Required math summations
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Required Math - Summations. The summation symbol should be one of the easiest math symbols for you computer science majors to understand – if you don’t now, you will!. Required Math - Summations.

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Required Math - Summations

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Required math summations

Required Math - Summations

  • The summation symbol should be one of the easiest math symbols for you computer science majors to understand – if you don’t now, you will!

CS 4953 The Hidden Art of Steganography


Required math summations1

Required Math - Summations

  • The summation symbol should be one of the easiest math symbols for you computer science majors to understand – if you don’t now, you will!

  • This symbol simply means to add up a series of numbers

  • The equivalent in C is:

    • int j, sum = 0;

    • for(j = 0; j < n; j++)

    • { sum = sum + Xj; }

  • How many times will this loop?

CS 4953 The Hidden Art of Steganography


Required math summations2

Required Math - Summations

  • n = total number of elements

  • P = probability of occurrence of a particular element

  • X = element

  • j = index

  • If pj is the same for all elements (this is called equiprobable), then what is a simple, everyday name for ‘a’?

  • Sometimes, ‘n’ is not shown so it just means to SUM over the entire set, whatever the size

CS 4953 The Hidden Art of Steganography


Required math logarithms

Required Math - Logarithms

  • Definition: logbN = x is such that bX = N

  • Read as “the logarithm base b of N equals x”

  • You have two logarithm buttons on your calculator

    • “log” and “ln”

    • log is base 10 and ln is base e (e ~ 2.71)

    • ln is called the natural log and has numerous scientific applications

  • You also have three inverse log buttons

    • 10X, eX, yx

  • Unfortunately, we will deal with log base 2, and you do not (likely) have this buttons available 

  • However, there is a formula to help you out 

CS 4953 The Hidden Art of Steganography


Required math logarithms1

Required Math - Logarithms

  • logbN = logaN/logab

  • The value of ‘a’ is arbitrary, so you can use either log base 10 or log base ‘e’

  • Some other properties of logarithms (base is irrelevant)

    • log (N * M) = log N + log M

      • note: 10x * 10y = 10(x + y)

    • log (N / M) = log N – log M

    • log NM = M log N

    • logbb = 1 (base matches number)

    • log 1 = 0

    • log 0 = undefined

  • For log base 2, we will use the notation “lg”

    • log2N = lg N

  • Unless otherwise indicated, log N will imply a base of 10

CS 4953 The Hidden Art of Steganography


Required math logarithms2

Required Math - Logarithms

  • Examples – should be able to answer by inspection

    • 3 + 5 = ?

  • You see how quickly you can answer the above question? That’s how fast you need to be able to answer these:

    • log 1?

    • log 10?

    • log 100?

    • log 1000?

    • log 10356?

    • lg 1?

    • lg 2?

    • lg 256?

    • lg 1024?

    • lg 21024?

  • Don’t wait, learn the properties now!

CS 4953 The Hidden Art of Steganography


Required math logarithms3

Required Math - Logarithms

  • A few other properties:

    • Log N > 0 if N > 1

    • Log N = 0 if N = 1

    • Log N < 0 if N > 0 && N < 1

  • What about the inverse lg?

  • Example, what is the inverse lg of 8?

  • inv log 6?

  • inv log 0?

  • inv lg 12?

CS 4953 The Hidden Art of Steganography


Background probability

Background - Probability

  • Probability may be defined in several ways

  • It may be the likelihood of outcomes of a certain set of events, for example, the flipping of a coin

    • How many possible outcomes are there?

  • Another way of looking at probability is that it is a measure of human surprise at the outcome

  • More surprise, more information, lower probability

  • Probability is always between zero and one

    • Probability = zero means it will NOT happen (is this EVER true?)

    • Probability = one means it will happen (is this ever true?)

CS 4953 The Hidden Art of Steganography


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