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Mathematics covers many disciplines, from simple addition to complex chaos and game theories. High school and early college years focus on algebra and geometry, followed by trigonometry and calculus. Statistics and probability are also important, with many subfields becoming specific in their applications.
Mathematics encompasses many disciplines that have evolved throughout history. Simple examples include addition and subtraction, while extremely complex forms include chaos and game theories. Traditionally, however, the high school and early college years focus on the following disciplines.
Algebra is the gateway to most mathematical studies. Students may study algebra in eighth, ninth or tenth grade, depending on their ability and scholastic requirements. Normally, first-year algebra is concerned with studying equations to find unknown elements. Students learn to solve equations for two or three variables, depending on the class.
Typically, the study of algebra is followed by the study of geometry, which is usually followed after a first-year algebra class. A second-year algebra course includes geometric principles. In colleges, the study of algebra is often combined with the study of geometry and students do not take a separate course.
Most teachers start teaching basic algebraic and geometric concepts long before students actually take those lessons. In many cases, students are now solving one- and two-step equations for a third- or fourth-grade variable. Familiarity with solving equations is thought to help prepare the student for working with more variables in the first year of algebra.
Students also often learn basic formulas for measuring objects, such as triangles, squares, and circles, by fifth or sixth grade. This early math grounding rarely questions the “why” of a formula, but prepares students to ask it. This question will be answered by the proofs and theorems that dictate and explain why the formulas for obtaining measurements in shapes actually work.
Some students finish their math education with the second year of algebra. Many, however, continue to study trigonometry, a branch that deals with the principles of angles and shapes. Some consider trigonometry to be advanced geometry, while others argue that it is an entirely separate area of study. It has broad applications, but one of the most familiar to people is its use in astronomy to measure the distance of stars and planets from each other in a process called triangulation.
After trigonometry, students often study calculus, which is developed from advanced algebra and geometry. In many colleges, students may study calculus or trigonometry as their final math course. Calculus is actually two different branches: differential and integral. Differential calculus deals with equations that measure things like distance and speed. Integral calculus evaluates geometry with attention to real-world applications, such as how time or temperature can affect an equation.
Both forms of computation are essential to understanding applications in major sciences such as physics. In fact, in most colleges, one must at least be eligible to take calculus courses before enrolling in physics courses. Some advanced science courses require you to have previously studied calculus, as calculus equations are fundamental to understanding the more complex aspects of a science.
Another branch of mathematics is the field of statistics and probability. Those studying business or accounting usually have to take a course in one or the other – or both – to meet the graduation requirements for college. Besides these branches, there are many other subfields that become very specific in their applications. Mathematics graduates will take these courses to earn advanced degrees.
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