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bluefox25

Some ?'s about Discrete Mathematics

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A couple of years ago, I took a course in discrete mathematics but wound up dropping it for personal matters. I kept the book(Discrete Mathematics and its Applications 4th ed.). I am now taking an intro course in C++ so I picked up the book earlier today and started reading. Is it possible to teach yourself Discrete Mathematics? I have litle math under my belt. If questions were to arise from my readings, who could I ask for assistance? My goal is to learn the math over the summer so that when I take the course in the Fal, I will have a headstart and hopefully do well. I already have questions!1 Comments, Thoughts, Suggestions welcomed!!! PS My ? is about propositions, p-->q(Implication), at first I thought I understood it but now..So it is kind of like using the OR operator or what? Can someone relate in programming terms?

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It can be done. You may have to use a little more effort, but I know from experience it's possible (I used the same book, just the 6th edition).

Quote:
My ? is about propositions, p-->q(Implication), at first I thought I understood it but now..So it is kind of like using the OR operator or what? Can someone relate in programming terms?

p->q simply evaluates to false when p=true and q=false and true for all other truth values. It may be thought of as an if-then statement. It is usually used as a way to state that q holds whenever p holds, but when p doesn't hold then it doesn't make any assumption about q. For example we have:
x is a real number -> x^2 >= 0
It is clearly true because x is real and the square of any real number is non-negative. Another way to think of it is:
if "x is a real number" then x^2>=0 else true
So it evaluates to true for x=5i because x isn't real. It doesn't state anything about complex numbers.

EDIT: In my opinion one of the most important outcomes of a discrete mathemtics course/book is that the student is often able to think about mathematical concepts like infinity and truth-values in a more natural way.

As for where to get help. The book has an excellent website (search Google) with resources. If you are still having problem with something then I suggest trying to find the information yourself. Being able to find information quickly might prove to be an additional benefiet of self-studying that you might not get in a normal course. If you really can't find the answer to something then you can either post here if the questions are rare or you may choose to register at a math forums (physicsforums.com seems to be a decent forum, it has a math area).

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Teach yourself.. sure I guess?

Asking for assistance.. I'm sure you could keep asking here, although some people will probably get annoyed if the questions are too many :)

As far as implication, yes I guess you can use it like an operator. The expression 'p -> q' could be true or false depending on what p and q are. In terms of programming language terms, it's equivalent to (!p) || Q . The only way that 'p -> q' can be false is if p is true and q is false.

The usage that you probably see in your textbook is more like an assertion than an operator though. If your textbook says 'p -> q', what they probably mean is: listen buddy, P implies Q, because I said so. In other words, they mean "the expression 'p -> q' is true". In this case it's not really like an operator; you can't evaluate it because they haven't told you what P and Q are.

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The easiest way to understand p-->q (i.e p implies q) is via a truth table, make a 3 columns, one for p one for q and one for "p-->q", make 4 rows filling in p and q columns with the possible valus of true and false, the last column is what value the statment "p-->q" is based off the values of p and q, in this case, "p-->q" is false only on the row where p is true and q is false. using truth tables one can easily see that q-->p is not the same as p-->q but !q-->!p is equivalent to p-->q ... though I would not call this discrete mathematics, I'd call this logic...

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Thanks for the advice guys. Your right the question has to deal with logic rather than discrete math. That is the first section of the chapter so...

Are most of the symbols used in math available on the keyboard? I was thinking of taking notes but I have no idea how to make some those characters e.g. negation,exclusive or, etc.

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Original post by bluefox25
Thanks for the advice guys. Your right the question has to deal with logic rather than discrete math. That is the first section of the chapter so...

Are most of the symbols used in math available on the keyboard? I was thinking of taking notes but I have no idea how to make some those characters e.g. negation,exclusive or, etc.


The immense majority of mathematical symbols (or layouts) are not available on a keyboard per se. Symbols are mostly available in Unicode, and can be emulated in HTML as well (¬ becomes ¬ for instance).

To get symbols and layouts correctly, you can use paper, LaTeX, Scientific Word, Maple, or the Microsoft Word Equation Editor. Of the above, only LaTeX is free.

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Quote:
Original post by bluefox25
Thanks for the advice guys. Your right the question has to deal with logic rather than discrete math. That is the first section of the chapter so...

Are most of the symbols used in math available on the keyboard? I was thinking of taking notes but I have no idea how to make some those characters e.g. negation,exclusive or, etc.


You should use programmers conventions. NOT a is ~a, a XOR b is a^b modulo is %... and so on.

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