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Mathematical analysis
Analysis is a subject of theorems, definitions full of quantifiers and classic expansions. Lumi has you recite the statements and key formulas so your reasoning never stalls on a forgotten word.
How to turn this subject into cards
Make one card per definition and per theorem, with the quantifiers written out in full. A limit, continuity, uniform convergence, each one needs an exact sentence you can recite. Add a card set for the standard Taylor expansions and another for the reference antiderivatives. The typical trap is knowing the idea without the wording, then losing marks on a swapped quantifier. Lumi asks for the exact wording and lets you correct its deliberate mistakes, which fixes the nuances. Testing yourself beat rereading a week later in a classic study (Roediger and Karpicke, 2006). Lumi helps you remember definitions, theorems, expansions and method steps.
Example card
Try it, Lumi turns it into fill in the blank questions in your browser.
Mathematical analysis · teach this card to Lumi
Every increasing sequence that is bounded above converges, by the monotone convergence theorem. Rolle’s theorem says that if f is continuous on [a, b], differentiable on (a, b) and f of a equals f of b, then the derivative vanishes somewhere. The fundamental theorem of calculus links integration and differentiation. The Taylor series of e to the x begins with 1 plus x plus x squared over 2.
Lumi’s question
Every increasing sequence that is bounded above converges, by the _____.
Pick the missing word
Answer right to light Lumi up
Its lamp fades when a fact slips away.
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Teach this to Lumi
Give Lumi your mathematical analysis notes, it gives them back as questions at the right moment.