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ABOUT THE COURSE:
This course starts with a reasonably detailed review of linear algebra and topology in Rn. Then we shall cover multivariable differential calculus. We shall also introduce manifolds via the implicit function theorem. We shall then cover an application or two to Optimisation/AI/ML – namely gradient descent (the continuous and discrete versions) and the backpropagation algorithm. The next few weeks will deal with ordinary differential equations, in particular solving linear systems, and existence (and dependence on parameters) theory for nonlinear ones. The latter part involves concepts of multivariable calculus. The course is meant for students of pure and applied mathematics, AI, CS, physics, and engineering.
INTENDED AUDIENCE: Undergraduates and Graduate students of mathematics, computer science, physics, and engineering
PREREQUISITES: One-variable real analysis (at the level of Rudin or Terence Tao, including metric spaces), Linear algebra (up to and including diagonalisation of Hermitian matrices).
INDUSTRY SUPPORT: Microsoft Research, Open AI, DeepMind
This course starts with a reasonably detailed review of linear algebra and topology in Rn. Then we shall cover multivariable differential calculus. We shall also introduce manifolds via the implicit function theorem. We shall then cover an application or two to Optimisation/AI/ML – namely gradient descent (the continuous and discrete versions) and the backpropagation algorithm. The next few weeks will deal with ordinary differential equations, in particular solving linear systems, and existence (and dependence on parameters) theory for nonlinear ones. The latter part involves concepts of multivariable calculus. The course is meant for students of pure and applied mathematics, AI, CS, physics, and engineering.
INTENDED AUDIENCE: Undergraduates and Graduate students of mathematics, computer science, physics, and engineering
PREREQUISITES: One-variable real analysis (at the level of Rudin or Terence Tao, including metric spaces), Linear algebra (up to and including diagonalisation of Hermitian matrices).
INDUSTRY SUPPORT: Microsoft Research, Open AI, DeepMind
