An interactive notebook · 8 figures
Matrix
A notebook of interactive figures for undergraduate mathematics and statistics.
Each figure here is a small working model of one idea. Press, drag and step through them until the idea stops being a sentence and becomes something you can predict. The figures are grouped by course and ordered by the week the idea first appears.
§ 1
Mathematics I
Functions, limits and derivatives, then graphs and the algorithms that walk them.
- Figure 1.1 Exponentials and logarithms Plot e^x, ln x and their relatives side by side, probe values, drag a parameter, and type your own function.
- Figure 1.2 Continuity and differentiability at a join Two formulas glued at one point: drag the parameters until the pieces meet, then until their slopes match.
- Figure 1.3 Critical points and extrema f, f′ and f″ stacked on one axis: read maxima, minima and saddles from the sign of the derivative, and find global extrema on a closed interval.
- Figure 1.4 Breadth-first and depth-first search Step a queue and a stack through the same graph and watch levels form, then test which extra edges the graph could have had.
- Figure 1.5 Depth-first search, line by line A recursive DFS procedure executed one action at a time, with the matrix row being scanned, the call stack and the parent map in view.
- Figure 1.6 Matrix multiplication and walks Click any entry of a product to see the row-times-column sum behind it, then read A² of a directed graph as a count of two-step walks.
- Figure 1.7 Bellman–Ford and Dijkstra Run both algorithms on a graph with negative edges: every arrow is an offer, and Dijkstra locks some vertices in too early.
§ 2
Mathematics II
Linear algebra: vectors, matrices, spans, rank and the null space.