Where can I learn the complete mathematics involved in LDA?
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I believe the Latent Dirichlet Allocation paper by Blei, Ng, and Jordan (all big names in AI/ML/NLP) is a point to start. They provided the math foundation as well as multiple examples.

See: Blei, David M., Andrew Y. Ng, and Michael I. Jordan. "Latent dirichlet allocation." Journal of machine Learning research 3.Jan (2003): 993-1022.