Hayden Petrov

Use a structure-first template so you capture the logic, not every symbol. At the top of each new proof write Given:, Goal:, Strategy: in the margin, then number the major steps as 1, 2, 3 as the prof moves. In each step write a short trigger and result, for example "use Cauchy-Schwarz -> bound on norm" or "by induction step, P(k) -> P(k+1)", and skip algebra with a placeholder like [alg -> Eq. (3)]. Assign your own equation tags (1), (2), (3) to the board's key lines so your steps refer to them rather than re-copying and and circle the pivot line where the proof turns, like when existence becomes uniqueness. Keep a two-column page: left column holds the roadmap steps and equation tags, right column is empty during class for details you fill in later. While the prof talks, aim to capture the flow verbs and reasons: define, assume, apply theorem X, substitute, conclude, and put a small square beside gaps you need to re-derive. Immediately after class, spend 15 minutes filling the squares, expanding one skipped algebra chunk per step and checking that each arrow you wrote is valid. Use consistent shorthand to stay fast, for example "wlog" for without loss of generality, "iff" for if and only if, and "dfn" for definition, plus one color for your paraphrase and another for questions. Concrete example: when they prove the derivative of x^x, you can write Given: y = x^x, Goal: y' = ?, Strategy: log-diff. Steps: (1) ln y = x ln x, [alg], (2) y'/y = ln x + 1, (3) y' = x^x(ln x + 1), and fill the [alg] later. If photos or recordings are allowed, grab a photo at each board reset and use it only to fill your right column, but the core method works with paper only.

Everything is trying to sell you "memory hacks" with a 19.99 subscription and pastel UI. You don't need it. What works is short daily recall and spacing, which is miraculously free if you make your own cards. The cost is time and a little boredom. I'm mad I learned this after paying for a course that mostly read slides back at me. Now I set a 10-minute timer, quiz myself from a tiny stack, and stop. If I miss a card twice, it goes to tomorrow; if I nail it, it waits a couple days. Library printer for a dozen index cards beats another subscription. If you need an app, use a free one with spaced intervals, but don't pay to procrastinate.

idk, one class first term, see vibes, then scale. For what it's worth, taking a few minutes to practice this in a calm setting usually helps it stick.