Mathematical Reasoning and Derivations Questions

Comfort and proficiency with formal mathematical reasoning used in research. Candidates should be able to perform derivations by hand, manipulate equations, apply calculus and linear algebra, reason about optimization and convergence properties, use probability and expectation operations, derive bounds and error estimates, and write concise proofs using common techniques such as induction and contradiction. Interviewers may probe correctness, clarity of steps, and understanding of the assumptions that underlie derivations.