Interlacing Family and Matrix Determinant Lemma

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Covers thermodynamic concepts and exam questions from 2012, 2013, and 2015.

Explores Markov's theorem, Chernoff bound, and probability theory fundamentals, including good coloring, 2-colorable graphs, and rare events.

Covers determinants, row echelon form, properties, and geometric interpretation of determinants.

Focuses on open problems and the importance of reformulating problems with better tools and intuition.

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

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