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 consider mathematics a way of finding and using patterns to formulate conjectures that resolve truth or lack thereof.
Numbers and symbols aid mathematics as a way of expressing and explaining logic itself, and giving a concrete manifestation of abstract ideas. Through mathematics, we can calculate, measure, count, and analyze both physical objects and theoretical ideas. We can study shapes, motions, logic, and physical laws of the universe. Mathematics is vital for many other fields such as natural sciences, medicine, finance, engineering, and even social sciences. Learn more about the theories and applications of the field through the mathematics articles in this category of Direct Knowledge.
As far back as 3000 BC, Mesopotamian states and other societies such as Egypt started using geometry, algebra, and arithmetic. These mathematical tools helped with practical uses such as taxation, trade, and keeping track of time. The most ancient mathematical texts available come from Mesopotamia, including mentions of parts of the Pythagorean theorem. This makes the theorem the most ancient and widely spread development in mathematics after basic geometry and arithmetic.
Later, around 500 BC, the Greeks further refined mathematical methods by introducing rigorous proofs with deductive reasoning. Of course proofs have become a key part of math today, and you'll find proofs for various concepts in the mathematics articles in this category. The ancient Romans focused on applied mathematics, using it for various types of engineering, surveying, bookkeeping, and making calendars. On the other side of the world (at the time), the Chinese made contributions such as a place value system and the use of negative numbers. The Hindu-Arabic numeral system evolved in the first 1000 years AD, giving us the system used throughout the world today.
Throughout the history of mathematics, long periods of relative non-development would be briefly punctuated by new discoveries. This started to change in the 15th century. At this time, the Renaissance came into play, allowing mathematical developments to interact with scientific discoveries. Since that time, new discoveries have been made at an increasing pace, including up to modern day. Mathematics articles in this category are sure to cover these changes and keep you up to date.
Mathematics Articles in Modern Fields
Within mathematics as a whole exists two main branches: pure, and applied mathematics. However, each of them doesn't necessarily exist completely independently with a distinct line between them. But the following descriptions give a good idea of the differences.
The branch of pure mathematics explores fundamental parts of the field out of intrinsic interest, including quantity, structure, space, and change. Quantity uses numbers, integers, rational numbers, real numbers, irrational numbers, complex numbers, and more, all combined with arithmetic. Structure is the consequence of relations and operations within sets of numbers. The structure can relate to arithmetic operations, and similarly structured sets can exhibit similar properties. This makes it possible to study larger groups at once, or branch into more abstract systems.
The study of space starts with geometry, combining numbers with space. This is where we find the Pythagorean theorem and trigonometry. Finally, the study of change is explored using calculus, where functions are the main concept used to describe changing quantities. The study of the rate of change (or the change in change) is differential equations, used to describe dynamical systems. Other areas of pure mathematics include number theory, algebra, combinatorics, and analysis. The pure mathematics articles on these topics often won't dwell on practical applications. Rather, they just stick to the math itself. These articles are where you can find in-depth explanations and examples of the methods, formulas, and terminology used in math.
The applied branch, on the other hand, aims to use mathematics in real world situations for solving real problems. For example, probability and statistics allow us to use numerical data from experiments or observations in order to make predictions. This is useful in almost every aspect of society. It is the best way we have to predict what might happen in certain situations, allowing us to make the best decisions possible.
Computational sciences use numerical analysis and computer algebra to make complex calculations. These are especially important when calculations need to be extremely precise, such as when dealing with advanced technology in medicine or navigation. The physical sciences also depend heavily on applied mathematics, using it for addressing how real-world objects behave in the presence of external forces. This is widely applicable to all types of engineering.
Careers in Mathematics and Related Articles
As one of the fundamental subjects, mathematics connects to most fields in some form or another. With a mathematics degree, you could gain another degree in a more specific field, or go straight in to a number of areas. Some professions that rely heavily on mathematics include economist, actuary, financial planner, statistician, investment analyst, professor/teacher, software engineer, accountant, or research scientist.
Of the more math-specific fields, one can expect to make a median salary of about 88,000 dollars per year after having earned a Master's degree. Growth in the field is very fast right now, so you can be confident that there's a position out there waiting for you. You can also be confident that Direct Knowledge will have thorough mathematics articles to help you with some of the toughest areas of math that you might be struggling with.
Mathematics applies to essentially every area of our lives and subject of study. Even so, a lot of people still shy away from the subject thinking it’s too difficult for them. But anyone can study it with the right assistance. Whether math is a personal interest, a requirement for school, or a way of enhancing what you do professionally, the math books in this category can help you learn the crucial parts of the subject in a way that's easy to understand.
Finding the Beauty in Math
Sometimes, classic mathematics books can be convoluted and hard to figure out. Complicated examples and unnecessary details can keep students from learning subjects that shouldn't be so difficult. But in reality, math is a method of making the world around us easier to understand, not harder. It gives us a language for describing the indescribable. And that language is beautifully consistent, concise, and pure.
A lot of students might scoff at that last statement, but it really is true. All you need are the right tools to help you understand mathematics at a fundamental level. The mathematics books in this category provide those tools. Sensible examples make the concepts clear as day, and save you study time by focusing on understanding the concepts at a fundamental level.
Which Math Books are Right for You?
The books found here span a wide range of topics that are perfect for many ages and levels. And any college student knows that math is generally required as one of the core classes in college, even if you're majoring in something else entirely. But that just shows that university course planners know math has relevance and importance in all fields. So embrace the subject with a positive attitude and see how the math books here can add to your major.
For example, math has had a long relationship with sculptors and painters over time. They often used geometry to create shapes and patterns with the most visually pleasing aspects possible, or to make structures in architecture both attractive and strong in terms of structure. Music, too, has a deep relationship with math. Numbers and their properties relate to elements of music such as rhythm and meter, pitch, tempo, pulse, and more. The golden ratio and Fibonacci numbers are even central parts of the work of some composers.
As most students know, calculus is a big deal in math. It has played an important role historically, and continues to be crucial for fields like engineering and science. Hence why most student need to take it in some form or another, and the math books here include a whole series that focuses on it. There are three levels included in this category that span calculus one, two, and three (multivariable). They follow typical class structures fairly well, making them great supplements for college courses or tools for AP exam prep.
Proofs, Number Theory, and More
Calculus isn't the only math you find in university, especially if you're majoring in math or science. In addition to Calculus, you'll find other advanced math books here on topics like Proofs (An Introduction to Mathematical Arguments). You'll also find some subjects which are great both for university and advanced high school students. High schoolers just starting to get into more advanced math can find books on subjects like linear algebra and number theory that can help them with AP exams for college credit. Or those already in college can use them as supplemental material for current classes. Each of them starts from the basics and guides students with thorough examples and practice.
Nothing to Lose
Forget anything anyone ever said about not being a “math person.” All it takes to get comfortable in the field is practice and dedication. From there, whatever your passion, mathematics can complement it. And this bookstore can complement your learning process with math books just a click away, wherever you are in the world.