Learn Linear Algebra – Theory of Everything! Master the techniques and theories of linear algebra.
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This specialization includes a series of three courses that will cover the core topics of undergraduate-level linear algebra. Simply put, linear algebra is the branch of mathematics that deals with vectors, matrices, lines, and the areas and spaces they create. These concepts form the basis of almost every industry and discipline, which is why linear algebra is informally called the “sink of everything.”
Upon completion of the internship, students will be prepared for advanced topics in data science, artificial intelligence, machine learning, finance, mathematics, computer science, or economics.
Students will have the opportunity to complete special projects during the course. The projects involve the exploration of advanced topics in mathematics and their relevant applications.
This is the first of three courses in the Linear Algebra Specialization, which introduces students to the fundamental concepts of the field, which is one of the most important areas of mathematics and has many practical applications. The core course material provides both theory and applications to topics in mathematics, engineering, and science. The content focuses on linear equations, matrix methods, analytic geometry, and linear transformations. In addition to mastering the techniques, students will also be exposed to the more abstract ideas of linear algebra. Lectures, readings, quizzes, and a project help students master the course content and learn to read, write, and even correct mathematical proofs. By the end of the course, students will be fluent in the language of linear algebra, learning new definitions and correspondences with examples and counterexamples. Students will also learn to use the techniques to sort and solve linear systems of equations. This course prepares students to continue their studies in linear transformations in the next course in the specialization.
This course is the second course in the Linear Algebra specialization. In this course, we will continue to develop the techniques and theory to study matrices as special linear transformations (functions) on vectors. In particular, we will develop techniques to manipulate matrices algebraically. This will allow us to better analyze and solve systems of linear equations. Moreover, the definitions and descriptions presented in the course allow us to identify the properties of an invertible matrix, to identify relevant subspaces in R^n. Next, we will focus on the geometry of matrix transformations by studying eigenvalues and eigenvectors of matrices. These numbers are useful for both pure and practical concepts in mathematics, data science, machine learning, artificial intelligence, and dynamical systems. We will see an application of Markov chains and the Google PageRank algorithm at the end of the course.
This is the third and final course in the Linear Algebra specialization that focuses on the theory and computations that arise from working with orthogonal vectors. This includes the study of orthogonal transformations, orthogonal bases, and orthogonal transformations. The course culminates in the theory of symmetric matrices, relating their algebraic properties to their geometric counterparts. These matrices appear more frequently in applications than any other type of matrix. The theory, skills, and techniques taught in this course have applications in artificial intelligence and machine learning. In these popular fields, the driving force behind systems that interpret, train, and use external data is precisely the matrix analysis that emerges from the content in this course.
Successful completion of this specialization will prepare students to take advanced courses in data science, artificial intelligence, and mathematics.
