Program Overview

Quantitative Studies for Finance Certificate

The Quantitative Studies for Finance program is designed for college graduates who have some background in mathematics and statistics and want graduate school preparation in the mathematics and statistics of finance and financial engineering, or are interested in a career change. The program includes a structured curriculum developed with the Departments of Mathematics and Statistics.

Program Overview

The program is part of the Columbia University School of Professional Studies. Students are required to maintain an overall minimum GPA of 3.0 (B). Every course creditable toward the certificate must be taken for a letter grade. Courses with a grade of P or below a C will not count toward the completion of the certificate.

Curriculum and Courses

The program includes the following courses:

• Calculus Courses (2 Courses)
  • Calculus II: Methods of integration, applications of the integral, Taylor's theorem, infinite series.
    • Course Number: MATH UN1102
    • Format: In Person
    • Points: 3
    • Prerequisite: MATH UN1101 or the equivalent.
  • Calculus III: Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramer's rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers.
    • Course Number: MATH UN1201
    • Format: In Person
    • Points: 3
    • Prerequisite: MATH UN1101 or the equivalent
• Advanced Mathematics Courses (Choose 4 Courses)
  • Linear Algebra: Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications.
    • Course Number: MATH UN2010
    • Format: In Person
    • Points: 3
    • Prerequisite: MATH UN1201 or the equivalent
  • Ordinary Differential Equations: Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications.
    • Course Number: MATH UN2030
    • Format: In Person
    • Points: 3
    • Prerequisite: MATH UN1102 and MATH UN1201 or the equivalent
  • Partial Differential Equations: Topics of linear and non-linear partial differential equations of second order, with particular emphasis to Elliptic and Parabolic equations and modern approaches.
    • Course Number: MATH GR8210
    • Format: In Person
    • Points: 4
    • Prerequisite: MATH GR8209
  • Analysis and Optimization: Mathematical methods for economics. Quadratic forms, Hessian, implicit functions. Convex sets, convex functions. Optimization, constrained optimization, Kuhn-Tucker conditions. Elements of the calculus of variations and optimal control.
    • Course Number: MATH UN2500
    • Format: In Person
    • Points: 3
    • Prerequisite: MATH UN1102 and MATH UN1201 or the equivalent and MATH UN2010
  • Introduction to Modern Analysis I: The second term of this course may not be taken without the first. Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces.
    • Course Number: MATH GU4061
    • Format: In Person
    • Points: 3
    • Prerequisite: MATH UN1202 or the equivalent, and MATH UN2010
• Statistics Courses (Choose 1 Course)
  • Introduction to Probability and Statistics: Introduction to Probability and Statistics
    • Course Number: STAT GU4001
    • Format: In Person
  • Probability Theory: Probability is the foundation on which statistics is built. The purposes of this course are 1) to introduce you to probability and 2) prepare you to take a sequel course on statistical inference.
    • Course Number: STAT GU4203
    • Format: In Person
    • Points: 3
    • Prerequisite: This is a master's level class. A solid grounding in calculus (including multivariable calculus) and linear algebra is minimally presupposed; of course, more mathematics is even better.
  • Statistical Inference: The aim of the course is to describe the two aspects of statistics {estimation and inference {in some details.
    • Course Number: STAT GU4204
    • Format: In Person
    • Points: 3
    • Prerequisite: GU4203 or GR5203, and a good working knowledge of single-variable calculus is necessary: differentiation, integration, infinite sums, Taylor expansions, limits.
• Computer Science Course
  • Programming in JAVA: This course is a foundation course for learning software programming using the Java language.
    • Course Number: SPMG PS5170
    • Format: In Person
    • Points: 3

Admissions

The program is designed for college graduates who have some background in mathematics and statistics. Students are required to maintain an overall minimum GPA of 3.0 (B). Every course creditable toward the certificate must be taken for a letter grade. Courses with a grade of P or below a C will not count toward the completion of the certificate.