• Maryland finishes fourth in the 2022 Putnam competition

     We are very excited to share the news that the University of Maryland Putnam team ranked fourth among 456 institutions in the 2022 Putnam Competition. This is the best result for our team in more than four decades. The first three teams are MIT, Harvard and Stanford. Our team members,… Read More

  • Congratulations to the 2023 elected Fellows of the Association for Women in Mathematics

    Please join me in congratulating Konstantina Trivisa,  Shelby Wilson (PhD, AMSC, 2012), and Kimberly Sellers (MS, 1998) for being elected as 2023 Fellows of the Association for Women in Mathematics. The official citation reads (see https://awm-math.org/ awards/awm-fellows/2023-awm- fellows/) Konstantina Trivisa, University of Maryland For her tireless efforts and dedication to increase diversity in the mathematical… Read More

  • Abba Gumel & Larry Washington elected as Fellows of the American Mathematical Society

    Please join us in congratulating Abba Gumel and Larry Washington for being elected as Fellows of the American Mathematical Society. Abba was noted for his contributions to the mathematical theory of epidemics, applied dynamical systems, and promoting the use of mathematics to help solve global health challenges. Larry was noted… Read More

  • Dmitry Dolgopyat Named Distinguished University Professor

    Congratulations to Dmitry Dolgopyat (Mathematics), Richard Greene (Physics) and Zhanqing Li (AOSC/ESSIC), who have been named Distinguished University Professors—the highest academic honor bestowed by the university. They will be honored at the Faculty and Staff Convocation on September 14, 2022. These faculty members are world-renowned in their fields and it’s wonderful to see their accomplishments recognized by the university in this way. You can… Read More

  • 2022 Interdisciplinary Competition in Modeling (ICM) Results

    Congratulations to Radu Balan and to the UMD Math Modeling teams. The teams participated in the 2022 Interdisciplinary Competition in Modeling (ICM). This year 12100 teams participated in the ICM competition. The results of our two teams are: Team 2228337 (Sally Zhao, Naveen Raman, Clarissa Xia) has been awarded a Honorable Mention for Problem… Read More
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Description

Basic concepts of linear algebra: vector spaces, applications to line and plane geometry, linear equations and matrices, similar matrices, linear transformations, eigenvalues, determinants and quadratic forms. All sections of the course will use the software system MATLAB. Credit will be granted for only one of the following: MATH 240 or MATH 341 or MATH 461.

Prerequisites

MATH 141; or a C- or better in MATH 131

Topics

Systems of Linear Equations

Gaussian elimination
Matrix operations
Finding the inverse
Solution spaces

Determinants

Definition
Evaluation
Minors
Cramer's Rule

Vectors in 2- and 3- space

Geometric and algebraic definitions
Dot product
Projections

Vector Spaces

Euclidean space
Subspaces
Linear independence
Basis and dimension
Row space, rank
Length and angle
Gram-Schmidt
Least squares

Linear Transformations

Definition
Kernel and range
Representation as matrices

Eigenvalues and Eigenvectors

Definition
Diagonalization
Orthogonal diagonalization
Symmetric matrices

Applications

Differential equations
Quadratic forms
Numerical methods

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