Summary. We did a lot of theorems this week.
An absolute ton. I didn't even prove them all, I didn't have them all in this slideshow.
I actually didn't include Finding a Prime Factor,
right, that a prime factor must be less than the square root of the number if it exists.
So if a number’s not prime, if a number’s composite,
then it has a prime factor that's less than the square root of the number.
That's FPF,
again, I didn't think it’s as major as the other theorems,
but there's a ton, a ton, a ton of theorems in this course, okay?
Even just this week alone had like 8 or 9 or whatever was, right, there's just a ton.
There are theorem cheat pages, they are available on the Math 135 Resources Page.
Practice so…
do I like using these? I mean,
yes or no. You should practice with them at the beginning, it's hard,
but you should also practice without the cheat sheet.
Why should you do that? I mean
in many offerings of this course, they do give you -
or they have given you - a cheat sheet on the final,
so if you do or don't get a cheat sheet on the final, that shouldn't matter.
You should still practice with and without the cheat sheet.
By practicing without the cheat sheet, what are you doing?
You're forcing yourself to actually remember what you did in the week,
and by trying to remember what you actually
did in the week is actually going to help you long-term remember the content,
and remembering the content is really what you should be trying to do.
You shouldn't be trying to cram for a test. That's
definitely not the philosophy of Math 135.
This is a course that you're going to use the core ideas for
in almost every single math course you take.
You really want to make sure that you know these ideas,
and you have them down solidly, okay?
This is not something you want to goof around with, and
it’s not something you want to just cram and forget.
Math, in general, is not something you want to cram and forget,
but this course especially will hurt you long-term if you do that.
So practice. Practice is important,
practice recalling theorems with and without the cheat sheet,
practice in different settings, practice with multiple questions, practice the first, you know,
mix in a problem from week 3 and try some gcd problems,
practice with mixing is
absolutely vital towards success in this course, okay?
Don't just pocket your theorems. Try to mix them up.
That's what this is trying to reiterate.
The toolbox analogy. Again, if you get stuck, just
calm yourself down, don't panic, panicking is always bad,
and just ask yourself, “Okay. Do I understand the question?
That's true, then what tools do I have to answer the question?
Oh, well I have GCDWR, does that apply here?” Well GCDWR applies
usually really well when the gcd…
when the parameters in the gcd depend on each other.
So if that's the case, then using GCDWR a couple of times will help you out.
You know, if that didn't work, well maybe
there's a gcd condition in the hypothesis and I should use
Bézout’s Lemma, or Extended Euclidean Algorithm.
Maybe the gcd is in the conclusion, I can use GCDCT,
I mean you have a toolbox. Go through it step by step
and ask yourself, “Which of these tools makes sense to use? Am I going to get closer
to my goal by using this tool?”
So hopefully that gives you just a
brief outline of the gcd content.
Again this is a really packed week,
so this video is probably a lot longer than I want it to be.
I really want it to be 10 minutes and I'm sure I'm over 30 right now
but hopefully you do it bit by bit, piece by piece,
and get a little bit out of it… out of what you're doing.
So thank you very much for your time. Thank you for listening,
hopefully this helped you out and best of luck.