University of Pennsylvania

Overview

The PhD in Applied Mathematics and Computational Science at the University of Pennsylvania equips students with the skills necessary to address complex problems at the intersection of advanced mathematics and large-scale computation. This comprehensive program promotes research in various critical areas, including applied analysis, probability, optimization, and machine learning.

What you'll study

The program structure integrates advanced coursework with rigorous research training. In the initial years, students engage in both core and elective courses, gradually transitioning to a significant focus on dissertation research under faculty mentorship.

• Core topics:
  • Numerical and Applied Analysis
  • Probability Theory
  • Stochastic Processes
  • Mathematical Statistics
  • Optimization Theory
  • Modern Convex Optimization
  • Machine Learning
• Research component: Students will undertake dissertation research aligned with their interests in applied mathematics and computational science, guided by faculty.
• Electives: Additional graduate-level courses can be selected to complement research objectives, such as computational methods or advanced optimization topics.
• Capstone: The program culminates in a PhD dissertation based on original research, with specific milestones to be confirmed with the department.

Entry requirements

Academic background: A strong foundation in mathematics and/or computational sciences is essential, typically demonstrated through a relevant bachelor’s or master’s degree.

Standardized tests: The GRE is generally required; applicants should verify the current policy with the department prior to applying.

English language proficiency:

• TOEFL iBT: A minimum score of 100 is generally expected.
• IELTS: A minimum score of 6.0 is typically required.

Other requirements: Applicants should prepare to submit letters of recommendation, transcripts, essays or statements, standardized test scores, and an application fee. Specific requirements may vary, so it is important to consult the University of Pennsylvania’s graduate admissions page and the program’s departmental website for the most current information.

Career prospects

Graduates of the PhD program in Applied Mathematics and Computational Science at the University of Pennsylvania are well-positioned for careers in academia, industry, and research institutions. With expertise in computational methods and mathematical analysis, alumni may pursue roles in data science, machine learning, optimization, and beyond, contributing to advancements in technology and scientific research.