# AMATH 840: Advanced Numerical Methods for Computational and Data Sciences

Winter

## Offered:

2022

Course Description: The course will present some computational and mathematical perspectives of machine learning and data science. We will discuss some theoretical results as well as have some programming experiences. Tentative topics for Winter 2022 are Sparse Optimization and Compressed Sensing, Supervised Learning and Kernel Methods, Neural Networks, and Randomized Linear Algebra. More details can be found in the course outline (attached below).

Lectures Information:

• From Jan 5th to Feb 4th: Monday &...

# Math 146: Linear Algebra 1 (Advanced Level)

Winter

## Offered:

2021
MATH 146 is an advanced-level version of MATH 136. Topics includes vector spaces, linear dependence and span, bases and dimension, linear transformations, rank, change of coordinate matrices, and system of linear equations. We also discuss various topics of matrices such as rank, determinants, eigenvalues and eigenvectors, characteristic polynomial, and diagonalization.  Read more about Math 146: Linear Algebra 1 (Advanced Level)

# Math 138: Calculus II for Honours Mathematics

Winter

## Offered:

2021
Introduction to the Riemann integral and approximations. Antiderivatives and the fundamental theorem of calculus. Change of variables, methods of integration. Applications of the integral. Improper integrals. Linear and separable differential equations and applications. Tests for convergence for series. Binomial series, functions defined as power series and Taylor series. Vector (parametric) curves in R2. Suitable topics are illustrated using computer software. Read more about Math 138: Calculus II for Honours Mathematics

# AMATH 731: Applied Functional Analysis

Fall

## Offered:

2020
This is a core course for graduate students in Applied Mathematics. It will also be of interest to students in Engineering and Science who wish to understand and use methods from functional analysis. Basic concepts from functional analysis are introduced and illustrated with applications in various areas such as numerical analysis, control theory, boundary value problems for PDEs, and optimization. Read more about AMATH 731: Applied Functional Analysis

# MATH 235: Linear Algebra 2

Winter

## Offered:

2020

Topics include orthogonal and unitary matrices and transformations; orthogonal projections; the Gram-Schmidt procedure; and best approximations and the method of least squares. Inner products; angles and orthogonality; orthogonal diagonalization; singular value decomposition; and other applications will also be explored.

# MATH 146: Linear Algebra 1 (Advanced Level)

Winter

## Offered:

2020

MATH 146 is an advanced-level version of MATH 136. Topics includes vector spaces, linear dependence and span, bases and dimension, linear transformations, rank, change of coordinate matrices, and system of linear equations. We also discuss various topics of matrices such as rank, determinants, eigenvalues and eigenvectors, characteristic polynomial, and diagonalization.

# Math 235: Linear Algebra 2

Winter

## Offered:

2019

Topics include orthogonal and unitary matrices and transformations; orthogonal projections; the Gram-Schmidt procedure; and best approximations and the method of least squares. Inner products; angles and orthogonality; orthogonal diagonalization; singular value decomposition; and other applications will also be explored.

# AMATH 731: Applied Functional Analysis

Fall

## Offered:

2019

This is a core course for graduate students in Applied Mathematics. It will also be of interest to students in Engineering and Science who wish to understand and use methods from functional analysis. Basic concepts from functional analysis are introduced and illustrated with applications in various areas such as numerical analysis, control theory, boundary value problems for PDEs, and optimization.

# Math 136: Linear Algebra 1

Winter

## Offered:

2018

Topics include systems of linear equations, matrix algebra, elementary matrices, and computational issues. Other areas of the course focus on the real n-space, vector spaces and subspaces, basis and dimension, rank of a matrix, linear transformations and matrix representations. Determinants, eigenvalues and diagonalization, and their applications are also explored.

# Math 235: Linear Algebra 2

Winter

## Offered:

2018

Topics include orthogonal and unitary matrices and transformations; orthogonal projections; the Gram-Schmidt procedure; and best approximations and the method of least squares. Inner products; angles and orthogonality; orthogonal diagonalization; singular value decomposition; and other applications will also be explored.

# Math 348: Scientific Computation in Numerical Analysis @ UT Austin

Spring

## Offered:

2017

This course gives an introduction to numerical methods and their applications in computational science and engineering. It presents various numerical methods, discusses their mathematical properties, and provides practice in scientific computer programming. The main topics include computer arithmetic, nonlinear algebraic equations, polynomial interpolation, numerical differentiation and integration, initial-value problems for ordinary differential equations, and direct methods for solving linear systems.

Read more about Math 348: Scientific Computation in Numerical Analysis @ UT Austin

# Math 373K: Algebraic Structures I @ UT Austin

Fall

## Offered:

2017

This course is a rigorous course in pure mathematics. The syllabus for the course includes topics in the theory of groups and rings. The study of group theory includes normal subgroups, quotient groups, homomorphisms, permutation groups, the Sylow theorems, and the structure theorem for finite abelian groups. The topics in ring theory include ideals, quotient rings, the quotient field of an integral domain, Euclidean rings, and polynomial rings.