I also have some courses to recommend that get more into mathematical methods and techniques. For example, you can learn pre-calculus, calculus, and trigonometry with various courses like Pre Calculus, Calculus, and Trigonometry and Become a Calculus 1 Master. There is also the course Master Discrete Mathematics that covers sets, logic, and more. All include practice problems so you can try out the material first hand.
Formal Sciences Frequency Asked Questions
For your most pressing questions, I have included this list of go-to answers that get straight to the point. The above article gives more details as well as additional resources for all of the topics, but this is a good place to start.
What subjects are included in the formal sciences?
The formal sciences help us work with and understand complex information, especially in systems that involve math and logic. Thus, formal sciences are most important in areas that apply math and logic, including computers, statistics, and even linguistics. The main areas I cover in higher detail here are accounting, actuarial science, computer science, programming, and mathematics.
What does a degree in the formal sciences entail?
A base in math and logic is extremely important for a degree in the field of formal sciences. Core classes will center on mathematics and logic. These topics will then extend into higher levels and start relating to other topics such as business, finance, and technology.
What is the difference between formal science and science?
Pure science is a method of studying and understanding the world around us. It builds knowledge through testing phenomena. Formal science, on the other hand, is a way of organizing and understanding systems of knowledge and information. It uses patterns and languages to characterize information in fields like mathematics, statistics, and computer science.
What jobs can you do with a degree in a formal science?
Because managing large amounts of information is a big part of the modern world, formal scientists are in high demand. Popular jobs include accountant, actuarial scientist, mathematician, professor, programmer, and computer scientist.
I hope it’s now clear that the formals sciences form a cornerstone of quantitative science. They are a unique way of applying math and logic to a wide variety of critical modern fields like computer science, business, and more.
The formal sciences information, articles, and books that I provided in this article are intended to help you get involved in these topics in the way that’s best for you. The online format allows easy access anytime, anywhere. And, I am sure that 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.
Remember, the formal sciences is only one of five main sections of material on you can find on this site. Other sections including applied sciences, humanities, natural sciences, and social sciences are also available to help build knowledge and skills in all areas.
If you’re unsure where to begin, I suggest starting off with something small. Read on of the linked articles here, or even watch a summary video on YouTube. Then you can decide if you want to go deeper with a book or even an academic course.
What information here surprised you most about the formal sciences? Have you already had some experience in the field?