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Explores finite fields, vector spaces, commutative groups, and field properties, highlighting their significance in coding theory and algebraic computations.
Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.
Covers the Heisenberg group representation, including shifts, multiplications, and the Fourier transform, extending to finite fields and metaplectic groups.
Explores a priori error estimation in the finite elements method, covering convergence analysis, orthogonality, weak formulations, and optimal precision.
