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# Graduate Courses

## FEATURED COURSES [SPRING 2022]

**MATH 800 - Introduction to Complex Geometry**

In this introductory course, we will begin by learning the necessary basics of multivariate complex analysis. Armed with a good understanding of the local situation, we will then begin our study of complex manifolds. Topics discussed will include differential forms, (almost) complex structures, sheaves, and vector bundles.

## Featured Course [Summer 2021]

**APMA 940 - Mathematics of Data Science**

Theory and algorithms for problems in data science with an emphasis on mathematical aspects. Topics may include dimension reduction, supervised learning, including regression and classification, unsupervised learning, including clustering and latent variable modeling, deep learning, algorithms for big data, and foundations of learning.

## Featured Courses [Spring 2021]

**APMA 930 - Computational Fluid Dynamics**

Basic equations governing compressible and incompressible fluid mechanics. Finite difference and finite volume schemes for hyperbolic, elliptic, and parabolic partial differential equations. Practical applications in low Reynolds number flow, high-speed gas dynamics, and porous media flow. Software design and use of public-domain codes. Students with credit for MATH 930 may not complete this course for further credit.

How do we represent formulas on a computer? How fast can we multiply integers and polynomials? Can we factor polynomials in polynomial time? This course is about computing with mathematical objects symbolically. This includes numbers, polynomials, and elementary functions.

**MATH 740 - Galois Theory (cross-listed with MATH 440)**

Galois theory studies roots of polynomial equations, combining field theory and group theory to study symmetries of these equations. Famously, these ideas led to a proof that (unlike the quadratic formula for degree-2 polynomials) no formula exists to solve polynomial equations of degree 5 or more. Proving this theorem is one goal of this class.

**APMA 990 - Complex Analysis**

Complex analysis is a subject whose importance has a broad reach within mathematics. This course will revisit the foundations of the study of analytic functions, as well as aim to demonstrate the reach of complex analysis over a wide scope of theoretical, calculational, geometrical and computational questions in mathematics. Special topics may include the Riemann mapping theorem, conformal mapping and Fourier integral theory.

## Featured Courses [Fall 2020]

**APMA 920 - Numerical Linear Algebra**

The course is aimed at students interested in scientific computing and modeling. We will cover a variety of topics in numerical linear algebra and its applications with an emphasis on understanding stability (robustness) and speed. We will develop, analyze and implement a range of algorithms and see how they work in practice and theory. We program and test our methods in Matlab – almost no prior knowledge is assumed.

**MATH 708 - Discrete Optimization (cross-listed with MATH 408)**

Discrete optimization is a field that has grown almost from scratch in the past 70 years. This development is driven in part from its applicability to a wide range of practical problems, such as scheduling and network design, and its close ties to computer science. However, it is also a beautiful mathematical topic that connects to diverse areas of mathematics, including classical problems in combinatorics, algebra and geometry.

**MATH 747 - Coding Theory (cross-listed with MATH 447)**

How did the Mariner 9 space probe transmit high-resolution photos of Mars to Earth 50 years ago? How can a compact disc play back music perfectly even after the disc surface is damaged? How do cellphones maintain call quality despite signal reflections from buildings and noise from other calls? Explore the hidden mathematics behind modern communications.

## SFU Calendar Listings

**Mathematics 600-Level Courses**

MATH 603-4: Foundations of Mathematics *

MATH 604-4: Geometry *

** These courses cannot be taken toward Mathematics MSc or PhD program requirements*

**Mathematics 700-Level Courses**

MATH 701-3: Computer Algebra

MATH 708-3: Discrete Optimization

MATH 709-3: Numerical Linear Algebra and Optimization

MATH 716-3: Numerical Analysis II

MATH 718-3: Partial Differential Equations

MATH 719-3: Linear Analysis

MATH 724-3: Applications of Complex Analysis

MATH 725-3: Real Analysis

MATH 739-3: Algebraic Systems

MATH 740-3: Galois Theory

MATH 741-3: Commutative Algebra and Algebraic Geometry

MATH 742-3: Cryptography

MATH 743-3: Combinatorial Theory

MATH 745-3: Graph Theory

MATH 747-3: Coding Theory

MATH 748-3: Network Flows

MATH 761-3: Continuous Mathematical Models

MATH 762-3: Fluid Dynamics

MATH 767-3: Dynamical Systems

MATH 770-3: Variational Calculus

MATH 795-3: Selected Topics in Applied Mathematics

MATH 796-3: Selected Topics in Mathematics

**Mathematics 800-Level Courses**

MATH 800-4: Mathematics: Selected Topics

MATH 801-4: Computer Algebra

MATH 808-4: Advanced Linear Programming

MATH 817-4: Groups and Rings

MATH 818-4: Algebra and Geometry

MATH 819-4: Algebra: Selected Topics

MATH 820-4: Graph Theory

MATH 821-4: Combinatorics

MATH 827-4: Discrete Mathematics: Selected Topics

MATH 831-4: Real Analysis I

MATH 833-4: Analysis: Selected Topics

MATH 841-4: Topology: Selected Topics

MATH 842-4: Algebraic Number Theory

MATH 843-4: Analytic and Diophantine Number Theory

MATH 845-4: Number Theory: Selected Topics

MATH 846-4: Cryptography

MATH 875-0: PhD Preliminary Examination

> *Resources*

MATH 876-0: PhD Comprehensive Examination

> *Resources*

MATH 877-1: Supplementary Reading

MATH 879-0: PhD Thesis Proposal

MATH 880-6: MSc Project

MATH 888-0: Ph.D. Comprehensive Examination: Operations Research

MATH 890-0: Practicum I

MATH 891-0: Practicum II

MATH 894-2: Reading

MATH 895-4: Reading

MATH 898-6: MSc Thesis

MATH 899-12: PhD Thesis

**Mathematics 900-Level Courses: Applied and Computational Mathematics**

APMA 900-4: Asymptotic Analysis of Differential Equations

APMA 901-4: Partial Differential Equations

APMA 905-4: Applied Functional Analysis

APMA 912-4: Advanced Partial Differential Equations

APMA 920-4: Numerical Linear Analysis

APMA 922-4: Numerical Solution of Partial Differential Equations

APMA 923-4: Numerical Methods in Continuous Optimization

APMA 929-4: Selected Topics in Numerical Methods

APMA 930-4: Computational Fluid Dynamics

APMA 934-4: Selected Topics in Fluid Dynamics

APMA 935-4: Analysis and Computation of Models

APMA 939-4: Selected Topics in Mathematical Image Processing

APMA 940-4: Mathematics of Data Science

APMA 981-4: Selected Topics in Continuum Mechanics

APMA 982-4: Selected Topics in Mathematical Physics

APMA 990-4: Selected Topics in Applied Mathematics

APMA 995-0: PhD Oral Candidacy Exam