Discrete Math - 4.1.2 Modular Arithmetic

Introduction to modular arithmetic including several proofs of theorems along with some computation.

Video Chapters:
Introduction 0:00
Modular Arithmetic and First Theorem 0:04
Modular Arithmetic Second Theorem 4:09
Modular Arithmetic Third Theorem 8:26
Modular Arithmetic Proof 11:51
Modular Arithmetic Example 18:21
Arithmetic Modulo m 20:49
Up Next 22:15

Textbook: Rosen, Discrete Mathematics and Its Applications, 7e

[trippin]

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!!!

[craiggray]

Best modulo training video I have come across. Thank you.

[nooruzuneel]

HOW IS THIS I paid my kidneys worth for university and i have a professor here explaining it much better and that too for free 😭.

[bestyoueverhad.]

Tried doing Equivalence Relation without knowing this bit, huge mistake!

[jinanashour]

you are the greatest person in the universe

[vleraa]

1:56 *-1/4 with a reminder of 3 - for those who are confused ig she just mistakenly said -4 but she meant -1

[uiu.x]

I'm so grateful for your efforts, thank you so much

[melisaozen]

Love these videos, thank you so muchh!!!!

[rozakhakimova]

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!

[Light-evdt]

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)?

[BeeshoStudying]

you are the best. thank you very much for the video

[jaydeestrada]

so at 21:42 where you state 4+5 = 9 == 0 mod 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.

[atviking]

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.

[ShotoTodoroki-hhrt]

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...

[AHADOPT-jfdx]

could anyone tell me how can I say her thanks!

[gackerman]

"-1 would actually be -4/4 with a remainder of 3." what?