Metamath Proof Explorer

Table of Contents - 14. BASIC REAL AND COMPLEX FUNCTIONS

  1. Polynomials
    1. Polynomial degrees
    2. The division algorithm for univariate polynomials
    3. Elementary properties of complex polynomials
    4. The division algorithm for polynomials
    5. Algebraic numbers
    6. Liouville's approximation theorem
  2. Sequences and series
    1. Taylor polynomials and Taylor's theorem
    2. Uniform convergence
    3. Power series
  3. Basic trigonometry
    1. The exponential, sine, and cosine functions (cont.)
    2. Properties of pi = 3.14159...
    3. Mapping of the exponential function
    4. The natural logarithm on complex numbers
    5. Logarithms to an arbitrary base
    6. Theorems of Pythagoras, isosceles triangles, and intersecting chords
    7. Solutions of quadratic, cubic, and quartic equations
    8. Inverse trigonometric functions
    9. The Birthday Problem
    10. Areas in R^2
    11. More miscellaneous converging sequences
    12. Inequality of arithmetic and geometric means
    13. Euler-Mascheroni constant
    14. Zeta function
    15. Gamma function
  4. Basic number theory
    1. Wilson's theorem
    2. The Fundamental Theorem of Algebra
    3. The Basel problem (ζ(2) = π2/6)
    4. Number-theoretical functions
    5. Perfect Number Theorem
    6. Characters of Z/nZ
    7. Bertrand's postulate
    8. Quadratic residues and the Legendre symbol
    9. Gauss' Lemma
    10. Quadratic reciprocity
    11. All primes 4n+1 are the sum of two squares
    12. Chebyshev's Weak Prime Number Theorem, Dirichlet's Theorem
    13. The Prime Number Theorem
    14. Ostrowski's theorem