Build up proof-building ability?

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This is embarrassing, but I'm a graduate student in a mathematics program and I'm terrible at writing proofs. My computational skills are strong but proofs, not so much. I want to go on to complete a PhD in math but know this area needs improvement. Are there any texts or other resources you suggest?

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A really great book for acquiring the ability to write proofs, and gain confidence in doing so, is Daniel Velleman's "How to Prove it: A Structured Approach".

Even using it for self-study, or as a reference, will prove helpful. It covers logic, and is very logic-oriented, so you may really like it.