Math can be described as the application of mathematical procedures and data to solve a problem. Mathematicians describe math as a systematic way of representing the natural world by the use of numbers, symbols, or other things that are determined by observation. There are various branches of mathematics. Arithmetic is one branch that deals with the application of numbers to solve problems. Trigonometry is a branch that deals with shapes and the application of their measurement. Geometry deals with the arrangement of objects and the interrelationship among them.
Mathematicians are also known as the “cogitrists” because they can combine numbers with real world objects to come up with new knowledge about nature. For example, knowing where an apple tree is located by finding the angles between its centers and its neighbor’s centers is a result that a Mathematician may find by using some math tools. This is called geometric physics. On the other hand, scientists and technologists utilize math to design machines, build equipment, and perform scientific research. Physicists use math to test theories about the universe and test predictions about the future of technology based on past phenomena. Astrophysicists use math to design telescopes and observe space weather.
Math has four main branches: pure mathematics, algebra, calculus, and geometric/topological/astronomical. Pure mathematics deals with all the topics that don’t have any connections to science in particular. Algebra is a branch of pure mathematics that is used to define and classify objects. Calculus is the language of mathematics, it abstracts from physical systems and the use of symbols for expressing complex ideas in a simple way.
Some of the topics in applied mathematics that are purely a matter of mathematics are plane traveling, straight line flight, aviation, and optics. Many scientists’ work in applied mathematics also has direct connections to the physical sciences because the subjects rely on observations and calculations of phenomena. For example, physicists cannot model the behavior of subatomic particles without using math, and vice versa. Thus every model built by physicists must also be able to be modeled by an algebraist who uses calculus.
Deductive Reasoning. Deductive reasoning is an artistic way of deducing a fact from a set of observations. The subject of math falls under the category of natural sciences because math is a part of the natural world. Many math professors teach deductive reasoning as part of their classes, but some students do not understand the concepts behind the reasoning.
Complex Learning. Another part of math is complex learning, which consists of an area of science and math that are closely related but are not considered part of each other. It includes such areas as genetics, anatomy, physiology, and microbiology. All of these topics can be taught using different methods. Some math courses teach these subjects as separate fields of study, but most math teachers integrate all of these subjects into a bigger curriculum.
The Science of Numbers. Many math teachers have a difficult time teaching their students the ideas of math and its underlying principles, especially those who lack a scientific background in the subject. Many advanced math courses use concepts from science and engineering, especially those that deal with the natural world. Math can be taught using the same tools that are used by scientists, engineers, and physicians. Examples include calculus, genetics, astronomy, and physics.
Life Sciences. One of the most common areas of math education that students are interested in is the life sciences. These include anatomy, physiology, pharmacology, biology, and immunology. Students might be interested in math science courses that teach these areas, or they might want to double their math education by enrolling in a Life Sciences class instead. If your student would like to pursue a career in a field that utilizes one or more of the Life Science areas, then math might be a great choice for him or her.