# Complete Guide to an Online Mathematics Degree

Mathematicians apply multiple mathematical processes, formulas, and techniques to real-world and theoretical situations in order to find efficient, accurate solutions to complex problems. During the course of an online mathematics degree program, students will work to find solutions for a multitude of economic, engineering, scientific, medical, and military problems by using computational, algorithmic, and theory-based techniques.

Online math degrees can be earned at every educational level, from the associate degree to the doctorate. When you are weighing your options and researching schools, be sure to pay close attention to institutional accreditation. Accreditation is a general term for the validating of a college’s credentials, by a nonpartisan organization. Because there is no specific programmatic accrediting agency for mathematics, understanding and assessing institutional accreditation is an important aspect of choosing a quality degree program. Read More

### Comprehensive List of Colleges & Universities for an Online Mathematics Degree

### Overview of Available Online Mathematics Degrees

At the undergraduate level, math students take courses in a wide variety of math theories and applications, such as statistics, calculus, differential equations, linear algebra, and economic modeling. A bachelor's degree in math can lead to careers in finance, economics, computer engineering, and other fields that require a strong quantitative understanding. Master's degree students complete a thesis in a theoretical or applied area of mathematics; this is a research project that is overseen by the student's faculty adviser. Master's graduates can land a greater variety of jobs in research and development areas. The PhD programs typically require a dissertation and often last a minimum of five years; graduates can become college professors, economists, mathematicians, and computer scientists.

Mathematicians are separated into two general specializations: theoretical and applied math. These specializations are different in terms of application versus derivation of theory, but they both require mathematicians to be well versed in previous studies of theories as well as contemporary mathematical ideas. Internships in mathematics are popular for students completing their bachelor’s degree, since they are expected to move on to the higher degrees before seeking full-time employment. Internships are commonly used as a way to break up the long sequences of education required for mathematics. Many students of mathematics enjoy that kind of opportunity to get firsthand experience applying their coursework in a real-world setting.

### Online Associate Degrees in Mathematics

Associate degree programs in mathematics acquaint in students with foundational concepts in algebra, calculus, trigonometry, statistics, and geometry. They also take classes in general education subjects, such as English composition, social sciences, and fine arts. Examples of coursework include measurement, functions, real numbers, polynomials, functions, integers, graphs, probability, and equations. Most schools require a commitment of two years of full-time study and up to 64 credit hours. Programs accept candidates who are high school graduates or GED certificate holders with an excellent background in mathematics. Students may decide to enroll in an Associate of Art (AA) program, which features a wider range of liberal arts classes, or an Associate of Science (AS) program, which includes more technical courses and may better prepare students to enter the workforce.

Associate degree holders in math are likely to find employment in bookkeeping, accounting, and auditing. Graduates may also become payroll clerks, computer technicians, or insurance sales representatives. Those who want to advance into other roles should consider earning a bachelor's degree.

### Online Bachelor's Degrees in Mathematics

Online bachelor’s degrees in math can be useful for individuals that want to prepare for math education, math-intensive careers, or future math-related study. Students in the mathematics bachelor’s degree program gain a working knowledge of major areas of math and problem-solving skills. Full-time students can complete the degree in four years or 120 credit hours. During the first two years of the bachelor’s degree, students take classes in many liberal arts areas, such as social science, natural science, humanities, and fine arts. The theory behind this curriculum is that it allows all students to develop useful critical thinking and communication skills, as well as cultural knowledge. The final two years of the math degree cover a number of math topics, such as college algebra, calculus, trigonometry, ordinary differential equations, and analytic geometry.

Some bachelor’s programs have specialization tracks in relevant quantitative areas, such as actuarial science, industrial mathematics, or systems analysis. Other bachelor’s degrees are designed for math teacher preparation and include courses in curriculum design and instruction, as graduates are typically qualified to apply for state certification to become primary or secondary mathematics teachers. Postsecondary teaching requires a master's or doctoral degree.

The quantitative analysis skills of the math bachelor’s degree are highly valued in a number of career areas. Possible roles in the industry include actuary, operations research specialist, investment analyst, bioinformatics analyst, and statistician. Many departments within the federal government -- such as internal revenue, census procedures, and defense -- require a bachelor's or the equivalent of 24 semester hours of math coursework for their entry-level positions.

### Online Master's Degrees in Mathematics

The mathematics master’s program provides students with the opportunity to deepen their understanding of a particular mathematical area in order to prepare for a math career or further study in a doctoral program. The master's degree requires two years of work and a thesis or teaching practicum. Applicants need a bachelor’s degree in math or another quantitative area.

