I suppose I can back off my initial assertion. It’s just that…I’m now in my fourth semester back at school and every other class, I’ve gotten an A or an A-, and the classes have been fun and interesting.
Discrete math has been hard from the get-go. Here we are not even three weeks into the semester and I am frustrated.
To answer your question, Jragon, I have been anxiously looking ahead to the sets chapter - which is on sets. The algebra of proportions is what has got me so down. I remember truth tables, but I never did such complicated ones, and the rules for the algebra of proportions are not explained in our textbook, just stated, and I feel like they just made them up. I know they didn’t, but I’m having real trouble.
Comfortingly so is the rest of the class…teacher is holding a livechat tomorrow evening just to discuss this very thing.
I love general education humanities stuff. I love most of my schoolwork. As I said, I even got a B in calculus. I’m not dumb, actually I’m pretty book-smart. But this stuff just doesn’t make much sense.
My other two classes are actually far more interesting - Database systems and management information systems.
I honestly have no idea what the “algebra of proportions” is, I’ve probably done it by a different name.
As for truth tables, I don’t think we ever spent more than a week or two on them. They generally just become intractable for any expression that can’t be heavily reduced. We focused more on formal logic proofs than truth tables (given a->b, b->c, and a, prove c is true sort of stuff).
Edit: Okay, I’ve never done Algebra of Proportions in a discrete math course, and it seems odd to be in there. I don’t think I’ve touched that stuff since 7th grade algebra. Pre-calc at the latest. (Unless you count the times it kind of comes up by accident in other fields).
Here is one of my homework problems for this week:
Prove that p and q implies p or q is true by the algebra of propositions.
I understand implications and I pretty much got the hang of those…but proving them with rule of Double Negativity, or DeMorgan’s Laws, or some other rules (there are like 13 listed in the book and only two of them have examples) is difficult.
I’m glad to hear it will be over soon. THE PAIN, THE PAIN.
The hardest one that I came across was “Complex Methods” for electrical engineering. Take everything you’ve learned (Calc, Diff Eq, Linear) and “give the cat a bath” by redoing the whole thing with the addition of a complex imaginary dimension/vector/space/whatever.
Afterwards, my shit was blown, I saw cascading green symbols in my vision, and I could talk to whales.
I remember reading something on this in (I think) Feynman’s Lectures on Computation. To a student, differentiation is a deterministic algorithm – given a bunch of elementary functions combined using the four operations and composition, at every step you know the transformation to make to express the problem as a simpler problem working from outside to inside and left to right, and you are certain that repeatedly applying the rules will accomplish the result. If you know the rules, getting the answer is a “sure thing”.
For integration, it’s a much more “artistic” process. You have a bunch of techniques, and you can’t tell from inspection which one you should apply or how you should apply it, so integration is more of a pain in the ass than differentiation.
It turns out that there is an algorithm that does integration in such a way as to make it as much a “sure thing” as differentiation, but that algorithm is too complicated to be applied by non-computers.
Yes, that is exactly the way we must do it. The way you mention, we have homework problems that require that way, too, and those I understand, but trying to apply those laws makes my eyes cross.
Okay, I’m writing an educational computer science series which will probably include propositional and first order logic, so I feel compelled to ask: what kind of examples would you like? To me, the rules themselves are kind of examples and I can’t really imagine how to make an example of them.
I don’t really see how p ^ (p v q) = p can really be rolled into an example, or what kind of example you can use to give people a sense of DeMorgan’s. At least not beyond the silly examples like (p ^ (p v q)) v q = p v q, which is kind of obvious IMO. What sort of thing do you think would help you/people like you grasp it?
One way to do this, or similar problems, is to make a truth table and use it to show that it is a tautology (true for all possible values of p and q). Wolfram Alpha can do the truth table for you.
