Difference between revisions of "Math for CS Review"

From Computer Science
Jump to: navigation, search
(Memorize)
(Memorize)
Line 22: Line 22:
 
** Possible values - true, false - can mean on, off - often represented by 1, 0
 
** Possible values - true, false - can mean on, off - often represented by 1, 0
 
** and, or, not - read about in [https://www.khanacademy.org/computing/ap-computer-science-principles/computers-101/logic-gates-and-circuits/a/logic-gates Khan academy]
 
** and, or, not - read about in [https://www.khanacademy.org/computing/ap-computer-science-principles/computers-101/logic-gates-and-circuits/a/logic-gates Khan academy]
 +
** De Morgan's laws: not (A and B) is equivalent to (not A) or (not B).  not (A or B) is equivalent to (not A) and (not B).
 
** Should be able to answer questions about truth tables for and / or / not, and evaluate expressions of and's / or's / not's
 
** Should be able to answer questions about truth tables for and / or / not, and evaluate expressions of and's / or's / not's

Revision as of 01:24, 7 January 2020

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
    • 2a+b = 2a * 2b
    • ya+b = ya * yb
    • 2-a = 1 / (2a)
    • 220 = 1024 × 1024, roughly 1 million
    • 230 = 1024 × 1024 × 1024, roughly 1 billion
  • Logarithms
    • logbx = y, means by = x, for any b > 1
    • log101000 = 3
    • log21024 = 10
    • logbx = logcx / logcb, for any b > 1, c > 1
    • log210 is about 3.32
    • logb(xy) = y logb x, for any b > 1
  • Formulae
    • Arithmetic Sum: (1 + 2 + ... + n) = n * (n+1) / 2
    • Geometric Sum: 1 + r + r2 + r3 + ... + rn = (rn+1-1) / (r-1)
  • Boolean logic
    • Possible values - true, false - can mean on, off - often represented by 1, 0
    • and, or, not - read about in Khan academy
    • De Morgan's laws: not (A and B) is equivalent to (not A) or (not B). not (A or B) is equivalent to (not A) and (not B).
    • Should be able to answer questions about truth tables for and / or / not, and evaluate expressions of and's / or's / not's