Mathematics
Limits and number-theory sketch
Limits, continuity, primes, congruences.
Basics
Limits and continuity
If f(x)→L as x→a, values near a sit near L. Continuity: the limit equals f(a). Divergence or oscillation means no limit. ε–δ is the precise language.
Integers
A prime has no positive divisors but 1 and itself. Fundamental theorem: prime factorization is unique. a≡b (mod n) means n divides a−b. This underpins crypto and hashes.
Formulas
Euclidean algorithm
Greatest common divisor. Extended form gives ax+by=gcd.
Modular arithmetic
Clock arithmetic. Addition and multiplication respect the modulus.
In this field
Algebra and geometry
Equations, exponentials and logs, Pythagoras, circles.
Trigonometry and calculus
Trig ratios, identities, derivatives, integrals.
Statistics and linear algebra
Mean, variance, Bayes, matrices, eigenvalues.
Discrete, complex, series
Sequences, series, complex numbers, combinatorics.
Differential equations and series
First-order linear, harmonic oscillator, Taylor and geometric series.
Vectors and space
Vectors, dot and cross products, planes, and distance in 3D.
Conic sections
Parabola, ellipse, hyperbola, eccentricity, foci, and an orbit sketch.
Fourier sketch
Sines that rebuild a periodic function, coefficients, spectra, and a discrete-transform note.
Probability, continued
Expected value, variance, normal density, and a CLT one-liner.
Graph-theory sketch
Vertices and edges, degree, paths, Euler, and the adjacency matrix.