Mathematics: Applied Linear Algebra

Vectors, matrices, linear independence, vector spaces (with focus on real n-space), determinants, linear transformations, eigenvalues and eigenvectors. Applications from engineering and the sciences incorporated through required computer assignments. Credit not given for both MATH 2522 and MATH 2544. Prerequisite: MATH 1248 or MATH 1242.

Prereqs enforced by the system: MATH 1248 or MATH 1242; Open to Degree and PACE students

Course Description: Vectors, matrices, linear independence, vector spaces (with focus on real n-space), determinants, linear transformations, eigenvalues and eigenvectors. Applications from engineering and the sciences incorporated through required computer assignments. Credit not given for both MATH 122 and MATH 124. Prerequisite: MATH 022 or MATH 023. Credits 3.0; Detailed list of topics: Matrices and Systems of Linear Equations, Echelon Form and Gauss-Jordan Elimination, Vector Spaces and Subspaces (with focus on real n-space), Linear Independence in real n-space, Bases and Dimensions, Curve Fitting, Traffic Flow, Addition, Scalar Multiplication, and Matrix Multiplication, Symmetric Matrices and Trace, Inverse of a Matrix, Matrix Transformations, Rotations, Dilations, Linear Transformations and Computer Graphics, Markov Chains and Population Movements, A Communication Model (Digraphs), Determinants and Properties of Determinants, Eigenvectors and Eigenvalues, Demography, Weather Prediction Example, and Leslie Matrix Models, The Column Space, Rank, and the Rank-Nullity Theorem, One-to-One Transformations and Inverse Transformations, Dot Product, Norm, Angle, Distance, Least Squares

Topics will be presented with a level of depth and rigor appropriate for students pursuing degrees in technical fields such as mathematics, statistics, engineering, or the physical sciences. Materials: WebAssign access for Linear Algebra with Applications, 9th edition, by Garreth Williams ISBN 1284154696 . WebAssign includes access to an e-text, as well as homework exercises. Matlab Assignments: No prior experience with Matlab is assumed. Matlab is used throughout the course and is available on the UVM CEMS computers. It can be downloaded to your computer (for free): https://www.uvm.edu/cems/installing_matlab_students

Weekly homework, 5 Matlab assignments, 6 quizzes, 2 midterms and 1 final exam