Applied Mathematics and Computational Science, PhD

Advanced mathematics is continually finding new applications in natural science, biology, engineering, medicine, and social sciences, and these fields are  providing new directions for the development of mathematics itself. The graduate group in Applied Mathematics and Computational Science takes a very broad view of mathematics and its applications in our mission to train mathematical scientists for careers in academia, research and industry.

In addition to providing a rigorous conceptual foundation for the application of mathematics, our diverse faculty gives AMCS students the opportunity to work in a “wet lab” environment where mathematics is actually being applied to real world problems. The AMCS graduate groups offer a full program of study in mathematics and its applications, offering both doctoral (Ph.D.) and masters (A.M.) degrees.

For more information: http://www.amcs.upenn.edu/

The degree and major requirements displayed are intended as a guide for students entering in the Fall of 2026 and later. Students should consult with their academic program regarding final certifications and requirements for graduation.

Curriculum 

Core Courses 16
AMCS 6025
Numerical and Applied Analysis I
AMCS 6035
Numerical and Applied Analysis II
AMCS 6081
Analysis I
AMCS 6091
Analysis II
MATH 6480
Probability Theory
MATH 6490
Stochastic Processes
Electives 212
Teaching Requirement 3
Dissertation3
AMCS 9950
Dissertation
Total Course Units21
1

Or other courses approved by the Graduate Group Chair.

2

Advanced Coursework in AMCS, BSTA, CIS, ESE, MATH, STAT, or any course that has been approved by the Graduate Group Chair.

A maximum of 4 elective courses can be Independent Studies: AMCS 9999

3

Two semesters of teaching is required for Benjamin Franklin Scholars.

University PhD Benchmarks

In addition to Program requirements, the following milestones must be completed:

Qualifying Evaluation
Candidacy Examination
Dissertation Defense/Oral Exam
Dissertation Deposit


For more information view the University’s Academic Rules for PhD Programs.