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Carl Mummert

I am a mathematics professor at Marshall University. My research is in mathematical logic (particularly reverse mathematics, second-order arithmetic, and computability theory) and in combinatorics. In Mathematics, Pennsylvania State University, 2005. In Mathematics and Computer Science, Honors College, Western Carolina University, 2000. Associate Professor, Department of Mathematics, Marshall University, 2015–present. Assistant Professor, Department of Mathematics, Marshall University, 2009–2015. Comment...

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Carl Mummert | m6c.org Reviews

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I am a mathematics professor at Marshall University. My research is in mathematical logic (particularly reverse mathematics, second-order arithmetic, and computability theory) and in combinatorics. In Mathematics, Pennsylvania State University, 2005. In Mathematics and Computer Science, Honors College, Western Carolina University, 2000. Associate Professor, Department of Mathematics, Marshall University, 2015–present. Assistant Professor, Department of Mathematics, Marshall University, 2009–2015. Comment...

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Carl Mummert | m6c.org Reviews

https://m6c.org

I am a mathematics professor at Marshall University. My research is in mathematical logic (particularly reverse mathematics, second-order arithmetic, and computability theory) and in combinatorics. In Mathematics, Pennsylvania State University, 2005. In Mathematics and Computer Science, Honors College, Western Carolina University, 2000. Associate Professor, Department of Mathematics, Marshall University, 2015–present. Assistant Professor, Department of Mathematics, Marshall University, 2009–2015. Comment...

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Computable roots of computable functions | Carl Mummert

http://m6c.org/w/2012/02/computable-roots

An incompleteness theorem for β. Quiz on public peer review →. Computable roots of computable functions. February 14, 2012. Here are several interesting results from computable analysis:. If $f$ is a computable function from $ mathbb{R}$ to $ mathbb{R}$ and $ alpha$ is an isolated root of $f$, then $ alpha$ is computable. If $p(x)$ is a polynomial over $ mathbb{R}$ with computable coefficients, then every root of $p(x)$ is computable. A quickly converging Cauchy sequence in $ mathbb{R}$ is a sequence $(a...

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LaTeX | Carl Mummert

http://m6c.org/w/resources/latex

Is a typesetting system for publishing mathematics. Originally developed in the 1970s by Donald Knuth, it is now used by virtually all mathematics journals. Thus learning to use LaTeX is a universal rite of passage for mathematicians. LaTeX itself is available free of charge, and the software itself is under an open-source license. My advice is to just install LaTeX and start working. Use one of the template files below to get started. LaTeX distributions and editors. A First LaTeX Document. Set-theoreti...

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Filter quantifiers | Carl Mummert

http://m6c.org/w/2014/11/filter-quantifiers

Talk on Reverse Mathematics and the Modal Logic of Reverse Mathematics. Talk on the existence of connected components of graphs →. November 30, 2014. PDF) by Leo Goldmakher and Ramsey Theory. PDF) by Imre Leader (lecture notes transcribed by Stiofáin Fordham). The latter is particularly nice because it uses the formalism of filter quantifiers. Here are my questions for you:. 1 Is this material covered in a textbook somewhere? Dave L. Renfro pointed out a post of his. This entry was posted in Results wort...

4

Teaching | Carl Mummert

http://m6c.org/w/teaching

In Fall 2016, I am teaching the following courses. Additional course information is available on request or from MU Online. Math 229H: Honors Calculus 1. Math 331: Linear Algebra. Math 589: Graduate Mathematics seminar. My office hours are shown in MU Online; please click the “My Professor” link on the left side of the class homepage. Set-theoretic potentialism, CUNY Logic Workshop, September, 2016. August 28, 2016. Quote by Paul Wallace. August 26, 2016. Dana C. Ernst. August 25, 2016. August 24, 2016.

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Blog | Carl Mummert

http://m6c.org/w/blog

Reverse Mathematics of Matroids. April 22, 2016. This post is about the paper Reverse Mathematics of Matroids. By Jeff Hirst and me. We look at basis theorems for countable vector spaces, countable graphs, and countable enumerated matroids. These three kinds of structures turn out to be extremely similar from the point of view of their dependence relations. Continue reading →. An example with Dedekind cuts. April 19, 2016. Continue reading →. Talk on Reverse Mathematics and Ramsey Theory. March 18, 2016.

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PSU Mathematics Department - Math Ph.D. Alumni

http://www.math.psu.edu/directory/alumni.php

Eberly College of Science. Math Ph.D. Alumni. The invariant theory and geometry pertaining to tensor networks and some further applications. Postdoc, Mathematics, University of Amsterdam, Amsterdam, Netherlands. Studies on the weak convergence of partial sums in Gibbs-Markov dynamical systems. Special visiting researcher, Instituto de Mathematica, Universidade Federal do Rio de Janeiro, Brazil. Victor Nistor and Xiantao Li. Associate, Fixed income division, Morgan Stanley, New York, NY. Quaternion algebr...

logic.dorais.org

Papers | François G. Dorais

http://logic.dorais.org/papers

François G. Dorais. Mathematical Logic and Foundations. On uniform relationships between combinatorial problems. With D. Dzhafarov, J. Hirst, J. Mileti, P. Shafer. Transactions of the American Mathematical Society 368 (2016), 1321–1359. Comparing the strength of diagonally non-recursive functions in the absence of $ Sigma 0 2$ induction. With J. Hirst, P. Shafer. Journal of Symbolic Logic 80 (2015), 1211–1235. Doi:10.1017/jsl.2015.43. Reverse mathematics of compact countable second-countable spaces.

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Carl Mummert

I am a mathematics professor at Marshall University. My research is in mathematical logic (particularly reverse mathematics, second-order arithmetic, and computability theory) and in combinatorics. In Mathematics, Pennsylvania State University, 2005. In Mathematics and Computer Science, Honors College, Western Carolina University, 2000. Associate Professor, Department of Mathematics, Marshall University, 2015–present. Assistant Professor, Department of Mathematics, Marshall University, 2009–2015. Comment...

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