What is Finite Mathematics?

This Fascinating Field of Study Focuses on Math Concepts in the Finite Universe and Has Tremendous Real-World Applications.

Math can be a challenging subject, especially at the college level, but it can also be incredibly rewarding as the subject has practical applications that are useful in essentially every career path imaginable. This post will explore Finite Mathematics, what it entails, how difficult it is, and how it differs from calculus.

What is Finite Mathematics?

Finite Mathematics is an extremely interesting branch of math that primarily deals with concepts applicable to the finite (as opposed to infinite) universe. Despite its technical name, finite mathematics is primarily concerned with applying mathematics problem-solving and reasoning to real-world phenomena, making it a critical area of knowledge for students pursuing careers in business, social sciences, computer science, and other practical career disciplines.

Typical Finite Mathematics courses will cover any or all of the following math topics:

Linear algebra: This topic focuses on vectors, vector spaces, linear transformations, and systems of linear equations. Linear algebra is integral to various fields of study ranging from business economics to applied physics.
Set theory: This topic focuses on the study of sets, or collections of distinct numbers/objects. Set theory serves as a key foundation to several branches of mathematics.
Combinatorics: This topic is the study of counting, arrangement, and combination of numbers/objects including permutations, combinations, and counting principles.
Probability: This topic focuses on the analysis of uncertainty and random occurrences. The study of probability is a cornerstone of statistics.
Graph theory: This topic focuses on the exploration of graphs and is highly applicable in computer science, where data structures are often represented in graphical form.
Logic: While more abstract, this topic focuses on formalizing mathematical statements and investigating their validity in a mathematical/systematic way.
Matrix algebra: This topic focuses on the study of matrices and their algebraic properties. Matrix algebra is closely tied to linear algebra.
Finite calculus or difference equations: This topic focuses on discrete change, such as sequences and series. Finite calculus is often a precursor to calculus, which deals with the infinite universe.

Before moving on, it is worth noting that not all Finite Mathematics courses or textbooks will cover all these topics.

Is Finite Mathematics Hard?

As with any math course, the difficulty level of Finite Mathematics varies from student to student. Since Finite Mathematics relies heavily on logical reasoning, critical thinking, and the application of math formulas and algorithms, the difficulty is often directly related to how well you understand these related topics. If these areas are your strengths, you will likely find Finite Mathematics appropriately challenging for you (i.e. not too hard and not too easy).

Still, Finite Mathematics can be tricky at times even if you are proficient in logical reasoning, critical thinking, and the application of math formulas and algorithms. Why? Because, as previously mentioned, Finite Mathematics courses often cover a diverse range of topics that require students to be proficient in a variety of math skills and concepts.

However, with the right attitude and approach, most students can be successful in Finite Mathematics and you are likely to struggle much less than you would in a typical Calculus course. In any case, it is always important to remember that, when it comes to mathematics, once you understand the basic principles, more complex ideas become easier for you to grasp.

Finite Mathematics vs. Calculus

So, what is the difference between Finite Mathematics and calculus?

The main difference between Finite Mathematics and calculus is the subject of infinity. Finite Mathematics restricts itself to finite sets, meaning that it does not explore the concept of infinity or infinite sets. On the other hand, calculus delves into the concept of infinity to describe continuous change.

In essence, Calculus takes the study of Finite Mathematics to the next level, which is why it is typically considered to be a more complex and challenging field of mathematics.

Because calculus is more complex than Finite Mathematics, it is often divided two sections: differential calculus and integral calculus. The topics covered in calculus are fundamental to physics, engineering, and economics, among other fields.

In contrast, Finite Mathematics focuses on discrete phenomena related to the finite universe of numbers. Unlike calculus, which focuses on exploring and describing smooth and continuous change, Finite Mathematics excels at analyzing distinct elements and systems that are countable and often rooted in real-world scenarios and data. As such, the topics covered in finite mathematics are often applicable to computer science, statistics, and operations research.

Despite these differences, Finite Mathematics and calculus share a very strong common foundation rooted in the exploration and application of logic and mathematical reasoning.

Conclusion: Finite Mathematics

In conclusion, whether or not Finite Mathematics is the right math course for you depends on your math skill level, personal interests, career aspirations, and comfort with mathematical logic and reasoning. While not as complex as calculus, Finite Mathematics is an engaging course with many real-world and career-relevant applications. Mastering this field of math will allow you to continue to pursue careers in a variety of desirable fields and industries. With the right mindset and approach, and a willingness to challenge yourself, you are likely to find the journey that is Finite Mathematics to be both valuable and rewarding.