Graduate programs in computational mathematics are widely available as traditional on-campus programs at universities across the countries. Students have a number of options when selecting which type of program to attend, as well as a variety of career options once they graduate. Below, we will discuss computational mathematics programs in greater detail, focusing on courses that are commonly found in these programs and requirements for admission.
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Graduate Degree Programs in Computational Mathematics
Students who are interested in enrolling in a graduate program in computational mathematics have the option to pursue the degree as a Master of Science, a graduate or post-master's certificate, or as a Doctor of Philosophy (Ph.D.). These programs are designed to equip students with advanced mathematical problem-solving skills that can be applied to a number of different industries, like business, engineering, and public policy. While the specific focus of the degree will vary--as some focus more heavily on engineering, statistics, or applied mathematics and students may be allowed to select an emphasis or concentration track--these programs generally do have some courses in common. Below, we will look at five courses that are commonly found in these programs.
Programs in computational mathematics typically include several courses in applied mathematics, from introductory level to more advanced and topical courses. In these courses, students will gain a solid understanding of a variety of mathematical topics that are often used in computational mathematics like linear algebra, differential equations, matrix theory, and theory of algorithms. Students will learn how these concepts can be applied to different fields, like engineering and science.
Stochastic Processes and Probability
These programs also include courses that cover stochastic processes and probability. Students will learn about topics like independence and conditional probabilities, joint distribution, conditional expectation and variance, discrete and continuous distributions, and central limit theorem. In addition, students may learn about different stochastic modeling methods and how these methods and models differ depending on the field, whether that be finance, engineering, or a science field like biology.
Courses in differential equations are also commonly found in programs in computational mathematics. Students will take course that cover introductory-level work in different equations and then move on to more advanced topics, like partial differential equations. Topics covered in these courses include Fourier series, Green's functions, finite element numerical methods, and separation of variables. Students may also begin working with computing languages in this course.
Statistical Methods and Theory
Statistical methods and theory may be taught as one course or be split across several different courses. Students will learn about different statistical methods and how they can be used in the world of computational mathematics, as well as their applications in other fields. Some topics discussed will likely include descriptive statistics, random variables, hypothesis testing, and confidence intervals. This course will likely require students to use statistical software.
Another common course in computational mathematics is number theory. In this course, students study the principles of number theory, which may include arithmetic theory and topics like congruence, cryptography, and the RSA methods. In addition, the course may cover ideas like primitive roots, multiplicative functions, and polynomial congruencies.
General Admission Requirements for Graduate Degree Programs in Computational Mathematics
To be admitted into a graduate program in computational mathematics, students will need to possess a bachelor's degree, which can typically be in any field as long as students have taken an adequate number of mathematics and computing courses during their degree. These prerequisite courses often include an advanced calculus course, advanced algebra, and a course in a computing language, though each program will likely have specific prerequisites. Students who enroll in a Ph.D. program can typically do so without having to first obtain a master's degree. When applying to a graduate program, you will need to submit an application form, your undergraduate transcripts, letters of recommendation, and a personal statement. Some programs may specify a minimum GPA requirement.
In summary, there are many different graduate programs in computational mathematics to choose from, like master's, certificate, and doctoral. Each program generally offers similar courses and has similar admission requirements.