MTH 235, Linear Algebra

Note: If this course is being taught this semester, more information can be found at the course home page.

Cross Listed

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Prerequisites

MTH 165. Note that MTH 163 (ordinary differential equations) is NOT a sufficient prerequisite for MTH 235. Take MTH 165 instead.

This course is a prerequisite or co-requisite for

MTH 236, MTH 248, MTH 253, MTH 255, MTH 263, MTH 265, MTH 280

Description

This is usually the first mathematics course which uses a more mathematically sophisticated approach than that found in the calculus courses. The notions of linear algebra are fundamental in almost all higher mathematics. In calculus courses the concept of a function is what one arrives at after studying graphs and simple mechanical motion in physics and stripping away the information which is not essential to doing calculations.The concepts of a vector space, linearity and so forth found in MTH 235 (linear algebra) are what comes of stripping away the unnecessary information involved in solving simultaneous equations, studying systems of differential equations, higher order differential equations, multivariable calculus, as well as the physics of three (or four) dimensional space and advanced econometrics models. Just as a function is a higher level of abstraction than the quantity the function represents, vector spaces are more abstract than the functions, equations, or physical or economic situations which they represent.

Topics covered

Finite-dimensional vector spaces over R (real numbers) and C (complex numbers) presented from two view points: axiomatically and with coordinate calculations. Forms, linear transformations, matrices, eigenspaces.

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