Math for CS Review

Memorize

These are things you need to memorize.

• Order of operations: first parenthesis, then exponents, then multiplication/division/modulus, then addition and subtraction. And left to right.
• Powers/exponents
  • 2¹⁰ = 1024, roughly 1 thousand
  • 2^a+b = 2^a * 2^b
  • y^a+b = y^a * y^b
  • 2^-a = 1 / (2^a)
  • 2²⁰ = 1024 × 1024, roughly 1 million
  • 2³⁰ = 1024 × 1024 × 1024, roughly 1 billion
• Logarithms
  • log_bx = y, means b^y = x, for any b > 1
  • log₁₀1000 = 3
  • log₂1024 = 10
  • log_bx = log_cx / log_cb, for any b > 1, c > 1
  • log₂10 is about 3.32
  • log_b(xy) = y log_b x, for any b > 1
• Formulae
  • Arithmetic Sum: (1 + 2 + ... + n) = n * (n+1) / 2
  • Geometric Sum: 1 + r + r² + r³ + ... + rⁿ = (r^{n+1)-1) / (r-1)}