Exercises in Applied Mathematics

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Focusing on mathematical exercises, this collection guides readers through statistical physics, equilibrium thermodynamics, and information theory, highlighting their interconnections. It covers essential tools from linear algebra, functional analysis, and probability theory, applying them to topics like entropy, machine learning, and quantum channels. The text includes exercises from various domains, with notes providing motivation and hints or solutions for many. Aimed at senior undergraduates and beginning graduate students in mathematics, physics, or engineering, it prepares them for advanced studies.