The PhD program in applied mathematical and computational sciences is autonomous, broadly based, and interdisciplinary. It is designed to help students achieve a command of theoretical and applied mathematics and obtain basic knowledge in another area (e.g., in physics, engineering, operations research, chemistry, computer science, economics, statistics, geography, or in the biological, medical, or social sciences). The program is flexible; students can concentrate on applied mathematics, such as differential equations and numerical analysis, or on other applicable techniques in mathematics. Scientific computing is an important part of applied mathematics, so it is often a part of student training and dissertation research. Prospective students should have a desire to apply mathematical techniques or theory to relevant problems in an outside area.
Learning Outcomes
Students will gain:
 proficiency in core applied mathematics subjects and broad knowledge in mathematics;
 proficiency in computer programming/scientific computing;
 excellent knowledge in at least one application area outside mathematics;
 ability to communicate knowledge and research work to various audiences; and
 ability to carry out research and work independently at a professional level.
The Doctor of Philosophy program in applied mathematical and computational sciences (AMCS) requires a minimum of 72 s.h. of graduate credit.
Course of Study
Faculty members can help each student plan a course of study that is consistent with the student's background, interests, and goals.
These individual plans are designed to help students develop expertise in methods of applied mathematics and build a good foundation in related topics of mathematics. The individual plans also provide sufficient knowledge in an outside area to enable students to use mathematical techniques in that area.
Students may arrange their study plans to earn a master's degree from another department after they complete part of their plan. Students find suitable thesis problems and supervisors with the help of the faculty.
Required Courses in Core Areas
Students must successfully complete these three core course sequences in the first two years of graduate study.
Outside Area Courses
Students must take and pass PhDlevel courses in areas in which mathematics is applied: one preparation course in the first two years and then two advanced courses outside of mathematics numbered 6000 or above.
Advanced Mathematics Course Requirement
In order to establish a solid foundation in mathematics, students must successfully pass two more mathematics courses (prefix MATH) numbered 5000–5999 and complete at least 12 s.h. of graduate mathematics courses numbered 6000–7799, with the exception of seminar courses. The courses should be chosen to obtain mathematical breadth and must be approved by the AMCS chair.
Comprehensive Examination
Students complete a comprehensive examination that covers their outside research area within three and a half years after beginning graduate study. The examination is typically based on the outside area courses and/or directed readings.
Applicants must carefully follow the applied mathematical and computational Sciences (AMCS) application procedures and they must meet the Graduate College Admission Requirements on the Graduate Admissions website. Those interested in applying may also view Admissions on the Graduate College website.
To be prepared for graduatelevel coursework in applied mathematics, applicants should have a bachelor's or master's degree with a strong mathematics or computational component.
Applications for fall admission are due on Jan. 15. For more information about the academic program, contact the chair of the Applied Mathematical and Computational Sciences Program. The Manual of Rules and Regulations on the Graduate College website also can provide additional information.
Financial support in the form of teaching assistantships is provided to every student admitted. Students may apply to various fellowships during their study. Research assistantships for qualified applicants also may be available from certain graduate advisors. Summer support is generally available to students.
Career opportunities for applied mathematicians include positions in colleges, universities, governmental laboratories, business, industry, and consulting firms.
Sample Plan of Study
Sample plans represent one way to complete a program of study. Actual course selection and sequence will vary and should be discussed with an academic advisor. For additional sample plans, see MyUI.
Applied Mathematical and Computational Sciences, PhD
Plan of Study Grid (Manual)
Academic Career 
Any Semester 
^{a} 

 Hours  0 
First Year 
Fall 
MATH:5200 
Introduction to Analysis I ^{b} 
3 
MATH:5600 
Nonlinear Dynamics with Numerical Methods ^{b} 
3 
MATH:5800 
Numerical Methods I ^{b} 
3 
MATH:5900 
FirstYear Graduate Seminar 
1 
 Hours  10 
Spring 
AMCS:5900 
Seminar: Applied Mathematical and Computational Sciences 
1 
MATH:5210 
Introduction to Analysis II ^{b} 
3 
MATH:5700 
Introduction to Partial Differential Equations ^{b} 
3 
MATH:5810 
Numerical Methods II ^{b} 
3 


 Hours  10 
Summer 
MATH:5950 
Qualifying Exam Preparation Seminars 
0 
^{c} 

 Hours  0 
Second Year 
Fall 
MATH:6600 
Ordinary Differential Equations I ^{d} 
3 
MATH:6850 
Advanced Numerical Methods I ^{d} 
3 
^{e, f} 
3 
 Hours  9 
Spring 
MATH:4820 
Optimization Techniques 
3 
MATH:6610 
Ordinary Differential Equations II ^{d} 
3 
MATH:6860 
Advanced Numerical Methods II ^{d} 
3 


 Hours  9 
Third Year 
Fall 
AMCS:7990 
Reading and Research 
2 
MATH:5750

Mathematical Biology I ^{d}
or Fundamental Groups and Covering Spaces or Abstract Algebra I 
3 
^{e, f} 
3 
 Hours  8 
Spring 


AMCS:7990 
Reading and Research 
2 
MATH:5010

Abstract Algebra II ^{d}
or Introduction to Smooth Manifolds or Mathematical Biology II 
3 
^{e, f} 
3 
 Hours  8 
Fourth Year 
Fall 
MATH:4700 
Partial Differential Equations and Applications 
3 
AMCS:7990 
Reading and Research 
3 
 Hours  6 
Spring 
MATH:4060 
Discrete Mathematical Models 
3 
AMCS:7990 
Reading and Research 
3 
 Hours  6 
Fifth Year 
Fall 
MATH:4840 
Mathematics of Machine Learning 
3 
AMCS:7990 
Reading and Research 
2 
 Hours  5 
Spring 
GRAD:6003 
Doctoral Final Registration 
1 
^{g} 

 Hours  1 
 Total Hours  72 