The required courses in the math master’s degree depend on the degree's focus. Common specializations include pure mathematics, applied math, and math education. Pure math students generally take a broad array of advanced courses in areas like calculus, numerical analysis, geometry, and algebra. Applied mathematics programs are interdisciplinary and help students gain the quantitative skills to work in areas like actuarial science, finance, mathematical biology, or operations research. Math education students complete courses in instruction, as well as teaching practicums in classroom settings. Math master’s students must complete a large graduation requirement in order to be awarded the degree. Many students complete thesis projects in areas of math theory or applied research. Others opt for a comprehensive examination and more coursework instead of the thesis.

The mathematics master’s degree opens up a variety of careers in many sectors. Those interested in business could become financial analysts, market research analysts, statisticians, actuaries, operations researchers, or software developers. Others go on to apply math skills to particular science areas, like geosciences and biology. Positions in the government, applying knowledge of statistics and modeling, are also common. Math education majors are prepared to become math instructors at the high school or community college level.

### Online Doctoral Degrees in Mathematics

The mathematics doctorate, or PhD, allows students to study a breadth of advanced math topics and complete research in a specialized math area. These lengthy programs take about five years to complete and require 15 to 25 courses, as well as the completion of the dissertation and a comprehensive exam. Applicants need an accredited bachelor’s or master’s degree in mathematics or a closely related quantitative area. The math doctorate curriculum typically requires a few core classes, as well as many courses in the student’s specialization area. Core classes might discuss topics such as numerical analysis, abstract algebra, or topology. Along with these courses, students choose electives in their focus area and complete seminars in novel math research.

While coursework is a key part of the degree, math students must also develop a dissertation project as a prerequisite to graduation. This project might look into an unanswered question in mathematical biology, math education, algebra, combinatorics, statistics, or another subspecialization area, depending on the student’s interests. The student's faculty adviser helps shape and direct the research. A successful defense of the dissertation is one of the main requirements for being awarded the PhD.

Math doctorate graduates are prepared to become practicing mathematicians with private engineering and development firms, working alongside other scientists. The federal government employs about one-third of all mathematicians, and doctorate grads can also apply for government positions. Doctorate holders can apply for faculty positions at colleges and universities to teach mathematics and conduct research. According to the US Bureau of Labor Statistics, math PhD graduates with a strong understanding of a related industry area, such as computer science or operations research, are likely to have the best job prospects.

A doctoral degree is the best option for prospective mathematicians, and since most professional positions in mathematics are in the fields of research and development, the experience from the dissertation experience gained during the master’s and doctoral programs is extremely beneficial. Doctoral programs normally include specialization in a subfield of mathematics, alongside research and advanced courses. These doctoral programs normally take place in lab settings and involve highly collaborative team-based projects with students from mathematics as well as physics, engineering, and other science-based fields.

### Online Certificates in Mathematics

There are many certification options available to math professionals. These certificates are not required for employment but can prove to be good options for anyone who is interested in networking or seeking advanced employment. The American Mathematical Society is the most popular certifying organization, requiring a series of exams and completion of a degree. There are other organizations that are more specialized, geared toward statisticians, applied mathematicians, engineers, or even women, minorities, or Europeans.

People who are interested in applying to a certificate in mathematics program must hold bachelor's degrees. Applicants will need to submit official transcripts from their prior postsecondary programs and Graduate Record Examination (GRE) scores for consideration. Some schools set a minimum grade point average or GRE score that applicants must achieve to be accepted into a program. An 18-credit hour program can be completed in less than one year. This certificate program will give teachers the credentials they need to teach advanced-level mathematics at the high school or college level. Students may be able to transfer the credits earned in their certificate program to a master's degree in mathematics.

Students who choose to enroll in a math certificate program will take courses in advanced calculus, advanced linear algebra and matrix theory, and differential geometry. Other courses in the program may include topics such as complex variables, scientific computing, and special functions. Along with specific core courses, these programs may also include a number of credits to be taken from elective courses. Students who choose a specialization in secondary grades may be able to choose to take courses in numbers and operations or developing mathematical proficiency in algebra.

### The Importance of Accreditation

Though there is no specific programmatic accreditation agency governing the field of mathematics, it is still important for students pursuing online math degrees to understand and research accreditation. Any institution you consider should have earned this important designation, which indicates that a school has met certain academic standards of quality. The Department of Education maintains a list of recognized regional and national accrediting agencies. Recognition by one of these agencies will mean you’ll be eligible for government financial aid, and that your degree will be recognized by other educational institutions in the event that you choose to transfer credits or continue your education at another institution in the future.

