Students will learn fundamental principles of quantum mechanics, master mathematical details of atomic wavefunctions (especially for Hydrogen-like atoms), understand quantum mechanical treatment of angular momentum and spin, and know how to obtain atomic term symbols.

Introduction to variational methods; many-electron systems; semi-empirical methods; perturbation theory; computational methods.

Discrete Optimization II is a generic name for COMM 618; a more precise name for this edition of COMM 618 is Combinatorial Optimization.
In this class, we will study optimization problems with discrete variables. The purpose of this class is three-fold:
1. Describe various discrete optimization problems, along their applications.
2. Explore methods for solving various discrete optimization problems.
3. Discuss optimality certificates and duality in order to describe what seems to make a problem
`easy’ or `hard’.

This course is proof based.

This is a graduate-level topics course in quantum computation but assumes no prior knowledge of quantum information. The main focus will be on quantum algorithms and introducing open research problems.

Tentative list of topics:

- Simon's problem: quantum upper bound, classical lower bound
- Factoring: Shor's algorithm, Regev's optimization
- Grover's algorithm and its applications to the collision problem, graph problems, and dynamic programming
- Quantum walk and its applications to the element distinctness problem and glued-trees problem
- Hidden subgroup problem, Kuperberg's algorithm for the dihedral hidden subgroup problem
- Polynomial method and its application to symmetric functions
- Adversary method and its applications to total functions, AND-OR trees, and divide and conquer algorithms
- Direct reduction from polynomial method to adversary method
- Recording queries method and its application to average-case k-search
- Average-case complexity: Aaronson-Ambainis conjecture, Yamakawa-Zhandry problem
- Quantum signal processing and its applications to linear systems, quantum simulation, and ground state problems
- Quantum communication complexity: quantum fingerprinting, Holevo's theorem
- Quantum advantage from non-local games
- Classical simulation and dequantizing of quantum algorithms

Submodular set functions have played a central role in the development of combinatorial optimization and could be viewed as the discrete analogue of convex functions. Submodularity has also been a useful model in areas such as economics, supply chain management and recently algorithmic game theory and machine learning. There has been a huge amount of work recently in approximation algorithms for various constrained submodular optimization models arising in practice, perhaps most prominently the social welfare maximization problem. We develop the basic properties of submodular functions and then present both classical methods and recent trends. Topics include: algorithms for unconstrained submodular maximization and minimization, polymatroids, local greedy algorithms, multilinear extensions and pipage rounding, Lovasz Extension and convex minimization, matroid constraints, multi-agent optimization, and many applications.


The course will be more theoretically focused as opposed to numerical. Hence a reasonable mathematical background (say in linear algebra) is recommended.

Convex optimization is a key tool for analyzing and modeling a range of computational problems that arise in machine learning, signal and image processing, theoretical computer science, operations and logistics, and other fields. It’s also the backbone for other areas of optimization, including algorithms for nonconvex problems. This course aims to provide a self-contained introduction to a few of the many geometric and intuitive ideas in convex analysis and their usefulness for understanding and developing computationally-efficient algorithms for a range of scientific and engineering problems.

We introduce basic principles and techniques in the fields of data mining and machine learning. These techniques are now running behind the scenes to discover patterns and make predictions in various applications in our daily lives. We will focus on many of the core data mining and machine learning technologies, with motivating applications from a variety of disciplines.

(This course used to be called CPSC 532M, the course previously labeled CPSC 540 is now CPSC 440.)

Lectures offered at either:
12-1pm (Monday/Wednesday/Friday in Friedman Building 153)
4-5pm (Monday/Wednesday/Friday in MacLeod 2018)

In recent years deep learning has modified and continue to change the field of inverse problems.

In this course we will cover classical techniques for parameter estimation, regularization techniques and continue with deep learning techniques for inverse problems from generative models to learned regilarization operators

The purpose of this course is to a) introduce the student to the dynamical principles governing the large-scale, low-frequency motions in strongly rotating fluid systems (like the ocean, atmosphere, and liquid planetary core) and their consequences, and b) to develop the skills required to manipulate and use these principles to solve problems.

Schedule not set until beginning of term, but likely as stated.

Max/min problems in which the choice variable is a function of one real variable.

The classical theory as developed from Bernoulli and Euler to the present will be developed, with careful attention to both theoretical precision and practical consequences.

