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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.
Mastering Linear Algebra: An Introduction with Applications is the ideal starting point for this influential branch of mathematics, surveying the traditional topics of a first-semester college course in linear algebra through 24 rigorous half-hour lectures taught by Professor Francis Su of Harvey Mudd College. A multi-award-winning math educator, Professor Su was named “the mathematician who will make you fall in love with numbers” by WIRED magazine.
Linear algebra provides insights into complex phenomena that are part of our daily lives, making them less mysterious and showing the astonishing reach of mathematics in areas such as:
• Computer Graphics: The field of 3-D computer graphics exists because of linear algebra, which transforms shapes in 3-dimensional space by matrix multiplication.
• GPS: A Global Positioning Satellite (GPS) receiver, such as a smartphone, determines its position based on time signals from several satellites. Linear algebra shows how to take this seemingly complicated problem and make it accessible.
• Search Engines: The ability to find information quickly on the internet is a key feature of modern life, and it’s made possible by linear algebra, which keeps track of which nodes on a network are linked, and highlights structures that enable the ranking of important web pages.
• Recommender Systems: Most of us have experienced websites that seem to know more about our tastes than our own family members. The ability of linear algebra to reveal hidden structures lies behind many of these recommender systems.
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