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... points during a topic. You must notify me before (up to the morning of) the day the quiz is given if it becomes necessary for you to miss it. If no prior notice is given for missing the quiz, you will not be able to make up the quiz and a zero grade will be recorded. Exams: There will be 4-5 major e ...
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... with proof, I will not schedule a make-up exam and a zero grade will be recorded. In general, make-up exams may be of greater difficulty than regular exams because of the additional study time you have had. (The exams are usually announced one week in advance.) Homework Quizzes and Weekly Quizzes wi ...
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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.
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