Basic Mathematics of Data Science

Mathematics as a discipline

Basic symbols and terminology

Vectors and matrices

Logarithms/exponents

Key Points

  • An exponent of −1−1 denotes the inverse function. That is, f−1(x)f−1(x) is the inverse of the function f(x)f(x).
  • An inverse function is a function that undoes another function: If an input xx into the function ff produces an output yy, then inputting yy into the inverse function gg produces the output xx, and vice versa (i.e., f(x)=yf(x)=y, and g(y)=xg(y)=x).
  • The logarithm to base bb is the inverse function of f(x)=bxf(x)=bx: logb(b)x=xlogb(b)=xlogb⁡(b)x=xlogb⁡(b)=x
  • The natural logarithm ln(x)ln(x) is the inverse of the exponential function exex:b=elnbb=elnb

Set theory

Calculus

  • Functions of a single variable, limit, continuity, differentiability
  • Mean value theorems, indeterminate forms, L’Hospital’s rule
  • Maxima and minima
  • Product and chain rule
  • Taylor’s series, infinite series summation/integration concepts
  • Fundamental and mean value-theorems of integral calculus, evaluation of definite and improper integrals
  • Beta and gamma functions
  • Functions of multiple variables, limit, continuity, partial derivatives
  • Basics of ordinary and partial differential equations

Linear Algebra

  • Basic properties of matrix and vectors: scalar multiplication, linear transformation, transpose, conjugate, rank, determinant
  • Inner and outer products, matrix multiplication rule and various algorithms, matrix inverse
  • Special matrices: square matrix, identity matrix, triangular matrix, an idea about sparse and dense matrix, unit vectors, symmetric matrix, Hermitian, skew-Hermitian and unitary matrices
  • Matrix factorization concept/LU decomposition, Gaussian/Gauss-Jordan elimination, solving Ax=b linear system of equation
  • Vector space, basis, span, orthogonality, orthonormality, linear least square
  • Eigenvalues, eigenvectors, diagonalization, singular value decomposition
  • Sinan Ozdemir-Principles of Data Science (Packt)

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Desi Ratna Ningsih

Desi Ratna Ningsih

Data Science Enthusiast, Remote Worker, Course Trainer, Archery Coach, Psychology and Philosophy Student

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