Math Is Fun Forum

Sign up for a free Live.com email address, which will give you access to Microsoft's online version of Office. Google has an online productivity suite that opens PowerPoint files, also.

Alternately, you can download OpenOffice.org for free, which runs on Windows, Mac OS X, and Linux operating systems.

SuperLynx, that's the trick I use to remember the formula for 3×3 matrices. There are some tricks to make finding the determinant easier on larger matrices, but I don't recall exactly what they are at the moment. I'd have to reference my old Linear Algebra text, which isn't handy. I don't remember them because I don't manipulate matrices by hand regularly, and linear algebra is far less intuitive than working with scalars.

If you want to learn about them, your best option might be to find your own text. You should be able to find an old edition for very little money, and it would likely be more productive than trying to find the information in Internet forums.

Once upon a time, my College Algebra professor once told us that manipulating matrices is something we would likely never want to do by hand, that calculators and computers are much better suited for the task. While my Linear Algebra didn't share that sentiment, I've found it to be generally true.

Personally, I'm a big fan of R (the free, open source statistical software package), which is designed for manipulating large matrices.

Thanks Bob.

It seems my post wasn't clear regarding what it is that I don't understand. I'll try to give a concrete example to better illustrate my problem.

Let f = {(x, y) | y = x², x ∈ R, y ∈ R}.

What is f ⁻¹([0, ∞))? Is it defined? Is f ⁻¹([0, ∞)) = ∅? Is f ⁻¹([0, ∞)) defined as a relation (not a function) equal to the set of real numbers? Something else?

Also, is f(∅) = ∅?

At first I thought that the notation f ⁻¹(A) for some set A implied that f ⁻¹ is a function, which would imply that f is a bijection. But, being told that I can't assume f is a bijection leads me to believe that my initial belief is incorrect.

I'm pretty sure the risk of ruin depends on the size of the bettor's bankroll.

You might be interested in reading about the Kelly criterion. I assume you're already familiar with the law of large numbers.

You're welcome.

What answer did you give for C?

Pi is the ratio of a circle's circumference to its diameter. It would take ~3.14 times the length of the diameter to go around the circumference of a circle.

WWII started September 1, 1939 and ended six years and one day later, on September 2, 1945. 1939 can be used to remember the starting date: 1-9-39. Of course, you'll have to remember the year. It's easy enough to remember the century part: 19. But that's only ½ of it. You need to know the other half of the starting date for WW2. 19½ * 2 = 39. There's 1939.

You're not deriving stuff mathematically; you're just trying to give yourself ways to remember stuff. Some stuff you might be able to write in 733T (or however text-speak is written ) to give yourself clues (i.e. it might provide relevant numbers if spelled that way).

If you're a decent storyteller, you might be able to make up little stories that contain information to remind yourself of some things. Mnemonics works well for some people.

There lots of ways to help yourself remember stuff. Not many will work every time, but if you have a few different methods, most of the time one of them will work.

I use things like model years of favorite cars, friends'/family's birthdays, phone numbers, the pattern my hand makes when I dial a number (can be used for non-telephone numbers, also). Usually one method or another will render an easy to remember association.

How many decimal places of pi do you need to remember? I have 3.141592 memorized (no association tricks), which is far more accurate than I've ever needed for any calculation for which I needed to approximate pi without a calculator. 3.14 is usually sufficient. Some people prefer 22/7, which is also a reasonable approximation for hand calculations.

Like I said, go up-thread and you'll see where I specifically excepted Biology. If you have a relevant point to make, I'll be happy to address it. Your red-herrings, however, are getting old.

You've been throwing out red-herrings in attempt to counter my claims that they are precisely that. If you don't think they're not, why are you disputing the assertion?

That's like saying something isn't blue, it just reflects electromagnetic waves of the same wavelength as those reflected by blue items.

LOL. Please, share with us the history of the term applied.

If it is used outside of mathematics, then it is, quite literally, a part of applied mathematics. It doesn't matter if it's only taught to pure track maths majors, or even what the most eminent mathematicians claim. The definition of applied is clear.

They are in your posts.

You are trying to argue the point that because a word has a literal meaning, then any compound word containing that word must have a definition that is an exact combination of the literal definitions of the component words. That is not necessarily the case. For example, a bookend is not the end of a book. However, it is quite easy to understand the reasoning behind combining the words book and end to describe that object.

Applied mathematics, however, is not a compound word. It is a plural noun modified by an adjective. Are you suggesting that those who decided to use applied to describe the mathematics to which they wanted to refer were unaware of the meaning of the adjective applied? Did they just open a dictionary up to a random page and pick the first adjective they saw? Is it only by dumb luck that we don't call applied mathematics insane mathematics? Why do you suppose they would use the word applied if that wasn't what they meant? Is it just an obscure exception to mathematicians' obsession with precise definitions?

Can we refer to any set without many elements as the empty set? If a function is defined at a few places, without too many interruptions on a given interval, can we call it a continuous function on that interval?

Interesting article.

1+1+5+1+1=9

Have you ever given any consideration to leaving your arrogance and anger at the login screen? The OP did not list any such restrictions on the problem. My method is perfectly legitimate. If you have a different way, fine. I have no doubt I could also find other ways to do it. However, I posted what, thus far, appears to be the easiest way to go about it.

Do you really need someone to explain how a non-mathematical theory is completely irrelevant to a discussion about mathematics?

It has its problems, at least according to Wikipedia. Having said that, if the problems are of the same kind that evolution supposedly has (i.e. are fabricated by those who lack understanding of the theory), then that would be yet another reason why it is a topic wholly irrelevant to this discussion.

Your methodology is wholly devoid of logic.

Two possibilities: 1) There is overlap between pure mathematics and applied mathematics; or 2) those three examples are no longer in the realm of pure mathematics, despite your claim.

You're still having trouble understanding the implications of the descriptor applied, I see.