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Algebra
Algebra is built on structures, definitions and theorems that chain together. Lumi quizzes you on each brick so you can reach for it without hesitating during an exercise.
How to turn this subject into cards
Sort your course by structure, groups, rings, vector spaces, matrices. For each one, a set of definitions, a set of properties to know and a set of methods, such as diagonalising a matrix or finding a kernel. The usual trap is mixing up two neighbouring ideas, a subgroup and a normal subgroup, a spanning set and an independent set. Lumi asks questions that force you to tell them apart, and returns to them when you hesitate. Spreading revision out beats cramming it all at once (Cepeda et al., 2006). It helps you remember definitions, theorems and calculation steps.
Example card
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Algebra · teach this card to Lumi
A group is a set with an associative operation, an identity element and inverses. Lagrange’s theorem says the order of a subgroup divides the order of a finite group. The rank-nullity theorem says the dimension of the domain equals the rank plus the nullity. A set of n vectors in an n-dimensional space is a basis if it is linearly independent.
Lumi’s question
A group is a set with an associative operation, an _____ and inverses.
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 algebra notes, it gives them back as questions at the right moment.