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After graduating from high school, aspiring mathematicians and applied math experts must first attain a bachelor’s degree. Common university admissions requirements include some combination of the following: a competitive high school GPA (3.0 or greater), SAT or ACT scores, letters of recommendation, and a personal statement. A strong record in STEM classes, while not always a requirement, is highly recommended.

There are multiple routes to consider as an undergraduate. The most linear approach is to major in mathematics. But if you’re more interested in a specific application, then a math-based major such as computer science, biology, engineering, or finance may be right for you. A powerful but longer route is to double major (or make a major/minor pairing) between mathematics and another field.

The BS in mathematics program at the University of Florida is geared towards students who intend to pursue graduate study later on. Students are encouraged by the school to pick up a minor in computer science, industrial and systems engineering, physics, or statistics. Core coursework includes topics such as analytic geometry and calculus; elementary differential equations; sets and logic; and advanced calculus. The program consists of at least 120 credits and must be completed at the school’s Gainesville campus.

Southern New Hampshire University has an online BA in mathematics with a concentration in applied mathematics that can be completed online. The concentration track includes eight core courses in mathematics, three applied math courses, and 33 electives from which to choose. Typical course subjects include calculus, differential equations, applied linear algebra, mathematical modeling, and formal logic. Graduates are able to construct rigorous, logical mathematical proofs that can apply to real-world problems in the natural and social sciences.

Although there is always more to study in mathematics, there’s no better way to learn how to apply it than to start working in the real world. Mathematicians should feel confident applying to jobs with a variety of labels—employers asking for backgrounds in computer science, finance, statistics, or data science are often looking for skills that a background in mathematics covers.

Taking entry-level positions can help someone decide which area of applied mathematics they’d like to focus in. And this is a step that one need not undertake alone: the Society of Industrial and Applied Mathematics (SIAM) has a career page full of internships, fellowships, and job opportunities for those with a background in applied mathematics. Furthermore, SIAM provides a guide to relevant publications, conferences, and prizes for people in the field of applied mathematics.

If your undergraduate degree was primarily focused on a single area, then a graduate certificate is one way to fill the gap, either by adding capability in mathematics or in an area of its application. These certificates are often flexible enough to be pursued concurrently with a full-time job, but robust enough to qualify you to begin work in a specialized field upon completion.

The applied mathematics certification from thr Columbia University Fu Foundation School of Engineering and Applied Science is available fully online. Students must complete four graduate-level classes with a minimum of a 3.0 GPA in order to earn the certificate. Core class options include an introduction to nonlinear dynamical systems, functions of a complex variable, and numerical methods for partial differential equations. Elective options include an introduction to biophysical marking, the quantum physics of matter, geophysical fluid dynamics, and applied electrodynamics.

For those who wish to explore an area of application for their mathematics background, the professional certificate program in machine learning and AI offered by MIT is aimed at professionals with three years of work experience and an undergraduate degree in either computer science, statistics, or engineering.

Core courses focus on machine learning for big data and text processing, while electives cover a range of options such as advances in imaging and machine learning (medical, VR-AR, and self-driving cars); designing efficient deep learning systems; computational design for manufacturing; and deep learning for AI and computer vision. The program consists of four courses in total and takes place at MIT’s Cambridge, Massachusetts campus.

While many applied mathematicians can find work with just a four-year degree, a master’s-level education can provide the higher learning necessary to tackle the top problems in many industries. Do note that in some cases it’s possible to earn both a master’s degree and a PhD simultaneously (see step six below).

Admissions requirements vary drastically from school to school and program to program, but many include some combination of the following: a competitive undergraduate GPA (3.0 or better), GMAT or GRE scores, work experience, letters of recommendation, and a personal statement.

The MS in applied and computational mathematics offered by the Johns Hopkins Whiting School of Engineering prepares graduates to work in diverse areas such as business, defense, pharmaceuticals, and public policy. Students may choose to focus in applied analysis; IT and computation; operations research; probability and statistics; or simulation and modeling. The program consists of 32 credits and may be completed either online, on-campus, or in a hybrid fashion.

The University of Illinois at Chicago has an MS in mathematics with a concentration in applied mathematics that lays the groundwork for doctoral candidacy. Designed for students who have an academic background in mathematics, engineering, or computer science, the core coursework covers topics like complex applications analysis, applied differential equations, and applied partial differential equations. Students are also encouraged to complete classes in two of the following subjects: electromagnetic theory, continuum mechanics, statistical physics, fluid dynamics, electrical signal processing, biology, and plasma physics. The program consists of 32 credits.

It is certainly not a requirement, but those who wish to solidify their place as an expert in the field may choose to pursue a PhD—particularly if their area of interest lies in academia, data science, or the pharmaceutical industry.

PhD programs are highly individualized, both in their admissions requirements and in their curricula. Common admissions requirements may include some combination of the following: written and oral examinations, a competitive academic record and work resume, and multiple letters of recommendation. While the expected time to completion is often listed as five years, the true time necessary is a multivariable equation.

The PhD in applied mathematics at the University of Washington is primarily a research degree, although students are still required to take 15 advanced courses in the first two years. Once accepted into the program, students may simultaneously pursue either an advanced data science option or a certificate in computational molecular biology. Candidates take, on average, five years to complete this program.

The University of Pennsylvania has a PhD in applied mathematics that is an Ivy League option for those who want to pursue a career in research, teaching, or industrial work. Candidates may simultaneously earn a master’s degree while pursuing their PhD. In the course of completing their PhD, candidates will be required to teach, take advanced classes, pass written and oral examinations, and defend their research dissertation.

For a more specialized track, New York University offers a PhD in data science. Admissions requirements highly favor those with a background in mathematics, statistics, computer science, and engineering. Candidates must complete 72 credit-hours of advanced coursework, defend an original dissertation, and pass both a comprehensive exam and a depth qualifying exam in order to earn their PhD.

Mathematics, as a true science, is an inherently collaborative field. Only through an iterative process of trial and error can progress be made. If you want to listen in on the conversations swirling through mathematics today, check out some of the resources below, and get involved.

Financial engineers are expected to be in the know about the latest financial models, systems, and software. Professionals with a background in mathematics, statistics, and computer science can opt for a master’s program in financial engineering.

These mathematics professors have demonstrated expertise gained through years of study, research, experience, and service. Their contributions to the field consist of innovative research, an extensive body of published works, and teaching excellence.