# Nathan C. Carter

Associate Professor, Mathematical SciencesPh.D., Indiana University, 2004

M.S., Indiana University, 2004

M.A., Indiana University, 2001

B.S., University of Scranton, 1999

Office: Morison Hall 394 | 781.891. 3171 | ncarter@bentley.edu

Department Phone: 781.891. 2702 | Department Fax: 781.891.2457

### Bio

Nathan Carter uses computer science to advance mathematics. He studied both subjects at the University of Scranton and at Indiana University, earning a Ph.D. in mathematical logic in 2004. Besides work in logic, he has written a book on group theory visualization, and done a little work in social network analysis. His open source mathematics software, including packages for group theory visualization, games in formal logic, and a general validation environment for mathematical reasoning, is available at http://www.platosheaven.com.

### Teaching Interests

Mathematical Logic; Computer Graphics; Programming Languages

### Research Interests

Mathematics education software; Metamathematics, subclassical logics, intuitionism; Social Network Analysis

### Consulting/Practice Interests

Software development (cross-platform desktop apps using Qt, mobile apps for iOS and Android)

### Professional Links

http://web.bentley.edu/empl/c/ncarter/

http://www.platosheaven.com

### Awards and Honors

2016, Innovation in Teaching Award, Bentley University

2014, Innovation in Teaching Award, Bentley University

2012, Outstanding Scholarly Contribution, Bentley University

2012, Trevor Evans Award, Mathematical Association of America

2012, Beckenbach Book Prize, Mathematical Association of America

2010, Henry L. Alder Award, Mathematical Association of America

2007, Bentley Innovation in Teaching Award, Bentley University

2003, Rothrock Teaching Award, Indiana University Department of Mathematics

### Publications

**Journal Article(s)**

Carter, N. C., Predescu, M. (2010). A Study of the Effect of Density Dependence in a Matrix Population Model. *The Australian Journal of Mathematical Analysis and Applications**, 7* (1), 1-16.

Carter, N. C. (2008). Reflexive Intermediate First-Order Logics. *Notre Dame Journal of Formal Logic**, 49* (1), 75-95.
(link)

Adams, S. M., Carter, N. C., Hadlock, C. R., Haughton, D. M., Sirbu, G. (2008). Proactive Encouragement of Interdisciplinary Research Teams in a Business School Environment: Strategy and Results. *Journal of Higher Education Policy and Management**, 30* (2), 153-164.

Carter, N. C., Hadlock, C. R., Haughton, D. M. (2008). Generating random networks from a given distribution. *Computational Statistics & Data Analysis**, 52* (8), 3928-3938.

Adams, S. M., Carter, N. C., Hadlock, C. R., Haughton, D. M., Sirbu, G. (2008). Change in connectivity in a social network: a Bayesian perspective. *Connections**, 28* (2), 17-27.

Carter, N. C. (2006). Reflexive Intermediate Propositional Logics. *Notre Dame Journal of Formal Logic**, 47* (1), 39-62.
(link)

Adams, S. M., Carter, N. C., Hadlock, C. R., Haughton, D. M., Sirbu, G. (2006). A recipe for collaborative research. *BizEd September/October**, September/October*, 30-34.

Carter, N. C., Emmons, B. (2005). Group Theory Visualization with Group Explorer. *Journal of Online Mathematics and its Applications*.
(link)

Carter, N. C., Grimes, S. M., Reiter, C. A. (1999). Frieze and Wallpaper Chaotic Attractors with a Polar Spin. *Computers & Graphics**, 22* (6), 765-779.

