Linear Algebra and Calculus
Fundamental concepts in Linear Algebra and Calculus: vectors, matrices, linear systems, functions, limits, differentiation, eigenvalues, and diagonalization.
Learning objectives
Upon completion of the course, students will: Demonstrate a solid comprehension of fundamental concepts in Linear Algebra and Calculus, including vectors, matrices, linear systems, functions, limits and differentiation (Knowledge and Understanding). Apply mathematical techniques to solve basic exercises and problems across different levels of complexity within Linear Algebra and Calculus, such as solving linear systems or diagonalization, showcasing proficiency in computations and problem-solving strategies (Applying Knowledge and Understanding). Engage in rigorous mathematical reasoning by providing proofs of statements and theorems, and by explaining underlying concepts and principles (Applying Knowledge and Understanding; Making Judgments). Develop the ability to articulate mathematical solutions and explanations effectively, engaging clear communication of mathematical concepts (Communication Skills). Cultivate learning skills necessary for further study in mathematics and AI, including the ability to independently explore advanced topics, identify areas for improvement, and pursue self-directed learning opportunities (Learning Skills).
Calculus: Functions Limits Derivatives Partial derivatives Gradients Linear Algebra: Linear systems of equations Row reduction Linear maps Matrix and vectors operations Vector spaces Determinants Eigenvalues, eigenvectors and diagonalization Inner product, orthogonalization and Gram Schmidt
Assessment
Optional calculus midterm (30%) and final exam (70% or 100% if midterm skipped). The final exam covers both calculus and linear algebra. There is a resit exam with mandatory calculus (30%) + linear algebra (70%). Must achieve 5.5 average to pass.
Teaching methods
Lectures twice per week with tutorials. Incomplete notes are provided during lectures to encourage active participation — complete notes are available afterwards.
Literature
Adams & Essex, Calculus: A Complete Course (9th Edition). Lay, Lay & McDonald, Linear Algebra and its Applications (6th Edition).