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Explore the fundamental concepts of integrable systems in mathematics and theoretical physics through this comprehensive lecture series. Delve into the historical development of complete integrability in Hamiltonian mechanics, tracing its origins from the works of Jacobi, Hamilton, Liouville, and Poisson. Examine famous integrable cases of spinning top motion discovered by Euler, Lagrange, and Sofia Kovalevskaya. Investigate the extension of integrability to Hamiltonian systems with infinite degrees of freedom and quantum systems. Using the one-dimensional Heisenberg spin chain as an example, learn how classical integrability based on r-matrix formalism naturally leads to the quantum Yang-Baxter equation and other elements of quantum integrability. Gain insights into recent developments originating from physics in this engaging exploration of classical and quantum integrable systems.
