PhD Financial Mathematics at University of Manchester

Mathematics is a way of defining and solving problems by combining logic with insight, and by finding patterns and structure. At a most basic level, we use the abstract concept of “number” to understand what we observe, and we develop the method of “counting”; at a higher level, we use the language of “calculus” to understand motion, and we develop the methods of differentiation and integration. But mathematics is more than just computations with numbers and derivatives. Math is a way of thinking—an art that describes the abstract structure of logic, reason, and the scientific method. 

The Undergraduate program in the Department of Mathematics is intended both for students interested in preparing for graduate study and research in pure mathematics, and for students interested in using mathematics to pose and solve problems in the sciences, engineering, social sciences, or other areas. Undergraduate mathematics majors and minors will study:

The foundations of analysis, which begins with the study of functions and their derivatives and integrals

The fundamentals of advanced algebra, which is based on axiomatic systems involving operations of addition and multiplication in general settings

Additional subjects such as geometry, probability, and topology

Applications of mathematics to science and/or engineering.

The graduate program is designed primarily to prepare students for research and teaching in mathematics. It is naturally centered around the research areas of the faculty, which include algebraic geometry, algebraic number theory, data-intensive computation, geometric analysis, harmonic analysis, mathematical physics, partial differential equations, stochastic partial differential equations, and topology. The program can be supplemented in applied directions by courses in theoretical physics, computer science, mechanics, probability, and statistics offered in other departments of the Krieger School of Arts and Sciences and in the Department of Applied Mathematics and Statistics in the Whiting School of Engineering.

The Department of Applied Mathematics and Statistics is devoted to the study and development of mathematical disciplines especially oriented to the complex problems of modern society. A broad undergraduate and graduate curriculum emphasizes several branches of applied mathematics: Probability, the mathematical representation and modeling of uncertainty; Statistics, the analysis and interpretation of data; Operations Research, the design, analysis, and improvement of actual operations and processes; Optimization, the determination of best or optimal decisions; Discrete Mathematics, the study of finite structures, arrangements, and relations; Scientific Computation, which includes all aspects of numerical computing in support of the sciences; and Financial Mathematics, the modeling and analysis of financial markets. 

By applying some courses simultaneously toward the requirements for the Bachelor of Arts degree and a Master of Arts degree, an advanced student can qualify for both degrees during the four years of undergraduate study. Admission to the BA/MA Program is by the standard graduate application form, completed and submitted no later than April 30 of the undergraduate student’s junior year of study. With the application, the applicant must supply an official copy of the current transcript and a statement of purpose. The GRE exams are not required, and the graduate application fee is waived. In addition, the applicant must have one member of the faculty of the Department of Mathematics submit a letter of recommendation.