Formal Sciences
What is a set?
A set groups well-defined objects; membership, inclusion and operations describe its structure.
8 min readDiscover
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Computer Science
Algorithms: specify, execute and justify a maximum search
From contract to proof: follow a maximum search, test its limits and distinguish method, program, correctness and termination.
25 min readDiscover
Social Sciences
The law of diminishing returns
With technology unchanged, increasing one input while the others remain fixed often ultimately reduces its marginal product; if it is the only variable input, paid at a constant price, and as long as its marginal product remains positive, this decline raises marginal cost.
15 min readDiscover
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Computer Science
Algorithms: specify, execute and justify a maximum search
From contract to proof: follow a maximum search, test its limits and distinguish method, program, correctness and termination.
25 min readRead
Formal Sciences
Understanding the derivative: limit, tangent, and instantaneous change
A derivative measures instantaneous change: it arises as the limit of rates of change and is interpreted as the slope of a tangent.
18 min readRead
Formal Sciences
Rate of change: measuring change over an interval
Rate of change measures average change between two specified inputs. See how interval choice, units, and representation determine what the number actually means.
14 min readRead
Formal Sciences
Functions: domain, outputs, preimages, and representations
A function is more than a formula: each allowed input has exactly one output. Distinguish domain, image, preimages, and the main representations of the same rule.
12 min readRead
Formal Sciences
What is a set?
A set groups well-defined objects; membership, inclusion and operations describe its structure.
8 min readRead
Formal Sciences
Graphs, degrees, and Eulerian trails
In a multigraph whose vertices of nonzero degree are all connected, degree parity determines whether every edge can be traversed exactly once.
11 min readRead