Mathematical Fundamentals

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Mathematical Fundamentals
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Properties of Logarithms 1

• Logb is strictly increasing
• If xlty then logb x lt logb y
• Logb is one-to-one
• if logb x logb y then x y
• Logb 1 0
• Logb ba a (Logb b 1)

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Properties of Logarithms 2

• Logb (xy) Logb x Logb y
• Logb xa a Logb x
• xLogb y yLogb x
• Loga x (Logb x)/(Logb a)

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Probability

• X(x1, x2, ... , xn) X is a set of numbers
• P(p1, p2, ... , pn) P is a set of
  probabilities
• For all 1 i n, pn is the probability of xn
• Average x1p1x2p2 ... xnpn
• Usually written

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Summations
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Induction Basis Step
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Induction Inductive Step
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Integral Formulas
a-1
a
b
b1