Nathan Carter

  • Professor, Mathematical Sciences
  • M.S. Indiana University
  • Ph.D. Indiana University
  • M.A. Indiana University
  • B.S. University of Scranton
  • Office: Morison Hall - 375 | 781.891.3171 | NCARTER@BENTLEY.EDU
  • Department Phone: 781.891.2702 | Department Fax: 781.891.2457

Teaching Interests

Mathematical Logic; Computer Graphics; Data Science

Research Interests

Mathematics education software; Data Science

Consulting/Practice Interests

Software planning and development

Bio

Nathan Carter uses computer science to advance mathematics. He is a past winner of the Mathematical Association of America's Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member. His major projects have been books, beginning with Visual Group Theory (2009), which won the 2012 Beckenbach Book Prize from that same society. His second text, Introduction to the Mathematics of Computer Graphics (2016), was published by that same society and also won the Beckenbach Book Prize. His most recent book is an edited volume with many contributors, entitled Data Science for Mathematicians (2020), intended to help pure mathematicians make the transition into teaching and doing research in the ever-growing field of data science. He also writes open source mathematics software for university mathematics education in areas including mathematical logic and abstract algebra visualization.

Professional Links

Professional Memberships

  • OpenMath Society 2013 - Present
  • American Mathematical Society 2004 - 2018
  • Mathematical Association of America 2004 - 2014
  • Awards and Honors

  • 2021, Beckenbach Book Prize, Mathematical Association of America
  • 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 Articles


  • Aylesworth, A. B., Beneke, C. J., Betts, R., Carter, N. C., Dove, S., Moriarty, J. (2022). 7 Hard-Earned Lessons From a Curriculum Makeover. Chronicle of Higher Education.
  • Carter, N. C., Iyengar, A., Lanham, M., Nestler, S., Schrader, D., Zadeh, A. (2022). Clustering algorithms to increase fairness in collegiate wrestling. Journal of Quantitative Analysis in Sports. (Link)
  • Carter, N. C. (2019). Circuits in RGBExpress. Mathematics Magazine. 92 323-388. (Link)
  • Carter, N. C., Oury, D. T. (2018). Simple Course Management with RStudio Server Pro. Technology Innovations in Statistics Education, (11) 1 14. (Link)
  • 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.
  • 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., 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). 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. (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. (2006). A recipe for collaborative research. BizEd September/October, (September/October) 30-34.
  • Carter, N. C. (2006). Reflexive Intermediate Propositional Logics. Notre Dame Journal of Formal Logic, (47) 1 39-62. (Link)
  • 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. (2020). Data Science for Mathematicians. 528. Boca Raton, FL: Taylor and Francis (Link)
  • Carter, N. C. (2016). Introduction to the Mathematics of Computer Graphics. 495. Washington, DC: Mathematical Association of America (Link)
  • Carter, N. C., Magnus, P. (2013). forall x in Lurch. 194. self-published for free on the web (Link)
  • Carter, N. C. (2009). Visual Group Theory. 297. 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, (2008) FebruaryWashington, D.C.: (Link)

  • Conference Proceedings


  • 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)
  • 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 that can grade students' proofs CEUR-WS, (1010) (Link)
  • Carter, N. C.Monks, K. G. (2013). Lurch: a word processor that can grade students' proofs CICM 2013, (Conference on Intelligent Computer Mathematics)

  • Conference Papers


  • Carter, N. C. (2017). A Web-Based Toolkit for Mathematical Word Processing Applications with SemanticsSpringer, Lecture Notes in Artificial Intelligence. 15. (Link)
  • Carter, N. C., Emmons, B. (2004). Group Explorer - Visualization Software in the Abstract Algebra ClassroomMathematical Association of America and American Mathematical Society, Joint Meetings.

  • Other(s)


  • Aylesworth, A. B., Beneke, C. J., Betts, R. M., Carter, N. C., Dove, S., Moriarty, J. (2022). 7 Hard-Earned Lessons From a Curriculum MakeoverChronicle of Higher Education. (Link)
  • Carter, N. C., Ellis, R. (2019). Group Explorer 3.0 - Visualization Software in the Abstract Algebra Classroom. (Link)
  • Carter, N. C. (2019). ge-lib: Node.js module for accessing Group Explorer's core functionality. (Link)
  • Carter, N. C. (2019). GroupExplorer: Invoking Group Explorer from GAPGAP Distribution. (Link)
  • Carter, N. C. (2019). SemigroupViz: Visualization Tools for SemigroupsGAP Distribution. (Link)
  • Carter, N. C. (2019). JupyterViz: Visualization tools for Jupyter and the GAP REPLGAP Distribution. (Link)
  • Carter, N. C., Farrington, E. (2011). A Quick Tour of Manjul Bhargava’s 2011 Hedrick Lectures on Elliptic CurvesMath Horizons. 6-7.
  • Carter, N. C. (2004). Reflexive Logics - Intermediate logics that can prove their own completeness. (Link) Forthcoming.
  • Presentations

