wow, i watched lectures from mit and i have to say i learned very limited subject material from there! But your lectures really break it down to the basics, and explain the details that you truly need to understand in order to get the whole picture. Goes to show that the name of the institution doesn't really matter! It's the quality of instruction that matters which some schools don't offer! Excellent job!!!
so at 21:42 where you state 4+5 = 9 == 0 mod 3....... 0 is essentially the remainder of 9 (mod 3)... i guess my question or comment is r = a mod d. I keep getting confused with congruences given that there's situations where the a, in this case 0 is literally the remainder. I feel like I need clarification with this relation because I keep getting confused when it comes to remainders.
Learning python and all related math classes myself. Here's the note i made in python software, that's why you see all the hashtags: ######## You are given x mod m. Form a ≡ b (mod m) from x mod m: ######## 1). Get the remainder from x mod m ######## 2). Equation becomes: x ≡ remainder (mod m) ######## What if you are given (x + y) mod m. Form a ≡ b (mod m): ######## 1). Add x + y to get the total. ######## 2). Get the remainder from (x + y) mod m ######## 3). Equation becomes: (x + y) ≡ remainder (mod m) ######## You could also individually do: ######## 1). Get the remainder_1 of x mod m ######## 2). Set x ≡ remainder_1 mod m ######## 3). Get the remainder_2 of y mod m ######## 4). Set y ≡ remainder_2 mod m ######## 5). Add x and y to get the total ######## 6). Add remainder_1 and remainder_2 to get the total ######## 7). Set x + y = (remainder_1 + remainder_2) mod m ######## What if you are given (x * y) mod m. Form a ≡ b (mod m): ######## 1). Multiply x * y to get the total. ######## 2). Get the remainder from (x * y) mod m ######## 3). Equation becomes: x * y ≡ remainder (mod m) ######## You could also individually do: ######## 1). Get the remainder_1 of x mod m ######## 2). set x ≡ remainder_1 mod m ######## 3). Get the remainder_2 of y mod m ######## 4). Set y ≡ remainder_2 mod m ######## 5). Multiple x and y to get the total ######## 6). Multiple remainder_1 and remainder_2 to get total ######## 7). Set x * y = (remainder_1 * remainder_2) mod m
Im confused beginning at the slide at 20:46 and going forward. Before you wrote the remainder as "r = a mod d" but in that slide it looks like you are writing it as "a = r mod d" Can someone explain to me why this is? Thanks otherwise for some great content Kimberly.
The remainder would be written as r=a mod d. To rewrite a number in a new modulo, we would write it as a=r mod d. We generally don't write the r= version. Those examples were for you to understand we were looking for a remainder.
at 3:34 was said "differences in their remainders is divisible by 4". is it correct - differences in their remainders?? I do not get what this mean, though I seem to understand the concept of two numbers being congruent.. thnks for everything!
I don't quite get this part: 2 ≡ 6 (mod 4) because 4 | (2 - 6) which means that 4 | (-4), so that there exists a variable c such that 4 * c = -4, and c must be positive integer (stated from the previous video). But in this case, c must be negative for the equation to be true. So is the formula actually m | abs(a - b)?
The Last question on Arithmetic Equation why you changed the position of the remind its was like a = b mod m and u change it like b = a mod m i didn't get it
mam , where can i get your explaination for (a + b) mod m = ((a mod m) + (b mod m)) mod m... and for ab mod m = ((a mod m)(b mod m)) mod m ??...i really wanted that part...
wow, i watched lectures from mit and i have to say i learned very limited subject material from there! But your lectures really break it down to the basics, and explain the details that you truly need to understand in order to get the whole picture. Goes to show that the name of the institution doesn't really matter! It's the quality of instruction that matters which some schools don't offer! Excellent job!!!
You are a gem, you don't lecture and just talk like many university professors but do a phenomenal job explaining and simplifying concepts.
HOW IS THIS FREE!!!!!! I paid my kidneys worth for university and i have a professor here explaining it much better and that too for free 😭.
