• Maria Cameron Receives the 2024 MURI Award

    Congratulations to Maria Cameron for her MURI award. MURI are multidisciplinary university research initiative grants that are awarded by the department of defense. Cameron’s grant is sponsored by the office of naval research. Her team includes Balakumar Balachandran (ME) and Miao Yu (ME). This is a project on “disorder-influenced collective Read More
  • A $27.2M Gift to the Math Department by the Brin Family

    The university announced today a big gift to the Math Department. The very generous gift of $27.2M was made by Michael & Eugenia Brin. The gift will endow the Brin Mathematics Research Center, establish an endowed chair, and launch a summer camp for high school students. The official university’s press Read More
  • 2023 Putnam Competition Result

    We very excited to report that our Putnam team ranked 8th, honorable mention, among 471 institutions in the 2023 Putnam math competition.Our team members this year were Vincent Trang, Daniel Yuan, Omar Habibullah, and Andrew Parker.Vincent Trang ranked 43rd and Daniel Yuan ranked 64th among 3,857 participants. Read More
  • Simons Fellows - Darvas, Kanigowski, Rubinstein

    Congratulations to Tamas Darvas, Adam Kanigowski, and Yanir Rubinstein for being named Simons Fellows. Read More
  • Doron Levy is elected 2024 Class of Fellows of the AMS

    Congratulations to Dr. Doron Levy, as Fellow of the American Mathematical Society, Class of 2024 (https://www.ams.org/cgi-bin/fellows/fellows_by_year.cgi)!  Dr. Levy was elected  ``For his contributions to Mathematical Oncology and Mathematical Biology".  Read More
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Description

The course provides an introduction to linear algebra and matrix theory. It is intended primarily for engineering students. This course cannot be used toward the upper level math requirements for MATH/STAT majors. Credit will be granted for only one of the following: MATH 240, MATH 341, or MATH 461.

Prerequisites

MATH 141 and one MATH/STAT course for which MATH 141 is a prerequisite.

Topics

Systems of Linear Equations

Gaussian elimination
Echelon forms
Existence and uniqueness of solutions
Homogeneous systems

Matrices

Addition, scalar multiplication, multiplication of matrices
Elementary matrices and inversion
LU decomposition
Systems of linear equations as matrix equations
*Partitioned matrices
Determinants and their properties
Cramer's rule

Vector Spaces

Subspaces and spanning sets
Linear independence
Basis and dimension
Row and column spaces of a matrix
Rank of a matrix
Null space of a matrix

Linear Transformations

Kernel and range
Matrix representation
Change of basis and similarity of matrices

Scalar Products and Orthogonality

Cauchy-Schwarz and triangle inequalities
Length and angles
Pythagorean theorem
Orthonormal sets
Orthogonal complements of the null space and column space
Orthogonal projection
Least squares problems
Orthogonal matrices
Gram-Schmidt process and QR factorization

Eigenvalues

Complex eigenvalues
Diagonalization of matrices
Spectral theorem for symmetric (*hermitian) matrices
*Quadratic forms
Positive definite matrices
*Nonnegative matrices

Applications to include several of the following:

*Liontief Input-Output Model
*Markov Chains
*Computer Graphics
*Least squares data fitting
*Fourier Series
*Systems of Differential Equations
*Difference Equations
*Max-Min Theory for functions of several variables (Hessian Matrix)

MATLAB use

In assigned homework through the semester

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