2 - Mrs. Melott
... lesson. Remember, simplifying does not change the value of the expression. It only changes its appearance. Consider this: Three groups of musicians are coming to town to perform in a show. Each group consists of 5 women and 4 men. How many total women are there? How many total men? To find out, you ...
... lesson. Remember, simplifying does not change the value of the expression. It only changes its appearance. Consider this: Three groups of musicians are coming to town to perform in a show. Each group consists of 5 women and 4 men. How many total women are there? How many total men? To find out, you ...
7. Recursion Section 2.3
... The sum of the first N odd integers is N 2. Base case. True for N = 1. Induction step. The N th odd integer is 2N − 1. Let TN = 1 + 3 + 5 + ... + (2N − 1) be the sum of the first N odd integers. ...
... The sum of the first N odd integers is N 2. Base case. True for N = 1. Induction step. The N th odd integer is 2N − 1. Let TN = 1 + 3 + 5 + ... + (2N − 1) be the sum of the first N odd integers. ...
7 Catalan Numbers
... A stack is a list which can only be changed by insertions or deletions at one distinguished end, called the top of the list. When characters are individually inserted and deleted from the stack, the last one inserted must be the first one deleted from the stack (lifo). An insertion to the top of the ...
... A stack is a list which can only be changed by insertions or deletions at one distinguished end, called the top of the list. When characters are individually inserted and deleted from the stack, the last one inserted must be the first one deleted from the stack (lifo). An insertion to the top of the ...
4.1 Reduction theory
... √ on, for the rest of this section we assume ∆ < 0 is a fundamental discriminant. Let K = Q( ∆) be the imaginary quadratic field of discriminant ∆. Definition 4.3.1. Let I be an ideal of OK with ordered Z-basis {α, β}. Then the quadratic form associated to I is QI (x, y) = N (αx + βy)/N (I) = ax2 + ...
... √ on, for the rest of this section we assume ∆ < 0 is a fundamental discriminant. Let K = Q( ∆) be the imaginary quadratic field of discriminant ∆. Definition 4.3.1. Let I be an ideal of OK with ordered Z-basis {α, β}. Then the quadratic form associated to I is QI (x, y) = N (αx + βy)/N (I) = ax2 + ...
1-Integers - Laurel County Schools
... You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the ...
... You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.