1:56 *-1/4 with a reminder of 3 - for those who are confused ig she just mistakenly said -4 but she meant -1
that confused me lmao ty
Best modulo training video I have come across. Thank you.
you are the greatest person in the universe
I'm so grateful for your efforts , thank you so much
so at 21:42 where you state 4+5 = 9 == 0 mod 3....... 0 is essentially the remainder of 9 (mod 3)... i guess my question or comment is r = a mod d. I keep getting confused with congruences given that there's situations where the a, in this case 0 is literally the remainder. I feel like I need clarification with this relation because I keep getting confused when it comes to remainders.
Learning python and all related math classes myself. Here's the note i made in python software, that's why you see all the hashtags:
######## You are given x mod m. Form a ≡ b (mod m) from x mod m:
######## 1). Get the remainder from x mod m
######## 2). Equation becomes: x ≡ remainder (mod m)
######## What if you are given (x + y) mod m. Form a ≡ b (mod m):
######## 1). Add x + y to get the total.
######## 2). Get the remainder from (x + y) mod m
######## 3). Equation becomes: (x + y) ≡ remainder (mod m)
######## You could also individually do:
######## 1). Get the remainder_1 of x mod m
######## 2). Set x ≡ remainder_1 mod m
######## 3). Get the remainder_2 of y mod m
######## 4). Set y ≡ remainder_2 mod m
######## 5). Add x and y to get the total
######## 6). Add remainder_1 and remainder_2 to get the total
######## 7). Set x + y = (remainder_1 + remainder_2) mod m
######## What if you are given (x * y) mod m. Form a ≡ b (mod m):
######## 1). Multiply x * y to get the total.
######## 2). Get the remainder from (x * y) mod m
######## 3). Equation becomes: x * y ≡ remainder (mod m)
######## You could also individually do:
######## 1). Get the remainder_1 of x mod m
######## 2). set x ≡ remainder_1 mod m
######## 3). Get the remainder_2 of y mod m
######## 4). Set y ≡ remainder_2 mod m
######## 5). Multiple x and y to get the total
######## 6). Multiple remainder_1 and remainder_2 to get total
######## 7). Set x * y = (remainder_1 * remainder_2) mod m
Im confused beginning at the slide at 20:46 and going forward. Before you wrote the remainder as "r = a mod d" but in that slide it looks like you are writing it as "a = r mod d" Can someone explain to me why this is? Thanks otherwise for some great content Kimberly.
The remainder would be written as r=a mod d. To rewrite a number in a new modulo, we would write it as a=r mod d. We generally don't write the r= version. Those examples were for you to understand we were looking for a remainder.
@@SawFinMath Thank you very much. Hope you're doing well. Much appreciated.
at 3:34 was said "differences in their remainders is divisible by 4". is it correct - differences in their remainders?? I do not get what this mean, though I seem to understand the concept of two numbers being congruent.. thnks for everything!
Tried doing Equivalence Relation without knowing this bit, huge mistake!
I don't quite get this part:
2 ≡ 6 (mod 4) because 4 | (2 - 6) which means that 4 | (-4), so that there exists a variable c such that 4 * c = -4, and c must be positive integer (stated from the previous video). But in this case, c must be negative for the equation to be true. So is the formula actually m | abs(a - b)?
same confusion here
@@ukpkmkk8409 C can be negative, it says in the book. Hope this helps.
Love these videos, thank you so muchh!!!!
Hii
CcC türkler geldi
you are the best. thank you very much for the video
You're welcome!
The Last question on Arithmetic Equation why you changed the position of the remind its was like a = b mod m and u change it like b = a mod m i didn't get it
Thank u so much for these videos
Got confused starting 8:31 :(
lol
@@kingmikeyyy9939 mean
Thankyou ❤
1:56 I am confused.
We can't have a negative remainder but we can have a negative quotient.
@@SawFinMath Thanks so much!
mam , where can i get your explaination for (a + b) mod m = ((a mod m) + (b mod m)) mod m... and for ab mod m = ((a mod m)(b mod m)) mod m
??...i really wanted that part...
It's algebraic property, probably u could see her set theory at this first playlist
"-1 would actually be -4/4 with a remainder of 3." ........literally what?
-1 + 4 = 3
could anyone tell me how can I say her thanks!
thank you so much!
16:47
Thanks mam
You are welcome!
حلو
blm
12:06