Carter, N. C., Eagles, R. L., Grimes, S. M., Hahn, A. C., Reiter, C. A. (1998). Chaotic Attractors with Discrete Planar Symmetries. *Chaos, Solitons & Fractals**, 9* (12), 2031-2054.**Books**

Carter, N. C. (2016). *Introduction to the Mathematics of Computer Graphics*.
Washington, DC: Mathematical Association of America.
(link)

Carter, N. C, Magnus, P. (2013). *forall x in Lurch*.
self-published for free on the web.
(link)

Carter, N. C. (2009). *Visual Group Theory*.
Washington, DC: Mathematical Association of America.
(link)
**Book Chapters**

Carter, N. C, Monks, K. G. (2015). From Formal to Expository: Using the Proof-Checking Word Processor Lurch to Teach Proof Writing.
In Jennifer Franko-Vasquez, Rachel Schwell, Aliza Steurer (Eds.), *Beyond Lecture: Resources and Pedagogical Techniques for Enhancing the Teaching of Proof-Writing Across the Curriculum*. Washington, DC: . Mathematical Association of America**Book Reviews**

Carter, N. C. (2009).
[Review of the book *Five Minute Mathematics*]. *Math Horizons.*
(link)
**Conference Proceeding(s)**

Carter, N. C., Monks, K. G. (2013). Lurch: a word processor that can grade students' proofs. *CICM 2013**, Conference on Intelligent Computer Mathematics*.

Carter, N. C., Monks, K. G. (2013). Lurch: a word processor that can grade students' proofs. *CEUR-WS**, 1010*.
(link)

Carter, N. C., Monks, K. G. (2013). Lurch: a word processor built on OpenMath that can check mathematical reasoning. *CEUR-WS**, 1010*.
(link)

Carter, N. C., Monks, K. G. (2013). Lurch: a word processor built on OpenMath that can check mathematical reasoning. *CICM 2013**, Conference on Intelligent Computer Mathematics*.**Conference Paper(s)**

Carter, N. C. (2017). A Web-Based Toolkit for Mathematical Word Processing Applications with Semantics. *Springer**, Lecture Notes in Artificial Intelligence*, 15.
Forthcoming
(link)

Carter, N. C., Emmons, B. (2004). Group Explorer - Visualization Software in the Abstract Algebra Classroom. *Mathematical Association of America and American Mathematical Society**, Joint Meetings*.**Other(s)**

Carter, N. C, Farrington, E. (2011). A Quick Tour of Manjul Bhargava’s 2011 Hedrick Lectures on Elliptic Curves. *Math Horizons*, 6-7.

Carter, N. C. (2004). Reflexive Logics - Intermediate logics that can prove their own completeness.
(link)
Forthcoming

### Conference Presentations

Carter,
N.
C. (2017).
"A Web-Based Toolkit for Mathematical Word Processing Applications with Semantics."
Presented at the
University of Edinburgh's
*Conference on Intelligent Computer Mathematics*,
Edinburgh, UK.

Carter,
N.
C. (2017).
"Minicourse: Teaching an Introduction to the Mathematics of Computer Graphics."
Presented at the
Mathematical Association of America, American Mathematical Society's
*Joint Mathematics Meetings*,
Atlanta, GA.

Carter,
N.
C. (2016).
"Workshop: Teaching an Introduction to the Mathematics of Computer Graphics."
Presented at the
Mathematical Association of America's
*MathFest*,
Columbus, OH.

Carter,
N.
C. (2016).
"Assessment Facilitated by Technology."
Presented at the
Fields Institute, University of Toronto's
*Digital Open Mathematics Education*,
Toronto, ON.

Carter,
N.
C. (2015).
"Demonstration and Poster on "Lurch" Mathematical Software."
Presented at the
Conference on Intelligent Computer Mathematics's
*Conference on Intelligent Computer Mathematics*,
Washington, D.C..

Carter,
N.
C., Monks,
K.
G. (2014).
"Lurch: A Word Processor that can Grade Students' Proofs."
Presented at the
Mathematical Association of America's
*MathFest*,
Portland, OR.

Carter,
N.
C. (2014).
"The Value of Visualization in Group Theory."
Presented at the
Indiana University's
*An informal evening mathematics lecture*,
Bloomington, IN.

Carter,
N.
C., Monks,
K.
G. (2014).
"Lurch: A Word Processor that can Grade Students' Proofs."
Presented at the
Indiana University's
*Logic Seminar*,
Bloomington, IN.

