Note-taking for math-heavy lectures

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.

Stop chasing symbols. Capture structure. I keep a narrow left column for the why tag and write the goal, then the named moves the professor says, like substitution, induction step, or by Cauchy. In the main area I sketch the chain with arrows and leave triangles where the algebra is dense, then fill those within a day. I use a second color only for results and definitions so scanning is fast. Stars mark confusion and get resolved during office hours or from the book that same night.

Trying to transcribe every squiggle is how you lose the plot. Treat the proof like logging an incident: write the goal, the givens, the tool used, then the result arrow. When the prof says by XYZ, that is the only phrase you write verbatim, and you draw a big box around the final line. If recording is allowed, run a voice memo and jot tiny time stamps on the page so you can jump back. Trust me, I have watched people try to screenshot RAM, and this beats that chaos.

Write the aim at the top and then chain the big steps with arrows and theorem names. Leave blanks for heavy algebra and fill them the same day. Ten minutes of cleanup beats an hour later. You got this.

Forget complicated systems & just paraphrase the steps in your own words with key equations highlighted. You'll retain more and it's super easy to review. This approach changed my math game for the better!

All these so-called effective methods sound great until the prof switches gears mid-lecture and you're left scrambling. I tried abbreviating once and ended up with notes that made no sense a week later. It's frustrating how fast they go and like they forget we're not all geniuses. Complaining aside, maybe record the audio and note timestamps for tricky parts. But good luck sticking with any system when the workload piles up. I doubt it'll be simple all semester.

Everyone loves fancy systems until the first chalk speedrun. You will not win by buying a tablet or inventing a new shorthand every week. Grab the theorem name, the one identity or definition that unlocks the step, and a tiny note for why it is legal, then move on. Everything else is noise while the train is moving. Right after class, spend twenty minutes with the textbook or a buddy repairing the gaps, because if you wait until tomorrow it is gone.

I have this routine where I sketch the main structure of the proof first. Then I jot down key steps with abbreviations for symbols. It keeps me from getting overwhelmed. I use colors for different parts like assumptions in blue. That way I can review later without the full mess. Works for my ADHD brain.

Right, i've seen students try every gadget under the sun, only to end up with a notebook full of scribbles that look like alien code. Here's a tip: focus on the logic flow, not every symbol. Write the theorem statement, then bullet the major leaps with quick notes like 'by induction' or 'contradiction here.' Add your own examples later to fill gaps. It's hilarious how many think recording the lecture is the fix, but then they never watch it. Trust me, active noting beats passive recording every time.