No. What you should do is go to half.com NOW and buy some 10 year old calc and physics books, and use them. Freshman calc and physics hasn’t changed much for the last 50 years, so those ten dollar books are just as good as the 200 dollar ripoffs they make you buy for class. And if you have books from several different authors, AND READ THEM, then someone who sounds as intelligent as you should be able to “get” calc and physics. It’s entirely possible that your problem is not the difficulty of the material, but a bad prof and a bad book.
When I was an undergrad math major, I did so well in my classes that the department offered me a job as a tutor for guys like you. They gave me the teacher’s edition of the textbook for freshman calc they were using, which was by a different author than the one I had used a couple years before. And I swear to God, it was awful. I could barely understand it, and I don’t see how any freshman could have understood it. So a different book might make a big difference.
Go to half.com, or amazon (used books) and buy an old edition each of Anton, Stewart, Thomas, and Larson, max ten bucks each. You say you did well in trig, so look at the trig review section in each one, and decide which author’s style you like the best. Make him your primary, and read the section in his book about whatever topic the lecture is about BEFORE the lecture. If it’s clear, great. If it isn’t, read the same topic in a second book, then a third, until it is.
Math is not like English lit. It doesn’t depend on someone’s opinion. It is absolutely logical, and every question has a right and wrong answer. This is a HUGE advantage for smart people, because your prof’s opinion doesn’t matter, and you sound smart.
What is the best case, worst case and average case for a sort (bubble, merge, quick, etc.)
How many comparisons must be made when search a unordered tree vs an ordered tree? How does using a binary tree affect search time?
Oh but Cad, I’m IS not a programmer. OK, then should we talk about the topology of a network and whether it is a Hamiltonian or Eulerian path (or neither one?) If you don’t want more than than 50’ drop from your switches to a computer, how many switches do you need and where do you put them to minimize the total distance from the switches to the router?
Oh! I’m sorry to hear this is not being fun for you. For me, math logic (and philosophy logic) was easy, and fun. I got a perfect A in that class. I loved every second of it. It was all so…logical!
The proof you mention is easy…
p and q
therefore:
p (from a rule I learned as “Conjunction Out.”)
p
therefore
p or q (from a rule I learned as “Disjunction In.”)
Simple as that. And, lordy, it’s been over twenty years.
I wish I could make up a bundle of all the joy I had from that class and send it to you as a gift.
One of the things I really liked about my discrete math class was that on any assignment, quiz, or test we were allowed to use anything we proved in class or another homework if we remembered it. So you didn’t have to spend 20 minutes reinventing the wheel, the instructor just let you say
p (given)
p v q (given)
p v q ^ (a -> c) <-> g ^ f v t
t (As proven in the homework)*
<…>
What we were actually trying to prove
Disclaimer, you probably can’t derive t from those three things; it’s just a silly illustration.
Anybody want to tutor me?
I don’t know what kinds of examples I want, because I don’t know the subject matter well enough! But the proof Trinopus provided should help…I will sit down tonight and look at the other two problems as well and see if that helps.
She (the prof) is conducting a live chat tonight which I intend to attend, and hopefully that will help a little.
Thudlow Boink, we are specifically not supposed to use truth tables in these examples.
Why does Trinopus get all the credit? The proof is the same one I put in 106 :(. Oh well.
And I actually would tutor you, if you want. As for examples, I might email my discrete math teacher and see if he has anything. I just have trouble examplifying logical equivalences, because they tend to feel so arbitrary.
If you really don’t mind, can I PM/e-mail you with the other two questions and my work on them, and you can tell me if I’m totally off base? It will have to wait until tonight, because my HW is there, but I sure would appreciate it.
Well, I could PM you the questions for now…that might help, cuz then you’d know what was expected, and then PM you my answers later.
The algebra of proportions is what has got me so down. 
I remember truth tables, but I never did such complicated ones, and the rules for the algebra of proportions are not explained in our textbook, just stated, and I feel like they just made them up. I know they didn’t, but I’m having real trouble.
That was bad of me.