What are the Different Disciplines of Mathematics?
Mathematics comprises many disciplines that have evolved throughout history. Extremely complex mathematics may include chaos and games theories. However traditionally, the high school and early college years focus on the following disciplines.
Algebra is the gateway into most mathematics studies. Students may study algebra in 8th, 9th or 10th grade, depending upon skills and school requirements. Normally first year algebra concerns itself with the study of equations to obtain unknown elements. Students learn how to solve equations for two to three variables, depending on the class.
Generally the study of algebra is followed by the study of geometry, which is usually taken after a first year algebra course. A second year algebra course continues the study of mathematics combining geometric principals. In colleges, the study of algebra is often combined with the study of geometry, and students do not take a separate geometry course.
Usually the teachers have started teaching basic algebraic and geometric concepts long before students actually take algebra or geometry. In many cases students are now doing one and two-step equations solving for a variable by third or fourth grade. The familiarity with solving equations is thought to help prepare the student for working with multiple variables in first year algebra.
As well, students tend to learn basic formulas for measuring objects, like triangles, squares and circles by 5th or 6th grade. This early preparation in mathematics rarely questions the “why” of a formula, but prepares the students to ask why. This question will be answered by the proofs and theorems that dictate and explain why formulas for obtaining measurements in shapes actually work.
Some students end their mathematics education with second year algebra. Many, however, go on to study trigonometry. Trigonometry is a branch of mathematics dealing with the principles of angles and shapes. Some feel trigonometry is advanced geometry, while others argue it is a completely separate branch of mathematics. It has broad applications, but one 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, one can study either calculus or trigonometry as a final mathematics course. Calculus is actually two different branches: differential and integral. Differential calculus is a mathematics field that concerns itself with equations measuring things like distance and velocity. Integral calculus evaluates geometry with attention to real world applications like how time or temperature might affect an equation.
Both forms of calculus are essential to understanding applications in major sciences like physics. In fact, in most colleges, one must at least be eligible to take calculus courses prior to enrolling in physics courses. Some advanced science courses require that one has already taken calculus, since 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 economics or accounting must usually take a course in one or the other, or in both to meet graduation requirements for college. Beyond these branches of mathematics, there are numerous other sub-fields that become very specific in their applications. Mathematics majors will pursue these courses in order to earn advanced degrees.
Written by Tricia Ellis-Christensen
