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Mathematics 460

MATH 460: Linear Algebra

Prerequisites: MATH 152 and MATH 260

Credit Hours: 3

A study of the arithmetic, algebra and properties of vectors and matrices with applications to a variety of mathematical problems.  Topics covered include Euclidean vector spaces, eigenvalues and eigenvectors, abstract vector spaces, linear transformations, change of basis and matrix normal forms.  Applications these properties and techniques are applied to most or all of the following areas: stochastic processes, optimization, multi-variable calculus, and differential equations.

 

Detailed Description of Content of Course

The following topics in Linear Algebra will be covered:

a) Euclidean Vectors Space Properties

b) Determinants, Eigenvalues and Eigenvectors

c) Linear Transformations, Kernel and Range

d) Basis and Dimension, Change of Basis

e) Gram-Schmidt method for orthonormal basis

f) Matrix decomposition

g) Abstract vector spaces and subspaces

Time permitting, the following will be included:

h) Applications to optimization and stochastic processes

i) Applications to multi-variable calculus

j) Applications to the solution of ordinary differential equations

k) Computational aspects of Linear Algebra

 

Detailed Description of Conduct of Course

Most instructors will use the lecture method. Some may require students to solve problems in small groups. If a computational component is included, instructors may require students to use mathematical software and/or graphing calculators.

Goals and Objectives of the Course

1. Students are expected to develop a deeper knowledge base in Linear Algebra, and make connections between multivariable calculus and other areas of mathematics and statistics.

2. Students are expected to develop the skills required to solve theoretical and applied problems in the subject.

 

Assessment Measures

Graded tasks may include tests, quizzes, homework exercises, programs, class participation and attendance.

 

Other Course Information

None

 

Review and Approval

June 4, 2012