Are there any books that present theorems as problems? To be more specific, a book on elementary group theory might have written: "Theorem: Each group has exactly one identity" and then show a proof or leave it as an exercise. The type of book that I am imagining would have written "Problem: How many unit elements can a group have?" and similarly for all other theorems.
[Math] Are there any books that take a ‘theorems as problems’ approach
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Best Answer
Algebraic Geometry by Robin Hartshorne. An algebra professor once told me that almost every exercise is a lemma or theorem from SGA.
A friendlier and more accessible book for undergraduates is "Linear Algebra Problem Book" by Paul R. Halmos. Halmos is an awesome expositor and this one is no exception.