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- More Fun With Combinatorics: A Very Short Post
- The probability that $s$ integers are relatively $r$-prime for a class of probability distributions on the integers
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- On The Product of All Primes Between $N$ and $2N$ Compared to $2^{N}$
- All Harmonic Series Diverge — And a Consequence!
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Monthly Archives: May 2015
Freshman’s Dream Come True! (But only in characteristic $p$)
A well-known fallacy committed by students is the so-called “Law of Universal Linearity” (the link is to a discussion of this phenomenon on Mathematics Stack Exchange). The most famous example of this is the statement $$\left(x+y\right)^n = x^n + y^n,$$ … Continue reading
A Fun Integral Problem
I ask that anyone who has had multivariable calculus please stop right now and try to work out this problem. $$\int_0^1\int_0^1\frac{dx\,dy}{1-xy}.$$ Hint: The integrand looks familiar!
Posted in Problems
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Site Transfer Complete!
I have just finished moving all of my posts from the old location of this blog from a free webhost. I hope to be more productive from now on!
Posted in Uncategorized
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Studying for Comprehensive Exams (Part 1)
So as I study for my comprehensive exams, I will post some of my favorite problems from my studies.
Posted in Problems
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Divisibility Rules: An Introduction to Modular Arithmetic
There are many rules for determining whether a number is divisible by another. For example, we know that a number is even (divisible by 2) whenever the one’s digit is even. We also know that a number is divisible by … Continue reading
Posted in Basic Facts, Elementary Number Theory
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Primes and Probabilities
When I was in grade school learning about primes, I would ask myself: How many primes are there? If I pick a number at random, will it be prime?
Posted in Analytic Number Theory
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