These are review courses. You may not need them if you did other courses in the sessions before this one.

**Complex Analysis –****Tibra Ali**- Lecture 1 – Review of the basics of complex numbers,Â geometrical interpretation in terms of the Argand-Wessel plane. DeMoivre’s theorem and applications. Branch points and branch cuts
- Lecture 2 – Cauchy-Riemann equations. Holomorphic functions and harmonic functions. Contour integration
- Lecture 3 – Cauchy’s integral theorem. integral formula. Taylor and Laurent series. Singularities. Residue theorem
- Lecture 4 -Applications of the residue theorem. Semi-circular contours. Mouse hole contours. Keyhole integrals

**Algebra –****Anna Kostouki**- Lecture 1 – Lie Algebra (vector space, dual basis, matrix representations), the groups Cn and Sn.
- Lecture 2 – The groups O(n), SO(n), U(n), SU(n); Lie groups and Lie algebras; structure constants
- Lecture 3 – Lie algebras: the Adjoint representation, compact, simple and semi-simple Lie Algebras; highest-weight representations of su(2).
- Lecture 4 – The Cartan subalgebra, roots and weights, rank-2 and higher algebras

**Distributions & Special Functions –****Dan Wohns**- Lecture 1 – Distribuitions, Test functions, Derivatives of distributions, Multiplication of distributions with functions
- Lecture 2 – Composition of distributions with functions, Orthogonal functions, Sturm-Liouville theory, Parseval’s Theorem, Orthogonal polynomials
- Lecture 3 – Orthogonal polynomials, gamma function, Zeta function, Hypergeometric functions
- Lecture 4 – Asymptotic Series, Stirling’s approximation, Saddle point method

**Variational Calculus & Gaussian Integrals –****Denis Dalidovich**- Lecture 1 – One-dimensional and multi-dimensional Gaussian integrals. Averages with the gaussian weight, Wick’s theorem
- Lecture 2 – Imaginary Gaussian Integrals. Grassman variables, definitions. Gaussian Integrals with Grassman variables
- Lecture 3 – Functionals and functional derivatives. Euler-Lagrange equations
- Lecture 4 – Noether’s theorem. Functionals and Euler-Lagrange equations for continuous systems; energy-momentum tensor

**Integral Transforms & Green’s Function –****David Kubiznak**- Lecture 1 – 1d Boundary value problem, Poisson’s equation, Green’s identities, Method of image
- Lecture 2 – Fourier transform, Cauchy problem and diffusion equation, FT in quantum mechanics
- Lecture 3 – Classical electrodynamics, wave equation, Retarded potentials, Feynman-Wheeler theory
- Lecture 4 -Scalar field, Functional Integral, Propagator, Degrees of freedom in gauge theories

**Quantum Mechanics –****Agata Branczyk****Computational Methods in Physics –****Erik Schnetter****QFT 0 –****Freddy Cachazo**

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