  • Carter, N. C., Monks, K. G. (2023). “Introduction to Lurch” Presented at the American Institute of Mathematics Open-source cyberinfrastructure supporting mathematics research Pasadena, CA
  • Carter, N. C. (2023). “Large Language Models: Construction, Use, and New Discoveries” Presented at the New England Statistical Society Data Science Day University of Connecticut
  • Carter, N. C. (2019). “Cayley Graphs for Building Intuition in Group Theory” Presented at the American Mathematical Society Fall Southeastern Section Meeting Gainesville, FL
  • Carter, N. C. (2019). “The Surprising Pedagogical Value and Versatility of Cayley Graphs” Presented at the ICERM, Brown University Illustrating Number Theory and Algebra Workshop Providence, RI
  • Carter, N. C. (2017). “A Web-Based Toolkit for Mathematical Word Processing Applications with Semantics” Presented at the University of Edinburgh 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 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 MathFest Columbus, OH
  • Carter, N. C. (2016). “Assessment Facilitated by Technology” Presented at the Fields Institute, University of Toronto 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 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 MathFest Portland, OR
  • Carter, N. C. (2014). “The Value of Visualization in Group Theory” Presented at the Indiana University 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 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 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 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 MathFest Hartford, CT
  • Carter, N. C. (2013). “Lurch: A word processor built on OpenMath that can check mathematical reasoning” Presented at the CICM 2013 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 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 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 Joint Meetings San Diego, CA
  • Carter, N. C. (2012). “Mathematics of Computer Graphics” Presented at the Bentley University Mathematics Department 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 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 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 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 Joint Meetings New Orleans, LA
  • Carter, N. C. (2010). “From Zero to Galois Theory in 50 Minutes” Presented at the Gordon College 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 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 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 Joint Meetings San Francisco, CA
  • Carter, N. C. (2009). “Lurch: Software for Teaching Mathematical Proofs” Presented at the Clay Math Institute 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 MathFest Portland, OR
  • Carter, N. C. (2009). “Visual Group Theory” Presented at the Mathematical Association of America MathFest Portland, OR
  • Carter, N. C. (2008). “The Lurch Project: Can Computers Correct Mathematical Writing?” Presented at the Bentley University 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 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 theIASC 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 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 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 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 CUR National Conference DePauw University, DePauw, IN
  • Carter, N. C. (2006). “Reflexive Intermediate Propositional Logics” Presented at the Association for Symbolic Logic 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 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 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 Joint Meetings Phoenix, Arizona
  • Service

    Department Service


  • Center Director for Center for Analytics and Data Science 2022 - Present
  • Committee Chair for Tenure Track Search Committee 2021 - 2022
  • Committee Member for Curriculum Committee 2009 - 2010
  • Committee Member for Scholarly Activities Committee 2006 - 2009
  • University Service


  • Committee Member for Strategic Plan Focus Area Ambassadors 2023 - Present
  • Committee Member for Promotion and Tenure Committee 2022 - 2025
  • Special Institutional Assignment for Wilder Professorship 2020 - 2023
  • Perform occasional analysis/consultation for Consulting/Analysis for Curriculum Reform Task Force 5.0 2021 - 2022
  • Committee Member for Learning Management System Evaluation Committee 2021 - 2021
  • Task Force Chair for Curriculum Reform Task Force 4.0 2019 - 2021
  • Task Force Member for Curriculum Reform Task Force 3.0 2019 - 2019
  • Department Chair for Graduate Council 2014 - 2018
  • Department Chair for Graduate Curriculum Committee 2014 - 2018
  • Committee Member for Chief Finance Officer Search Committee 2018 - 2018
  • Committee Member for Analytics Common Core Subcommittee 2017 - 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


  • Conference/Workshop Organizer for Mathematical Association of America 2019 - 2019
  • Editorial Review Board Member for Math Horizons 2009 - 2018
  • Committee Member for Chauvenet Prize Committee, Mathematical Association of America 2014 - 2017
  • Graded math competition entries for The Moody's Foundation 2009 - 2013
  • 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