This specialization is a three-course sequence that delves into the main topics of undergraduate linear algebra, a branch of mathematics essential to various industries and disciplines. It assumes no prior knowledge of linear algebra or calculus and covers linear equations, matrices, lines, areas, and spaces.
Throughout the program, an equal emphasis is placed on both algebraic manipulation and geometric understanding of linear algebra concepts. The content gradually progresses from low dimensions to higher dimensions, with a focus on theory, applications, and examples. Upon completion, students will be well-prepared for advanced topics in data science, AI, machine learning, finance, mathematics, computer science, and economics.
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This three-course sequence begins with foundational topics such as linear equations and matrices. It then progresses to explore matrix algebra, determinants, eigenvectors, and concludes with a focus on orthogonal vectors and symmetric matrices.
This first course introduces students to the concepts of linear algebra, focusing on linear equations, matrix methods, analytical geometry, and linear transformations. It provides both theory and applications for topics in mathematics, engineering, and the sciences. Students will also learn to employ techniques to classify and solve linear systems of equations.
In this course, students continue to develop techniques and theory to study matrices as special linear transformations on vectors. Techniques to manipulate matrices algebraically are covered, enabling better analysis and solution of systems of linear equations. The course also explores the geometry of matrix transformations by studying eigenvalues and eigenvectors.
This final course in the specialization focuses on the theory and computations that arise from working with orthogonal vectors. It includes the study of orthogonal transformation, orthogonal bases, and culminates in the theory of symmetric matrices, linking the algebraic properties with their corresponding geometric equivalences. The content has applications to AI and machine learning.
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