Welcome to the homepage of

Noah A. Hughes
Assistant Professor
Department of Mathematics
Winston-Salem State University

My name is Noah Hughes and I am an Assistant Professor of mathematics at Winston-Salem State University. You can download a pdf copy of my cv here and reach me by email at: hughesna[at]wssu[dot]edu

I work in mathematical logic and more specifically computability theory. A nice intuivitve description of mathematical logic (credit to Paul Shafer) is that it is the "mathematics of mathematics" in much the way calculus is the mathematics of change and geometry is the mathematics of shape. Using appropriate formilizations we take the theorems, constructions, and arguments in mathematics as our objects of study. I am particularly interested in understanding the foundational connections between mathemtical principles and the fundamental ingredients needed to prove them. Computability theory provides the robust framework needed to carry out this analysis.

I am originally from Linville, North Carolina, a rural town in the Appalachian Mountains. Here I developed a love of the outdoors, but outside of that I love good books, playing the drums, and learning about nearly anything. The following picture was taken by Madelyn Hughes during an October snow in Hartford, CT.

Below you will find my scholarly work. Please note that all linked titles direct to unpublished drafts.

Journal articles

Reverse mathematics and marriage problems with finitely many solutions with Jeffry L. Hirst.
Archive for Mathematical Logic, 55(7) (2016) 1015--1024. Available online (DOI) 10.1007/s00153-016-0509-4 for subscribers. This article can be viewed through the Springer Nature Content Sharing Intiative.

Reverse mathematics and marriage problems with unique solutions with Jeffry L. Hirst.
Archive for Mathematical Logic 54 (2015) 49-57. Available online (DOI) 10.1007/s00153-014-0401-z for subscribers.

On the minuscule representation of type Bn. with William J. Cook.
Inolve 11 (2018), No. 5, 721-733. Available online (DOI) 10.2140/involve.2018.11.721 for subscribers.

Theses

Applications of Computability Theory to Infinitary Combinatorics
Ph.D. thesis, University of Connecticut, 2021.

Reverse mathematics: Calibrating logical strength in mathematics
Honors undergraduate thesis, Appalachian State University, 2014.

Listed below are all presentations I have given at scholarly meetings in chronological order.

2022

Department of Mathematical Sciences Colloquium Series
Appalachian State University, December (slides)

2019

IMS Graduate Summer School in Logic
National University of Singapore, July (slides)

AMS Spring Eastern Sectional Meeting, Special Session on Computability Theory
University of Connecticut, April

2018

New England Recursion and Definability Seminar
Springfield College, November (slides)

SIGMA Seminar
University of Connecticut, March (slides)

2016

Association for Symbolic Logic 2016 North American Annual Meeting
University of Connecticut, May (slides)

2015

Mathematical Sciences Colloquium Series
Appalachian State University, March (slides)

MAA-SE Spring Meeting
UNC Wilmington, March

S-STEM Seminar
Appalachian State University, January

Joint Mathematics Meetings
San Antonio TX, January

2014

UNCG Regional Mathematics and Statistics Conference
UNC Greensboro, November
Award: Outstanding Graduate Student Presentation. (slides)

National Conference on Undergraduate Research
University of Kentucky, April (slides)

Mathematical Sciences Colloquium Series
Appalachian State University, March (slides)

Logic seminar
Ghent University, March

2013

North Carolina Honors Association Conference
Appalachian State University, October (slides)

Mathematical Sciences Colloquium Series
Appalachian State University, April

MAA-SE Spring Meeting
Winthrop University, March

2012

UNCG Regional Mathematics and Statistics Conference
UNC Greensboro, November

North Carolina Council of Teachers of Mathematics Annual Meeting
with Eric Marland, Gregory S. Rhoads and Faith Miller
Greensboro NC, October

I am currently teaching:

Algebraic Structures II

Elementary Statistics

Linear Algebra

I have previously taught the following courses.

At Winston-Salem State University

Algebraic Structures I, Fall 2022

Elementary Statistics, Fall 2022, Fall 2021, Summer 2022

Linear Algebra, Spring 2021

At University of Connecticut:

Applied Linear Algebra, Spring 2019, Fall 2019, Summer 2020

Calculus I, BRIDGE 2018, Fall 2020; (You can learn more about BRIDGE here.)

Calculus II, Spring 2016, Fall 2016

Elementary Differential Equations, Spring 2017, Spring 2018

Multivariable Calculus, Fall 2017, Fall 2018

Problem Solving, Fall 2015

At Appalachian State University

College Algebra with Applications, Fall 2014, Spring 2015