Mathematics

Prerequisites: score of 550 on the mathematics portion of the SAT completed within the last year, or the appropriate grade on the General Studies Mathematics Placement Examination. For students who wish to study calculus but do not know analytic geometry. Algebra review, graphs and functions, polynomial functions, rational functions, conic sections, systems of equations in two variables, exponential and logarithmic functions, trigonometric functions and trigonometric identities, applications of trigonometry, sequences, series, and limits.

This course may not be taken for credit after the successful completion of any course in the Calculus sequence.

Prerequisites: (see Courses for First-Year Students). Functions, limits, derivatives, introduction to integrals, or an understanding of pre-calculus will be assumed. (SC)

Prerequisites: (see Courses for First-Year Students). Functions, limits, derivatives, introduction to integrals, or an understanding of pre-calculus will be assumed. (SC)

Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)

Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)

Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)

Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)

Prerequisites: MATH UN1101 or the equivalent Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramers rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)

Prerequisites: MATH UN1101 or the equivalent Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramers rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)

Prerequisites: MATH UN1101 or the equivalent Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramers rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)

Prerequisites: MATH UN1101 or the equivalent Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramers rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)

Prerequisites: MATH UN1101 or the equivalent Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramers rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)

Recitation section for MATH UN1205 - Accelerated Multivariable Calculus.
Students must register for both UN1205 and UN1215.

Recitation section for MATH UN1207 Honors Math A.
Students must register for both UN1207 and UN1217.

Introduction to understanding and writing mathematical proofs. Emphasis on precise thinking and the presentation of mathematical results, both in oral and in written form. Intended for students who are considering majoring in mathematics but wish additional training. CC/GS: Partial Fulfillment of Science Requirement. 

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent. 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.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent and MATH UN2010. 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. (SC)

Majors in Mathematics are offered the opportunity to write an honors senior thesis under the guidance of a faculty member. Interested students should contact a faculty member to determine an appropriate topic, and receive written approval from the faculty advisor and the Director of Undergraduate Studies (faculty sponsorship is limited to full-time instructors on the staff list). Research is conducted primarily during the fall term; the final paper is submitted to the Director of Undergraduate Studies during the subsequent spring term.

MATH UN3994 SENIOR THESIS IN MATHEMATICS I must be taken in the fall term, during which period the student conducts primary research on the agreed topic. An optional continuation course MATH UN3995 SENIOR THESIS IN MATHEMATICS II is available during the spring. The second term of this sequence may not be taken without the first. Registration for the spring continuation course has no impact on the timeline or outcome of the final paper.

Sections of SENIOR THESIS IN MATHEMATICS I and II do NOT count towards the major requirements, with the exception of an advanced written approval by the DUS.

Majors in Mathematics are offered the opportunity to write an honors senior thesis under the guidance of a faculty member. Interested students should contact a faculty member to determine an appropriate topic, and receive written approval from the faculty advisor and the Director of Undergraduate Studies (faculty sponsorship is limited to full-time instructors on the staff list). Research is conducted primarily during the fall term; the final paper is submitted to the Director of Undergraduate Studies during the subsequent spring term.

MATH UN3994 SENIOR THESIS IN MATHEMATICS I must be taken in the fall term, during which period the student conducts primary research on the agreed topic. An optional continuation course MATH UN3995 SENIOR THESIS IN MATHEMATICS II is available during the spring. The second term of this sequence may not be taken without the first. Registration for the spring continuation course has no impact on the timeline or outcome of the final paper.

Sections of SENIOR THESIS IN MATHEMATICS I and II do NOT count towards the major requirements, with the exception of an advanced written approval by the DUS.

Prerequisites: the written permission of the faculty member who agrees to act as a supervisor, and the director of undergraduate studies permission. For specially selected mathematics majors, the opportunity to write a senior thesis on a problem in contemporary mathematics under the supervision of a faculty member.

Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent. The second term of this course may not be taken without the first. Rings, homomorphisms, ideals, integral and Euclidean domains, the division algorithm, principal ideal and unique factorization domains, fields, algebraic and transcendental extensions, splitting fields, finite fields, Galois theory.

Recitation section for MATH GU4041 Intro to Modern Algebra I.
Students must register for both GU4041 and GU4941.

Recitation section for MATH GU4041 Intro to Modern Algebra I.
Students must register for both GU4041 and GU4941.

Recitation section for MATH GU4061 Intro to Modern Analysis I.
Students must register for both GU4061 and GU4961.

Recitation section for MATH GU4061 Intro to Modern Analysis I.
Students must register for both GU4061 and GU4961.

Recitation section for MATH GU4061 Intro to Modern Analysis I.
Students must register for both GU4061 and GU4961.

Recitation section for MATH GU4061 Intro to Modern Analysis I.
Students must register for both GU4061 and GU4961.

Required Prerequisite: Math GR5010 Intro to the Math of Finance (or equivalent). Recommended Prerequisite: Stat GR5264 Stochastic Processes – Applications I (or equivalent).

The objective of this course is to introduce students, from a practitioner’s perspective with formal derivations, to the advanced modeling, pricing and risk management techniques of vanilla and exotic options that are traded on derivatives desks, which goes beyond the classical option pricing courses focusing solely on the theory. It also presents the opportunity to design, implement and backtest vol trading strategies. The course is divided in four parts: Advanced Volatility Modeling; Vanilla and Exotic Options: Structuring, Pricing and Hedging; FX/Rates Components: Discounting, Forward Projection, Quanto and Compo Options; Designing and Backtesting Vol Trading Strategies in Python.

The application of Machine Learning (ML) algorithms in the Financial industry is now commonplace, but still nascent in its potential.  This course prepares the next generation of researchers and practitioners for the coming revolution, providing an advanced "deep dive" into machine learning methods (both theory and application) that are deemed to be useful for financial applications, including trading and investment management.

The course will cover the fundamentals of Algorithmic Trading, the discipline that brings together computer software, and financial markets to open and close trades based on programmed code. The goal of the course is to help the students to get familiar with the different techniques and strategies used in algorithmic trading and to let them experiment with classical and new algorithms they will create.

During the course, the students will use a Trading Market Simulator: The Rotman Market Simulator – a platform which allows students to transact financial securities with each other on a real time basis. Using the simulator, the students will familiarize themselves with specific decision tasks associated with financial securities, market dynamics, and investment or risk management strategies and get ready for the Rotman Competition.

Prerequisites: all 6 MAFN core courses, at least 6 credits of approved electives, and the instructors permission. See the MAFN website for details. This course provides an opportunity for MAFN students to engage in off-campus internships for academic credit that counts towards the degree. Graded by letter grade. Students need to secure an internship and get it approved by the instructor.

A guided reading and research in a specific area of mathematics or applications. This particular section is geared towards supervised readings and research in Mathematical Finance and related fields for Masters’ students.

A student who wishes to undertake individual study under this seminar must present a specific project to a member of the staff and secure this staff member's willingness to act as a sponsor. The course includes written reports and periodic meetings with the instructor.