Chapter 3 - Eric Tuzin Math 4371 Portfolio
... Any number can be written as the product of factors of primes. A prime number is any number that is only divisible by 1 and itself. Therefore if the FTA is applied to any integer, we know the number is either a prime number or a composite number, which would be a multiple of some prime numbers found ...
... Any number can be written as the product of factors of primes. A prime number is any number that is only divisible by 1 and itself. Therefore if the FTA is applied to any integer, we know the number is either a prime number or a composite number, which would be a multiple of some prime numbers found ...
Solutions
... To show that the given set (let’s call it E) is countable we need to construct a bijection between N and E. Let f : N → E be given by f (n) = 2n − 1. This function is 1-1 because if f (n1 ) = f (n2 ) then 2n1 − 1 = 2n2 − 1, which implies 2n1 = 2n2 , and then n1 = n2 . This function is onto because a ...
... To show that the given set (let’s call it E) is countable we need to construct a bijection between N and E. Let f : N → E be given by f (n) = 2n − 1. This function is 1-1 because if f (n1 ) = f (n2 ) then 2n1 − 1 = 2n2 − 1, which implies 2n1 = 2n2 , and then n1 = n2 . This function is onto because a ...
PERFECT NUMBERS - Dartmouth Math Home
... sum as the number itself. For the same reason twenty-eight, four hundred ninety-six, and eight thousand one hundred twenty-eight are called perfect numbers [2]. Saint Augustine (among others, including the early Hebrews) considered 6 to be a truly perfect number—God fashioned the Earth in precisely ...
... sum as the number itself. For the same reason twenty-eight, four hundred ninety-six, and eight thousand one hundred twenty-eight are called perfect numbers [2]. Saint Augustine (among others, including the early Hebrews) considered 6 to be a truly perfect number—God fashioned the Earth in precisely ...
review for Exam #1: 6.1-8.2
... questions with a,b,c, and d as their answer is 8,3,4, and 5, respectively, how many different answer keys are possible, if the questions can be placed in any order? d) How many ways are there to assign 24 students to five faculty advisors? e) A witness to a hit and run accident tells the police that ...
... questions with a,b,c, and d as their answer is 8,3,4, and 5, respectively, how many different answer keys are possible, if the questions can be placed in any order? d) How many ways are there to assign 24 students to five faculty advisors? e) A witness to a hit and run accident tells the police that ...
Lindstrom with weights
... So, problem 4 is in some ways a special case of problem 2. Note: If you try to apply Dodgson condensation directly to the tridiagonal matrix, you’ll run into lots of 0/0 situations. There’s a clever way to replace the 0’s by powers of epsilon and then send epsilon to 0. Lindstrom with weights (You m ...
... So, problem 4 is in some ways a special case of problem 2. Note: If you try to apply Dodgson condensation directly to the tridiagonal matrix, you’ll run into lots of 0/0 situations. There’s a clever way to replace the 0’s by powers of epsilon and then send epsilon to 0. Lindstrom with weights (You m ...
Fractals Rule!
... number of iterations N and determine whether the sequence is convergent, divergent or cyclic at that point. The Mandelbrot Set consists of those points c in C for which the sequence does NOT diverge, when N goes to infinity. ...
... number of iterations N and determine whether the sequence is convergent, divergent or cyclic at that point. The Mandelbrot Set consists of those points c in C for which the sequence does NOT diverge, when N goes to infinity. ...
Chapter 11
... 10. For many years, the state of California used 3 letter followed by 3 digits on its automobile license plates: a. How many different license plates are possible with this arrangement? ...
... 10. For many years, the state of California used 3 letter followed by 3 digits on its automobile license plates: a. How many different license plates are possible with this arrangement? ...
