Understand the Different Areas of Mathematics

There are many different fields of mathematics every student will encounter. This handy guide provides you with information on each type and what to expect.

Steps

  1. Understand that mathematics consists of a broad range of topics and is not a single subject. The following steps detail the different areas with which you will need to become familiar as you are studying mathematics.
  2. Begin with arithmetic. Arithmetic is the first branch of mathematics that you will have studied in elementary and middle school. It deals with the study of numbers and the use of the four fundamental processes:
    • Addition
    • Subtraction
    • Multiplication
    • Division
  3. Be aware that arithmetic is everyday math. It is important to get a solid grounding in this aspect of mathematics because you use it in your personal affairs, and arithmetic is the basis for most other mathematics.
  4. Learn about algebra. Algebra is used widely to solve problems in business, industry, and science by using symbols, such as x and y, to represent unknown values. The power of algebra is that it enables us to create, write, and rewrite problem–solving formulas. Without algebra, we would not have many of the items we use on a daily basis, for example, television, radio, telephone, microwave oven, etc.
  5. Proceed to geometry. Geometry is the branch of mathematics that deals with shapes. More specifically, geometry is the study of relations, properties, and measurements of solids, surfaces, lines, and angles. It is most useful in building or measuring things. Architects, astronomers, construction engineers, navigators, and surveyors are just a few professionals who rely on geometry.
  6. Become familiar with trigonometry. Trigonometry is mathematics that deals with triangular measurements. Plane trigonometry computes the relationships between the sides of triangles on level surfaces called planes. Spherical trigonometry studies the triangles on the surface of a sphere.
  7. Learn calculus. Calculus is high-level mathematics dealing with rates of change. It has many practical applications in engineering, physics, and other branches of science. Using calculus, we understand and explain how water flows, the sun shines, the wind blows, and the planets cycle through the heavens. Differential calculus deals with the rate of change of one quantity with respect to another, for example the rate at which an object’s speed changes with respect to time. Integral calculus deals with adding up the effects of continuously changing quantities, for example, computing the distance covered by an object when its speeds over a time interval are known.
  8. Understand the field of probability. Probability is the study of the likelihood of an event’s occurrence. It is useful in predicting the outcomes of future events. Probability originated from the study of games of chance. It is now used for other purposes, including (1) controlling of the flow of traffic through a highway system; (2) predicting the number of accidents people of various ages will have; (3) estimating the spread of rumors; (4) predicting the outcome of electronics; and (5) predicting the rate of return in risky investments.
  9. Learn statistics. Statistics is the branch of mathematics that helps mathematicians organize and find meaning in data. Anyone who listens to the radio, watches television, and reads books, newspapers, and magazines cannot help but be aware of statistics, which is the science of collecting, analyzing, presenting and interpreting data. Statistics appear in the claims of advertisers, in cost-of-living indexes, and in reports of business trends and cycles.

Tips

  • Powers, square roots, and cube roots, for example, may be considered arithmetic as well, because these can be calculated using the four basic arithmetic operations of addition, subtraction, multiplication, and division.
  • If you are good at mathematics, always try to do more complex work to build up your skills and learn beyond the classwork. This will increase your confidence and may even end up with you taking up a career in a field that uses mathematics.

Warnings

  • If you experience difficulties with mathematics, seek assistance early on before it becomes a mental stumbling block to proceeding further. It is important to have a solid grounding in one area before moving to another, so that you increase your confidence and skills.

Things You'll Need

  • Math texts and problems for solving

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