Carter,
N.
C. (2014).
"What does Rubik's Cube have to do with Quintic Polynomials?"
Presented at the
Western Illinois University's
*63rd Annual Western Illinois University Mathematics Teachers Conference*,
Macomb, IL.

Carter,
N.
C. (2014).
"Introduction to the Mathematics of Computer Graphics."
Presented at the
Western Illinois University's
*Mathematics Department Colloquium*,
Macomb, IL.

Carter,
N.
C., Monks,
K.
G. (2013).
"Using Lurch in an Introduction to Proofs Course."
Presented at the
Mathematical Association of America's
*MathFest*,
Hartford, CT.

Carter,
N.
C. (2013).
"Lurch: A word processor built on OpenMath that can check mathematical reasoning."
Presented at the
CICM 2013's
*Conference on Intelligent Computer Mathematics*,
University of Bath, Bath, UK.

Carter,
N.
C., Monks,
K.
G. (2013).
"Lurch: a word processor built on OpenMath that can check mathematical reasoning."
Presented at the
CICM 2013's
*Conference on Intelligent Computer Mathematics*,
University of Bath, Bath, UK.

Carter,
N.
C., Monks,
K.
G. (2013).
"Lurch: a word processor that can grade students' proofs."
Presented at the
CICM 2013's
*Conference on Intelligent Computer Mathematics*,
University of Bath, Bath, UK.

Carter,
N.
C. (2013).
"Lurch: A word processor that can check your math."
Presented at the
Mathematical Association of America and American Mathematical Society's
*Joint Meetings*,
San Diego, CA.

Carter,
N.
C. (2012).
"Mathematics of Computer Graphics."
Presented at the
Bentley University Mathematics Department's
*Bentley University Mathematics Department Seminar*,
Waltham, MA.

Carter,
N.
C. (2012).
"Lurch: A word processor that can check your math."
Presented at the
Mathematical Association of America's
*MathFest*,
Madison, WI.

Carter,
N.
C. (2012).
"Lurch: A word processor that can check your math."
Presented at the
Mathematical Association of America and American Mathematical Society's
*Joint Meetings*,
Boston, MA.

Carter,
N.
C. (2011).
"Lurch: A word processor that can check your math."
Presented at the
Bentley University Mathematical Sciences Department's
*Departmental Seminar*,
Waltham, MA.

Carter,
N.
C. (2011).
"Lurch: A word processor that can check your math."
Presented at the
Mathematical Association of America and American Mathematical Society's
*Joint Meetings*,
New Orleans, LA.

Carter,
N.
C. (2010).
"From Zero to Galois Theory in 50 Minutes."
Presented at the
Gordon College's
*Math Department Seminar*,
Wenham, MA.

Carter,
N.
C. (2010).
"The Lurch Project: A word processor that checks you rmath."
Presented at the
Mathematical Association of America's
*MathFest*,
Pittsburgh, PA.

Carter,
N.
C. (2010).
"Using Lurch in the Classroom."
Presented at the
Maryland/D.C./Virginia Section of the Mathematical Association of America's
*Section Meeting of the MAA*,
Virginia State University, Petersburg, MD.

Carter,
N.
C. (2010).
"Visualization Lessons from Visual Group Theory."
Presented at the
Mathematical Association of America and American Mathematical Society's
*Joint Meetings*,
San Francisco, CA.

Carter,
N.
C. (2009).
"Lurch: Software for Teaching Mathematical Proofs."
Presented at the
Clay Math Institute's
*Sage Education Day 1*,
Cambridge, MA.

Carter,
N.
C. (2009).
"Lurch: Software for Teaching and Writing Mathematical Proofs."
Presented at the
Mathematical Association of America's
*MathFest*,
Portland, OR.

Carter,
N.
C. (2009).
"Visual Group Theory."
Presented at the
Mathematical Association of America's
*MathFest*,
Portland, OR.

Carter,
N.
C. (2008).
"The Lurch Project: Can Computers Correct Mathematical Writing?"
Presented at the
Bentley University's
*Math Department Seminar*,
Waltham, MA.

