
Recent Posts
 Hilbert’s Basis Theorem June 18, 2017
 “One Line” Algebra Qual Problems June 17, 2017
 A good title for this blog post exists, but I don’t know what it is June 9, 2017
 Groups of order 4,312 are not simple: An application of Sylow Theory May 27, 2017
 Cauchy’s Theorem May 16, 2017
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Author Archives: tcgrubb
Hilbert’s Basis Theorem
If you have had some experience with rings and commutative algebra in the past, you may have encountered the idea of a Noetherian ring. This post will not deal with explaining Noetherian rings or their importance; instead I would recommend several … Continue reading
Posted in Ring and Field Theory
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“One Line” Algebra Qual Problems
Today I’m going to try to distill some solutions to previous algebra qual problems into one sentence answers. This will likely mean that the solutions are missing details, but my hope is to be able to give a decent overview … Continue reading
A good title for this blog post exists, but I don’t know what it is
Today we will look at one of my favorite topics in combinatorics: the probabilistic method. Championed by Paul Erdős in the 1940’s, the probabilistic method has since become a staple in extremal and Hungarianstyle combinatorics. While the applications of the probabilistic method … Continue reading
Groups of order 4,312 are not simple: An application of Sylow Theory
Today we will solve a problem from Wisconsin’s 2012 Algebra Qualifying Exam. The main tools used in the problem are Sylow Theory and group actions; we will take these tools for granted, but for great introductions to each topic I would … Continue reading
Cauchy’s Theorem
The famous Lagrange’s Theorem states that, in any finite group , the order of any element divides the order of . A natural follow up to this theorem is whether or not the converse holds. That is, if divides the order of … Continue reading
What are Permutation Patterns?
Today we examine a topic known as combinatorial pattern avoidance. There has been an explosion of interest in this field of late; see, for instance, the international permutation patterns conference, or any recent issues of your favorite discrete mathematics journal. I was … Continue reading
On the geometric mean of the binomial coefficients
Today we prove a remarkable asymptotic result regarding the binomial coefficients. Namely, let . We will show Before getting to the proof, I should say that this is most definitely not my creation; I believe the first publication of this … Continue reading
Posted in Asymptotics, Combinatorics, Contest Math
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