Students interested in programs that prepare graduates to become math teachers in public schools should also ensure that any teacher-preparation program they're considering has earned recognition from the state board of education where the student hopes to teach; this credential is required to earn a teaching license. TEACH.org (previously operated by the US Department of Education) has more information about the path to teaching in a public school setting.

### What Students Will Learn in an Online Mathematics Program

The core math curriculum covers several advanced mathematics topics. Calculus, linear algebra, statistics, abstract algebra, and real analysis are commonly required classes. Other courses, such as formal logic or computer algorithms, intersect with mathematics and support the study of math theories. Along with the core curriculum, students take upper-level math courses of their choosing or complete a minor in a related area. Math education students might take courses in geometry for teachers and applied math instruction, while students with a computer science minor would take courses in programming and operating systems.

Courses taken during a bachelor’s degree typically include calculus, linear and abstract algebra, statistics, differential equations, and discrete and logical mathematics, all taken in sequences of varying length. Most online master’s degree programs in mathematics are geared toward math education. Students can prepare to teach math at the elementary, middle school, or high school level. The master’s degree program contains upper-level mathematics classes, as well as perspectives on math education. Common coursework discusses classroom management, effective teaching strategies, diversity in the classroom, math instructional technology, and mathematics learning. Education-focused programs also require teaching practicums and internships in a real classroom setting so that graduates gain hands-on teaching skills.

Degree programs in math that are not oriented toward education can usually be completed 100 percent online. Students learn new math concepts through online video lectures and tutorials. Email, instant messaging, or video conferencing with instructors can aid student understanding. Programs that are designed to prepare graduates for the classroom will require some on-site work, usually in the form of teaching practicums (mock teaching workshops) and teaching work in a local school. Online programs work to accommodate online students by placing them in schools in their community.

### Career Specializations for Mathematics Graduates

Mathematics used to be one of the most popular college major options, but as more college majors have emerged, -- often heavily concentrated in mathematics to begin with -- it has decreased in popularity. However, there is still a broad range of careers available for mathematics majors, from engineers to accountants, actuaries, and economists. Math teachers are also usually in high demand.

There are also careers available as mathematicians, which come in two types: applied mathematicians and pure mathematicians. An applied mathematician collaborates with engineers, chemists, or anyone else who is in need of complex mathematic assistance. These mathematicians must be able to solve real-life, practically applicable math problems. A pure mathematician usually works in academia, creating and contributing to new mathematical disciplines, solving complex theoretical problems, and working with patterns. Pure mathematicians are relatively rare and usually have doctoral degrees that allow them to work as professors.

The following list provides additional career options for math majors:

**Applied Mathematics:**Applied mathematics is the most popular option for math majors, as it involves working with numbers to solve difficult yet practical problems. Applied mathematicians may work for engineering firms or can act as individual consultants, contracting their services to those who need mathematical assistance.**Economics and Finance:**Economists and financiers work with money. They track global economic trends to make predictions about the future of a nation's trade and commerce. Financiers help develop financial plans and make recommendations to individuals or companies about their financial futures.**Pure Mathematics:**Pure mathematicians work primarily in theory. They choose to work with complex patterns and some of the most difficult problems in the history of mathematics. Their primary goal is not to create practical solutions and apply them in a real-world setting but to expand the field of academic mathematics. Pure mathematicians usually work for research universities and attend conferences around the world where they present their work and findings to other mathematicians.**Statistics:**Statisticians conduct surveys and collect statistical information, which they then interpret and apply to practical situations. Statistics professionals work in many different disciplines, ranging from politics to biology, and must be able to think logically and work accurately.**Teaching:**Students in the United States struggle with the math segments of standardized tests more than they do in any other subject. Qualified teachers with innovative and motivating approaches to math education are always in high demand.**Theoretical Mathematics:**These mathematicians construct new principles and discover previously unrecognized connections with already existing principles, expanding knowledge and establishing new theoretical foundations in subfields of math.

### References

- American Mathematical Society. Accessed May 12, 2014. http://www.ams.org/home/page.
- Occupational Outlook Handbook. Bureau of Labor Statistics of the US Department of Labor. Accessed May 12, 2014. http://www.bls.gov/ooh/math/mathematicians.htm.
- TEACH.org. Accessed May 12, 2014. https://www.teach.org.

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