Applied Mathematics

Applied Mathematics at Case Western Reserve University offers a comprehensive and rigorous program designed to equip students with a strong foundation in mathematical theory and its practical applications across diverse scientific and engineering disciplines. The curriculum integrates advanced coursework in calculus, differential equations, numerical analysis, mathematical modeling, and computational methods, preparing graduates to analyze complex systems and solve real-world problems. Students have opportunities to engage in cutting-edge research projects and collaborate with faculty members renowned for their contributions to applied mathematics, data science, and computational techniques. The program emphasizes interdisciplinary approaches, encouraging students to apply mathematical principles to fields such as physics, biology, finance, engineering, and computer science. Through a blend of theoretical instruction and hands-on experience, students develop critical analytical skills, programming proficiency, and problem-solving strategies essential for careers in industry, government, or academia. The department fosters an innovative learning environment with access to modern laboratories and computational resources, supporting student research and projects. Graduates of the Applied Mathematics program at Case Western Reserve University are well-prepared to pursue advanced degrees or enter competitive job markets, contributing to technological advances, data analysis, and scientific discovery with a strong mathematical underpinning. With dedicated faculty mentorship and a vibrant academic community, the program aims to cultivate versatile professionals capable of addressing complex challenges in a dynamic world.

Qualifying Exams

Each student will be required to take two written qualifying exams. The exams will be in analysis and algebra for the mathematics track, and in numerical analysis and modeling for the applied mathematics track. Syllabi for the exams are available to students. Exams will be offered twice a year, usually in January and May. Students may attempt each exam up to two times. Under normal circumstances, students are expected to have passed both exams by the end of their fifth semester.

Area Exam

Each student will be required to pass an oral examination showing knowledge of the background and literature in the chosen area of specialization. The exam will be administered by the student’s advising committee, chaired by the principal advisor. The exam should normally take place within one year after final passage of the qualifying examinations and at least one year before the defense takes place. A student may retake the required exam once.

A written syllabus, with a list of the papers for which the student will be responsible, should be prepared and agreed upon by the student and advising committee at least two months before the exam takes place, at which time a specific date and time for the exam should be decided. Both the syllabus and the scheduled date of the exam should then be reported to the graduate committee. Once the syllabus and exam date have been reported to the graduate committee, the student will advance to PhD candidacy.

Yearly Progress Reports

After passing the area exam, students will present yearly progress reports to their advising committees, usually in April. These reports will consist of both a written summary of progress and an oral presentation delivered to the advising committee.

Dissertation, Expository Talk, and Defense

Students are required to produce a written dissertation and present an oral defense. The dissertation is expected to constitute an original contribution to mathematical knowledge. It must be provided to the defense committee (the composition of which is discussed below) at least 10 days prior to the defense. Students are required to give a colloquium-level presentation of their thesis work, open to all students and faculty, followed by an oral defense of the thesis work to the defense committee. The committee consists of at least four faculty members, including the student’s principal advisor and at least one outside faculty member.

Deadlines for the thesis defense and approval of the dissertation are determined by the School of Graduate Studies. It is the student’s responsibility to be aware of deadlines and make sure they are met.

A student in the applied mathematics track must demonstrate knowledge of scientific computing, mathematical modeling, and differential equations. This includes taking qualifying examinations in the areas of computational mathematics and mathematical modeling, and taking certain courses in these three areas, as specified below. 

Qualifying Examination

A doctoral student in the applied mathematics track must take written examinations in numerical analysis and in mathematical modeling, as well as an oral examination in his or her chosen area of specialization. Subjects include but are not restricted to fluid mechanics, statistical mechanics, epidemiology, neuroscience, and more traditional fields of mathematics.

A student with a master’s degree in a mathematical subject compatible with our program, as determined by the graduate committee, must take 18 credit hours of approved courses, which must include at least 6 credit hours of courses offered outside the Department of Mathematics, Applied Mathematics, and Statistics and at least 9 credit hours offered by the Department of Mathematics, Applied Mathematics, and Statistics. The graduate committee will determine which of the specific course requirements stated above have been satisfied by the master’s course work.

Sample study plans for students with concentrations in scientific computing, imaging, mathematical biology, and stochastics follow. The graduate committee will entertain ideas for other serious study plans or qualifying exam subjects in addition to the most common variants.

Scientific Computing Concentration

Imaging Concentration

Life Science Concentration

Stochastics Concentration

PhD students entering with a bachelor’s degree are subject to the same breadth requirements as students pursuing the MS degree in applied mathematics.

Petitions

Any exceptions to departmental regulations or requirements must have the formal approval of the department's graduate committee. Such exceptions are to be sought by a written petition, approved by the student’s advisory committee or thesis advisor, to the graduate committee.

Any exception to university rules and regulations must be approved by the dean of graduate studies. Such exceptions are to be sought by presenting a written petition to the graduate committee for departmental endorsement and approval prior to forwarding the petition to the dean.