Carter,
N.
C. (2008).
"A Talk Without Words: Visualizing Group Theory."
Presented at the
Mathematical Association of America and American Mathematical Society's
*Joint Meetings*,
San Diego, CA.

Carter,
N.
C., Hadlock,
C.
R., Haughton,
D.
M., Sirbu,
G. (2007).
"Generating Random Networks from p1 and p-star Models with Applications to Distributions of Graph-Level Indices."
Presented at the
*IASC 07 - Statistics for Data Mining, Learning and Knowledge Extraction*,
Aveiro, Portugal.

Carter,
N.
C. (2007).
"Visualizing Group Theory with Group Explorer."
Presented at the
Mathematical Association of America and American Mathematical Society's
*Joint Meetings*,
New Orleans, LA.

Carter,
N.
C. (2006).
"Visualizing Group Theory: From Zero to Galois Theory in 50 Minutes."
Presented at the
Marywood University's
*Math Department Seminar*,
Scranton, PA.

Carter,
N.
C. (2006).
"Visualizing Group Theory: From Zero to Galois Theory in 50 Minutes."
Presented at the
Wellesley College's
*Math Department Colloquium*,
Wellesley College Science Center 396.

Hibbard,
A., Carter,
N.
C., Maycock,
E. (2006).
"Technology in the Abstract Algebra Classroom."
Presented at the
Council on Undergraduate Research's
*CUR National Conference*,
DePauw University, DePauw, IN.

Carter,
N.
C. (2006).
"Reflexive Intermediate Propositional Logics."
Presented at the
Association for Symbolic Logic's
*Winter Meeting*,
Joint Meetings of AMS and MAA, San Antonio, TX.

Carter,
N.
C. (2005).
"Reflexive Intermediate Logics."
Presented at the
Massachusetts Institute of Technology's
*MIT Logic Seminar*,
Cambridge, MA.

Carter,
N.
C. (2004).
"Group Explorer – Visualization Software in the Abstract Algebra Classroom."
Presented at the
Northeast Section of the Mathematical Association of America's
*MAA Section Meeting*,
Worcester Polytechnic Institute.

Carter,
N.
C., Emmons,
B. (2004).
"Group Explorer - Visualization Software in the Abstract Algebra Classroom."
Presented at the
Mathematical Association of America and American Mathematical Society's
*Joint Meetings*,
Phoenix, Arizona.

### Service

**Department Service**

Committee Member for Curriculum Committee, 2009 - 2010

Committee Member for Scholarly Activities Committee, 2006 - 2009**University Service**

Committee Member for Analytics Common Core Subcommittee, 2017 - Present

Department Chair for Graduate Council, 2014 - 2018

Department Chair for Graduate Curriculum Committee, 2014 - 2018

Committee Member for Shared Governance Task Force, 2016 - 2017

Department Chair for Mathematical Sciences Department, 2014 - 2017

Department Chair for Interim Provost Interviews, 2017 - 2017

Moderator for Innovation Series Panel for Greater Media Boston/Bentley Marketing, 2015 - 2015

University Senate for Faculty Senate, 2013 - 2014

Committee Chair for Salary and Benefits Committee, 2013 - 2014

Associate Director for Honors Program, 2012 - 2014

Committee Member for Salary and Benefits Committee, 2010 - 2013

Task Force Member for LSM Assessment, 2011 - 2011

Committee Member for Curriculum Committee, 2006 - 2009

Committee Member for Nominations Committee, 2006 - 2009**Professional Service**

Editorial Review Board Member for Math Horizons, 2009 - Present

Graded math competition entries for The Moody's Foundation, 2009

Committee Member for Chauvenet Prize Committee, Mathematical Association of America, 2014 - 2018

Reviewer, Journal Article for American Mathematical Monthly, 2013 - 2013

Reviewer, Book for Princeton University Press, 2013 - 2013

Reviewer, Grant Proposal for National Science Foundation, 2008 - 2009

Graded AP Calculus Exams for The College Board, 2005 - 2005