I'm entering Week 3 of 8 with Discrete Mathematics and Linear Algebra online, and I just wanted to say thank you so much for making your videos available publicly. They have been a critical tool in helping me learn and understand the material. Next term Statistics, and I'll be back to utilize the videos you have for that course too!
Thank you so much! My professor just reads off the slides with a very thick accent. I don't understand anything that is going on in the class; however, your videos are quite helpful.
I love you soooo much Kimberley. I have a final coming very soon, and you have been very helpful. Besides, I like your pedagogical methods. Thank you!!!
There is a slight error in the original definition. a|b iff ∃c: ac = b (a, b ∈ Z, c ∈ Z+). c just has to be an element of Z, not Z+ (confirmed with the book). You use that fact later in the video for 10 | -112. Just wanted to point that out in case someone like me got confused with that portion of the video.
while studying this book some things feel very basic and I feel like i already know all this, but when I challenge myself with proofs or questions at the end of the section, I find some of them hard. I tend to get frustrated because sometimes the questions look very basic but i just don't know how to prove them. Is this normal or should i pursue something other than computer science as a career?
Hi Kimberly: I had a question regarding whether or not the following proof is legitimate. Prove that for all integers {a,b,c}, if a|b and b|c, then a|c. Let {a,b,c,k,j,m} all be integers. GIVENS: a|b ak = b a = b/k GIVENS: b|c bj = c PROVE: a|c am=c m = c/a To prove that a|c, we would have to show that m is an integer. We have to show that (c/a) simplifies to be an integer. c/a bj / (b/k) Copy Dot Flip bj * (k/b) j*k Integers Closed Under Multiplication We find that m was an integer. Thus, it is true that a|c. Is this a legitimate proof or is there a flaw in the argument? Thank you so much!!
But isn't it confusing...first it is said that a|b iff b/a € Z... Then we come to quotient and reminders because division isn't always even. Doesn't this conflict with the original defination? Like first we say in def that a|b only iff c is an integer... then we are okay with float values.😅 @Kimberly Brehm
I have one question here, from the definition of divisibility, is it true that a divides b if there is an unique integer c OR for some integer c such that ac=b?
I'm entering Week 3 of 8 with Discrete Mathematics and Linear Algebra online, and I just wanted to say thank you so much for making your videos available publicly. They have been a critical tool in helping me learn and understand the material. Next term Statistics, and I'll be back to utilize the videos you have for that course too!
Thank you for providing the explanations, which are far more understandable than reading them all in a book.
My professor is not very good at teaching these concepts, so this video is a lifesaver.
Thank you so much! I am in an online Discrete math class with no lecture! This resource has been essential to me understanding these concepts! Thanks!
I have been looking for such videos for a very long time, worth calling this a treasure !
can't thank you enough
Glad it was helpful! Spread the word!
Thank you so much! My professor just reads off the slides with a very thick accent. I don't understand anything that is going on in the class; however, your videos are quite helpful.
@Abdel-Rahman Samir Saad Mr.Ntafos
if i was in your class, i would pass this course with flying colors. id take it again and again just for the fun of it
I love you soooo much Kimberley. I have a final coming very soon, and you have been very helpful. Besides, I like your pedagogical methods. Thank you!!!
thank you very very much for very efficient and effective teaching videos. the way you teach empowers me so much.
Is there a secret to understanding proofs, I can do the math but these proofs absolutely kill me.
It's painstakingly easy but stupidly awkward in an unorthodox manner to regular classical math.
Calculus is the nest of proofing formula or even this kind of things
There is a slight error in the original definition. a|b iff ∃c: ac = b (a, b ∈ Z, c ∈ Z+). c just has to be an element of Z, not Z+ (confirmed with the book). You use that fact later in the video for 10 | -112. Just wanted to point that out in case someone like me got confused with that portion of the video.
I am confused too, thanks for your clarification, also one more point, a is not 0.
while studying this book some things feel very basic and I feel like i already know all this, but when I challenge myself with proofs or questions at the end of the section, I find some of them hard. I tend to get frustrated because sometimes the questions look very basic but i just don't know how to prove them. Is this normal or should i pursue something other than computer science as a career?
Thank you a lot. Helped me solve my assignment!
Nice explanation
Hi Kimberly:
I had a question regarding whether or not the following proof is legitimate.
Prove that for all integers {a,b,c}, if a|b and b|c, then a|c.
Let {a,b,c,k,j,m} all be integers.
GIVENS: a|b ak = b a = b/k
GIVENS: b|c bj = c
PROVE: a|c am=c m = c/a
To prove that a|c, we would have to show that m is an integer.
We have to show that (c/a) simplifies to be an integer.
c/a
bj / (b/k)
Copy Dot Flip
bj * (k/b)
j*k
Integers Closed Under Multiplication
We find that m was an integer.
Thus, it is true that a|c.
Is this a legitimate proof or is there a flaw in the argument?
Thank you so much!!
Hey there, is it mathematically correct to write a property's defintion using propositional logic? ex. (a | b) ^ (a | c) -> a | (b+c)
Very helpful video lecture.
thank you so much, this helps a lot!
I am not sure how b +c =a (s +t) translates to therefore a | (b+c)
a(s)=b and a(t)=c
a(s+t)=b+c
since 'a' is a factor of 'a(s+t)', 'a' must divide 'a(s+t)'
thus a|b+c
division by zero is undefinde 14|0=? shoud we write q and r = 0
But isn't it confusing...first it is said that a|b iff b/a € Z...
Then we come to quotient and reminders because division isn't always even.
Doesn't this conflict with the original defination?
Like first we say in def that a|b only iff c is an integer... then we are okay with float values.😅
@Kimberly Brehm
I have one question here, from the definition of divisibility, is it true that a divides b if there is an unique integer c OR for some integer c such that ac=b?
It doesn't have to be unique. The definition is for SOME integer c. That being said, there will be a unique c value for every b value.
@@SawFinMath really appreciated it, thank you so much
For some reason I was not subscribed. I fixed that.
thank you
Thank you !!
You are welcome!
خليفة يسلم عليكم
8:55 is funny for some "ASS" integer lol.
I am completely lost at the proof for properties of divisibility😭😭😭