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Aristotle defined mathematics as “the science of quantity.”  More recently, Benjamin Peirce (1809-1880), an American mathematician who taught at Harvard for 50 years, defined mathematics as “the science that draws conclusions.” The American Heritage Dictionary sums up the subject as the “study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols”. There are probably as many definitions and opinions on what is mathematics as there are professions to which the subject is applied.

Thousands of words could be devoted to mathematics-related professions and the application of it to each job. For the sake of brevity, we will name a few that may not come to mind when thinking of professions that require mathematics. Some of the vocations involving math are ecology, surveying, geodesy (measurement of the shape and area of the earth), design, photogrammetry (aerial imagery), attorney, and every field of engineering. A short list of firms that recruit mathematicians includes engineering and computer companies, banking, science and financial consulting firms, as well as biomedical and imaging enterprises. Even law and medical schools favor applicants with a major in math.

The educational process can begin with an associate degree in mathematics to the pinnacle or doctorate level. Here is a condensed look at the different degree levels:

Associate’s: Many community colleges offer an Associate of Science in Mathematics in a two-year program. At this level, a typical curriculum provides the development of skills in critical thinking, problem-solving, quantitative and empirical reasoning. In addition, a two-year program affords a pathway to transfer some of your credits to a  four-year bachelor’s degree.

Bachelor’s: At this level, there are specializations or concentrations to choose, such as the application of math or the teaching of the subject. Within the teaching route, there are further specialties depending on what academic level you wish to teach. For example, teaching math in grades K-6 or high school, or possibly at the community college level.

Master’s: At this graduate level, the areas of specialization are too numerous to mention. You can take degrees in anything from Financial Mathematics, Applied Mathematics, Economics, Mathematical Engineering, Computational Science, Education, and Applied Statistics. A typical master’s program (non-educational) will involve basic courses in real analysis, complex analysis, and linear algebra, followed by other fundamental courses such as probability, scientific computing, and differential equations. Check out our ranking of the top online master’s degrees in mathematics for more information.

Doctorate: There are online Ph.D. programs in Mathematics and Statistics, which may suit the working professional. Generally, prospective applicants to a Ph.D. math degree program must already have a master’s degree in that area, whether this is a Master of Science in Math or MS in Statistics. There are doctoral degrees devoted to mathematics education that usually require a master’s degree in mathematics, mathematics education, or a related field. If this degree is your ambition, then you may want to check with the admission’s department of prospective schools. Not all doctoral programs necessitate a master’s degree.

A degree in mathematics is about diversity. The college programs are as multifarious as the career opportunities for those with a math degree from any level. When contemplating your career, according to the U.S. Bureau of Labor Statistics (BLS), the highest median salary does not equate to the highest degree level. As of May 2016, the median annual wage for mathematicians was $81,750. The highest-paying category was for actuaries whose median income was $100,610 with a Bachelor’s degree. Mathematicians and statisticians followed at $81,950 with a Master’s degree. More importantly, the BLS projects the job growth to be 33% through 2026 or 13,300 mathematician/statistician jobs added/changed over a ten-year period.