Difference between revisions of "Math for CS Review"

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(Created page with "Miscellaneous Order of operations: first parenthesis, then exponents, then multiplication and division, then addition and subtraction. And left to right. Powers/exponents 2...")
 
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Miscellaneous
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=Memorize=
 
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These are things you need to memorize.
Order of operations: first parenthesis, then exponents, then multiplication and division, then addition and subtraction.  And left to right.
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* ''Order of operations:'' first parenthesis, then exponents, then multiplication/division/modulus, then addition and subtraction.  And left to right.
 
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* ''Powers/exponents''
Powers/exponents
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** 2<sup>10</sup> = 1024, roughly 1 thousand
2<sup>10</sup> = 1024, roughly 1 thousand
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** 2<sup>a+b</sup> = 2<sup>a</sup> * 2<sup>b</sup>
2a+b = 2a × 2b
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** y<sup>a+b</sup> = y<sup>a</sup> * y<sup>b</sup>
ya+b = ya × yb
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** 2<sup>-a</sup> = 1 / (2<sup>a</sup>)
2-a = 1 / (2a)
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** 2<sup>20</sup> = 1024 × 1024, roughly 1 million  
220 = 1024 × 1024, roughly 1 million  
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** 2<sup>30</sup> = 1024 × 1024 × 1024, roughly 1 billion
230 = 1024 × 1024 × 1024, roughly 1 billion
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* ''Logarithms''
Logarithms
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** log<sub>b</sub>x = y, means by = x, for any b > 1
logbx = y means by = x
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** log<sub>b</sub>x = log<sub>c</sub>x / log<sub>c</sub>b, for any b > 1, c > 1
logbx = logcx / logcb
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** log<sub>2</sub>10 is about 3.32
log210 is about 3.32
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** log<sub>b</sub>(xy) = y log<sub>b</sub> x, for any b > 1
logb(xy) = y logb x
 

Revision as of 19:00, 6 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
    • logbx = logcx / logcb, for any b > 1, c > 1
    • log210 is about 3.32
    • logb(xy) = y logb x, for any b > 1