I've read the introduction as you indicated; skipped the "Application of Dihedral Groups" chapter altogether; skimmed chapter 3 "Groups"; felt a strong urge to do the example problem sets because my brain kept saying, "oh, yes, I remember that" but I wonder if I really do.
if you're not planning on going back to it in the next few months, you could probably return it, but there's no real hurry on this end. i was more curious to hear how it was going. in related news, i'm into chapter 6 or 7 of your crypto book - it's my in-classroom reading for when students are working on assignments.
The definition given for modular arithmetic (pg 7) uses the "remainder" definition I learned in high school. My memory of this definition from university is that it's actually the set of all numbers in the set of (positive?) Integers with the property that they return this remainder. The idea being that:
3 mod 7 => (3, 10, 17, 24, ...)
But we usually represent the number as '3' for simplicity. Am I out to lunch? It's been a long time.
the two definitions are equivalent. the official mathematical machinery is as follows: we define an equivalence ~ by a ~ b if a-b is a multiple of seven. then the sets of which you speak are the equivalence classes of Z with respect to ~. it's fairly easy to show that each of those equivalence classes has precicsely one representative in the integers 0, 1, 2, 3, 4, 5, 6, and slightly more fiddly, but not too complicated to show that we can get away with just doing our arithmetic on those representatives.
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I should return it, then, yes?
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in related news, i'm into chapter 6 or 7 of your crypto book - it's my in-classroom reading for when students are working on assignments.
no subject
The definition given for modular arithmetic (pg 7) uses the "remainder" definition I learned in high school. My memory of this definition from university is that it's actually the set of all numbers in the set of (positive?) Integers with the property that they return this remainder. The idea being that:
3 mod 7 => (3, 10, 17, 24, ...)
But we usually represent the number as '3' for simplicity. Am I out to lunch? It's been a long time.
no subject
we define an equivalence ~ by a ~ b if a-b is a multiple of seven. then the sets of which you speak are the equivalence classes of Z with respect to ~. it's fairly easy to show that each of those equivalence classes has precicsely one representative in the integers 0, 1, 2, 3, 4, 5, 6, and slightly more fiddly, but not too complicated to show that we can get away with just doing our arithmetic on those representatives.