Requirements

• Applicants must have a good academic record, e.g., a B-average or rank in the upper third of his or her graduating class at an institution whose status and programs are readily assessed.
• Applicants must meet all of the undergraduate prerequisites for the proposed field of graduate study.
• Statement of Objectives — Some programs have this built into the application. If not, create your own using "Statement of Objectives" as the heading. The statement should be one to two pages and include your purpose in undertaking graduate work as well as an explanation of your study and research interests as they relate to your undergraduate/graduate study and professional goals.
• Academic Transcripts – You are required to identify all post-secondary educational institutions you have attended on your application form, and to submit an official transcript from each. Admission to the School of Graduate Studies is conditional on final certification of degrees awarded. Note to International Students: Documents in languages other than English must be accompanied by certified translations in English.
• Letters of Recommendation - Three letters of recommendation must be submitted from those individuals sufficiently familiar with you, and who can assess your academic preparation, abilities and accomplishments. Letters should be from your most recent instructors in your proposed field of study. If you have been out of school for several years, one letter may be from your employer, supervisor or other person familiar with your most recent activities.
• Test Scores – Your department will identify required standardized tests. When you fill out forms for these use 1105 as the institutional code for Case Western Reserve University. The School of Graduate Studies will forward all official score reports of standardized tests (GRE, TOEFL, etc.) to the program of interest. The department will inform you which standardized tests are required for your program. International students whose first language is not English must demonstrate English proficiency by taking the Test of English as a Foreign Language (TOEFL) and earn a minimum score of 577 if paper-based, or 90 if Internet-based. The International English Language Testing System (IELTS) is also accepted. The minimum acceptable score is 7.0. Some departments may require higher scores. International applicants cannot be admitted without receipt of an acceptable official TOEFL score. The TOEFL is valid for two years after the test date. The GRE is valid for five years after the test date.
• Application Fee - A nonrefundable application fee of $50 is required for each application submitted.

The financing options for the Applied Mathematics program at Case Western Reserve University are designed to support both domestic and international students in funding their education through a variety of means. Most students finance their studies through a combination of scholarships, fellowships, student loans, federal aid programs, and on-campus employment opportunities. Merit-based scholarships are awarded to outstanding applicants upon admission, reducing the financial burden for qualifying students. Additionally, the university offers need-based grants and awards intended to assist students with demonstrated financial need. International students may have access to specific scholarships or assistantship positions, though funding opportunities can be more limited compared to domestic students.

The university participates in federal financial aid programs; eligible students can apply for federal loans such as Direct Subsidized and Unsubsidized Loans, which can cover a portion of tuition and living expenses. Case Western Reserve University also encourages students to seek external funding sources, including private scholarships and grants from organizations related to science, mathematics, and engineering. For graduate students, teaching and research assistantships are common forms of financial support, providing a stipend and often a tuition waiver in exchange for work duties within the department.

Students are advised to complete the Free Application for Federal Student Aid (FAFSA) each year to determine eligibility for various aid programs. The university’s Office of Financial Aid provides personalized counseling and workshops to help students navigate the application process and explore all available funding options. Furthermore, students are encouraged to seek part-time employment opportunities on campus to supplement their income.

Overall, the university aims to make Applied Mathematics accessible by offering a comprehensive range of financial aid programs tailored to the needs of its diverse student body. Prospective students are urged to contact the university’s financial aid office early in the application process to discuss their specific circumstances and establish a suitable financing plan.

The Bachelor of Science in Applied Mathematics at Case Western Reserve University offers students a comprehensive education in mathematical methods and their practical applications across various industries and scientific disciplines. The program is designed to equip students with a strong foundation in both pure and applied mathematics, preparing them for careers in research, industry, government, or further graduate study. Students have the opportunity to explore areas such as numerical analysis, mathematical modeling, data analysis, differential equations, and computational science. The curriculum emphasizes problem-solving skills, critical thinking, and the ability to translate complex mathematical concepts into real-world solutions. Students can also participate in undergraduate research projects, internships, and collaborative work with faculty members who are active researchers in their fields. Case Western Reserve University supports a multidisciplinary approach, allowing students to integrate knowledge from physics, engineering, economics, and computer science to enhance their understanding and versatility. The program prepares graduates for diverse roles including data analyst, quantitative analyst, software developer, and research scientist. Additionally, the university offers resources such as dedicated tutoring, career counseling, and networking opportunities with alumni and industry partners. The applied nature of the program ensures that students are not only well-versed in mathematical theory but also adept at applying their skills to solve practical problems, often using programming languages and software tools commonly employed in the industry. The faculty involved in the Applied Mathematics program are distinguished scholars and experienced educators committed to fostering an engaging learning environment. Overall, the Applied Mathematics program at Case Western Reserve University aims to produce capable and innovative graduates ready to contribute to scientific advancements and technological progress in a rapidly evolving global landscape.