Theorems

All theorems are ordered alphabetically. If a theorem has more than one name, it will be listed under the name which appears first alphabetically. Please note that many theorems do not have specific names. For such theorems, please refer to the glossary.

A

I

Q

  1. Quadratic Equation.

B

  1. Bessel’s correction for sample variance estimator.
  2. Some element of linearly dependent set of vectors can be written as linear combination of other vectors in that set.

J

R

  1. Rolle’s theorem

C

  1. Cauchy-Schwarz Inequality.
  2. Chain Rule.
  3. Cramer’s rule.

K

S

  1. |s_n - s| <= k*|A_n|.

D

L

  1. Limit theorems (sequences).

T

  1. Triangle inequality.

E

  1. Empty set is a subset of every set.
  2. Every basis of a finite dimensional vector space has the same cardinality.
  3. Every set of vectors in a finite dimensional vector space can be extended to a basis.

M

  1. Mean value theorem

U

  1. Union and intersection properties.
  2. Uniqueness of coefficients in linear combination.
  3. Inequality involving refinement of partition and the upper and lower sums.
  4. L(f,Q) \leq U(f, P)

F

  1. Fundamental theorem of calculus.

N

V

G

O

  1. Orbit Counting theorem.
  2. Orbit-Stabiliser theorem.

W

H

P

  1. Principle of Archimedes.
  2. Product Rule (differentiation, single variable function).

X

  1. x <= e+y.

Y

Z