Contents: Type Motif Draft

An experimental version of the contents, drawn as letters in space. Each subject, and each chapter of Linear Algebra, is a structure that means something in that subject, spelled in its own words. Each figure ripples slightly when idle, and moving the pointer over it changes it.

Intensity

Stage 1

1Linear AlgebraA line turned by a rotation, sweeping out a helicoid

2Introduction to ProofsInduction as a line of dominoes, falling from the base case

Stage 2

3Calculus ReviewColumns of letters under a curve, with its tangent in blue

4Multivariable CalculusA saddle surface and its level curves

5Discrete MathematicsThe graph of the 4-cube, sixteen binary strings

Stage 3

6Differential EquationsOne orbit of the Lorenz system

7Real AnalysisA sequence closing in on its limit, inside epsilon

Stage 4

8ProbabilityA Galton board piling into a bell curve

9Linear Algebra IIA hyperboloid woven from the lines of a quadratic form

Stage 5

10Numerical MethodsPiecewise approximations closing in on a curve

11Abstract AlgebraAn icosahedron and its group of rotations

Stage 6

12Complex AnalysisThe Riemann sphere over the complex plane

13Real Analysis IIFunctions converging uniformly to their limit

Stage 7

14Metric Spaces and TopologyA trefoil knot as a tube of letters

Stage 8

15Algebra IIA tower of fields, rings of roots of unity

Linear Algebra Chapters

1Vectors and MatricesCombinations of two vectors filling a plane

2Solving Linear EquationsThree planes meeting at one solution

3The Four Fundamental SubspacesTwo pairs of perpendicular subspaces

4OrthogonalityA projection and its error at right angles

5DeterminantsA sheared deck that keeps its volume

6Eigenvalues and EigenvectorsPaths spiralling onto an eigenvector

7The Singular Value DecompositionA sphere carried onto an ellipsoid

8Linear TransformationsThe lattice of space under a shear

9Linear Algebra in OptimizationGradient descent down a quadratic bowl

10Learning from DataData, its best-fit plane and principal direction