Linear algebra may well be the most accessible of all routes into higher mathematics. It requires little more than a foundation in algebra and geometry, yet it supplies powerful tools for solving problems in subjects as diverse as computer science and chemistry, business and biology, engineering and economics, and physics and statistics, to name just a few. Furthermore, linear algebra is the gateway to almost any advanced mathematics course. Calculus, abstract algebra, real analysis, topology, number theory, and many other fields make extensive use of the central concepts of linear algebra: vector spaces and linear transformations.
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Discover that linear algebra is a powerful tool that combines the insights of geometry and algebra. Focus on its central idea of linear transformations, which are functions that are algebraically very simple and that change a space geometrically in modest ways, such as taking parallel lines to parallel lines. Survey the diverse linear phenomena that can be analyzed this way.
Discover that linear algebra is a powerful tool that combines the insights of geometry and algebra. Focus on its central idea of linear transformations, which are functions that are algebraically very simple and that change a space geometrically in modest ways, such as taking parallel lines to parallel lines. Survey the diverse linear phenomena that can be analyzed this way.
Linear algebra may well be the most accessible of all routes into higher mathematics. It requires little more than a foundation in algebra and geometry, yet it supplies powerful tools for solving problems in subjects as diverse as computer science and chemistry, business and biology, engineering and economics, and physics and statistics, to name just a few. Furthermore, linear algebra is the gateway to almost any advanced mathematics course. Calculus, abstract algebra, real analysis, topology, number theory, and many other fields make extensive use of the central concepts of linear algebra: vector spaces and linear transformations.
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