PhD in Applied Mathematics - Algorithms and Complexity in Ithaca United States | Cornell University

Graduate study options span all specialization areas represented by over one hundred faculty members across fourteen departments. These faculty come from the College of Engineering, College of Arts and Sciences, College of Agriculture and Life Sciences, and the Samuel Curtis Johnson Graduate School of Management. Students can further broaden their studies through minor subject selections. The Applied Mathematics program admits graduate students with diverse educational backgrounds featuring strong mathematical foundations, typically accepting only PhD candidates. The program currently enrolls approximately forty students, with completion generally taking four to five years.

Complexity examines the efficiency of computational algorithms. This field involves defining problems and pursuing two key objectives: identifying maximum possible efficiency for problem-solving algorithms, and creating algorithms that achieve this optimal efficiency. Proper complexity formalization requires a mathematical computer model to ensure rigorous definitions and proofs. While Turing machines dominate as the primary model, real number machines also play significant roles, particularly aligning with practical computational scenarios. This formalized study of computational efficiency constitutes complexity theory.