Officially, "Classical variational problems; necessary conditions of Euler, Weierstrass, Legendre, and Jacobi; Erdmann corner conditions, transversality, convex Lagrangians, fields of extremals, sufficient conditions for optimality, numerical methods; applications to classical mechanics, engineering and economics"

Partial differential equations (PDEs) model a vast range of problems from physics, chemistry, biology, engineering, meteorology, statistics, mathematical finance and many more disciplines. Virtually all real-life problems are too complex to be solved analytically and require numerical techniques such as finite differences, finite elements, finite volumes, spectral methods or even deep neural networks.

This course will be focused primarily on finite element methods, spanning theory, algorithms and implementation. It will to foster development of analytical, computational and professional skills. We will not only study how to solve PDEs numerically and how to assess the quality of the results, but also how to apply these skills in a mini research project, and practice communication skills by presenting the results in oral and written form.

This course gives students an overview of Non-Newtonian Fluid Dynamics, and discusses continuum and kinetic approaches to building constitutive models for complex fluids.

Evolution is the unifying theme in biology. Cooperation represents one of the key organizing principles in evolution. The history of life and of societies could not have unfolded without the repeated cooperative integration of lower level units into higher level entities. Cultural evolution follows the same basic selection principle as biological evolution but the lack of the genetic constraints of mutation, recombination and inheritance results in a largely unexplored dynamics governed by the more flexible mechanisms of innovation, learning and imitation.

This course provides an introduction into mathematical models of evolution and the theory of games. Modelling techniques that are covered include: stochastic dynamics of invasion and fixation of mutants in finite populations; evolutionary game theory; adaptive dynamics and the process of diversification and speciation through evolutionary branching; as well as modelling spatially structured populations.

Links to current challenges in research are emphasized by discussions of the literature as well as student presentations and by identifying research questions for term projects. All students develop their own project in consultation with the instructor. At the end of the term, all students present their project to the class, hand in a project report and participate in a peer review process.

MATH 605E, Section 201
The purpose of this graduate course is to equip graduate students with cutting-edge
techniques in data-driven mathematical and computational modelling, analysis
and simulations of semi-linear parabolic partial differential equations (PDEs) of
reaction-diffusion type. It will cover diverse areas in data-driven modelling using
PDEs in biology. I will cover approaches on formulating models from data using
first principles, mathematical analysis of reaction-diffusion systems such as linear
stability analysis, basic concepts on bifurcation analysis and numerical bifurcation
analysis. The second part will focus on numerical methods for PDEs including finite
difference methods, and finite elements. This part will also deal with time-stepping
schemes and nonlinear solvers for nonlinear PDEs. If time allows, we will look at
applications of reaction-diffusion theory to cell motility and pattern formation.
To support theoretical modelling and numerical analysis, numerical algorithms
will be developed and implemented in MATLAB as well as in open finite element
source software packages such as FeNiCs, deal.ii and others. Students will be allowed
to use packages of their choice as appropriate.

This course will introduce the major tools in stochastic analysis from an applied mathematics perspective. Topics to be covered include Markov chains (both discrete and continuous), Gaussian processes, Ito calculus, stochastic differential equations (SDEs), numerical algorithms for solving SDEs, forward and backward Kolmogorov equations and their applications. It will pay particular attention to the connection between stochastic processes and PDEs, as well as to physical principles and applications. The class will attempt to strike a balance between rigour and heuristic arguments: it will assume that students have seen a little analysis, particularly in the context of studying PDEs, but will generally avoid measure theory. The target audience is graduate students in applied mathematics or related fields, who wish to use these tools in their research for modelling or simulation.

Prerequisites include good upper-level undergraduate or early graduate knowledge of: probability, linear algebra, PDEs, and ODEs. Some prior experience with numerical analysis is helpful but not necessary.

Homework will be a critical part of the course, and will include some programming assignments.

Notes from previous versions of the course can be found here: https://personal.math.ubc.ca/~holmescerfon/teaching.html#asanotes

This is a list of topics that are covered in the course.

Continuum description of solids, Deformation Gradient and Stress and Strain measures, Equilibrium Equations, Linear Elasticity problems in small deformations, Constitutive Equations: Isotropic and Anisotropic Linear Elastic Materials, Resolution Strategies for Elasticity problems, Wave propagation and high strain rate testing of materials.

Statistical mechanics of second order phase transitions, solvable models, the renormalization group, elementary conformal field theory and the conformal bootstrap.

Basic group and representation theory with applications in physics