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Nathan Carlson Carter

Associate Professor, Mathematical Sciences
Ph.D., Indiana University, 2004
M.S., Indiana University, 2004
M.A., Indiana University, 2001
B.S., University of Scranton, 1999
Office: Morison Hall 375 | 781.891._3171 | ncarter@bentley.edu
Department Phone: 781.891._2702 | Department Fax: 781.891.2457
                       


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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

Professional Memberships

OpenMath Society
American Mathematical Society
Mathematical Association of America

Awards and Honors

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 Articles
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, 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. From Formal to Expository: Using the Proof-Checking Word Processor Lurch to Teach Proof Writing. In Jennifer Franko-Vasquez, Rachel Schwell, Aliza Steurer (Eds.), Innovative Techniques for Teaching Proof-writing. Washington, DC: . Mathematical Association of America

Book Reviews
Carter, N. C. (2009). [Review of the book Five Minute Mathematics]. Math Horizons. (link)

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 Proceedings and Presentations

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." 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
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 - 2016
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