Basic algorithms in number theory - Library
... A formalization of these ideas requires precise definitions for “algorithm,” “input,” “output,” “cost,” “elemental operation,” and so on. We will give none. Instead, we consider a series of number-theoretic algorithms and discuss their complexity from a fairly naive point of view. Fortunately, this ...
... A formalization of these ideas requires precise definitions for “algorithm,” “input,” “output,” “cost,” “elemental operation,” and so on. We will give none. Instead, we consider a series of number-theoretic algorithms and discuss their complexity from a fairly naive point of view. Fortunately, this ...
Mutually Orthogonal Latin Squares and Finite Fields
... Proof. Take any collection T1 , . . . Tk of mutually orthogonal Latin squares. Then notice the following property: if we take any of our Latin squares and permute its symbols (i.e. switch all the 1 and 2’s), the new square is still mutually orthogonal to all of the other squares. (Think about this ...
... Proof. Take any collection T1 , . . . Tk of mutually orthogonal Latin squares. Then notice the following property: if we take any of our Latin squares and permute its symbols (i.e. switch all the 1 and 2’s), the new square is still mutually orthogonal to all of the other squares. (Think about this ...
3. Modules
... called a module; we will introduce and study it in this chapter. In fact, there is another more subtle reason why modules are very powerful: they unify many other structures that you already know. For example, when you first heard about quotient rings you were probably surprised that in order to obt ...
... called a module; we will introduce and study it in this chapter. In fact, there is another more subtle reason why modules are very powerful: they unify many other structures that you already know. For example, when you first heard about quotient rings you were probably surprised that in order to obt ...
