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This course on linear algebra with a focus on geometry aims to explore the connections between linear algebra and various geometries, replacing Euclid's axiomatic approach with more solid definitions and proofs. The course adopts a more algebraic approach, utilizing ideas from Rational Trigonometry and emphasizing the role of the dot product. The learning outcomes include understanding the connections between linear algebra and Euclidean geometry, as well as exploring foundational concepts like Pythagoras' theorem and perpendicularity. The course teaches skills in applying linear algebra to geometrical problems and aims to provide a deeper understanding of the relationship between algebra and geometry. The teaching method involves lectures and discussions, with a focus on theoretical concepts and practical applications. The intended audience for this course includes students and professionals interested in mathematics, geometry, and linear algebra.
