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Exploring Pedagogical Approaches in Writing Advanced Mathematical Books
The chapter delves into the process of writing a book suitable for PhD students or advanced undergraduates, focusing on classical theory, optimality conditions, and applications in geometric and functional inequalities. It discusses the historical background of optimal transport, tracing its origins to the French Revolution and highlighting recent interest in the field. The conversation transitions to educational approaches in mathematics, emphasizing deep learning, foundational concepts, and the balance between traditional and interdisciplinary perspectives.