Darren Narayan
Professor
School of Mathematics and Statistics
College of Science
585-475-2514
Office Hours
My office hours are on Mondays from 4:00-5:00 and Wednesdays from 1:00-2:00 on Zoom. See the links on mycourses. Additional times are available by appointment.
Office Location
Office Mailing Address
Gosnell Building 08 Room: 2228
Darren Narayan
Professor
School of Mathematics and Statistics
College of Science
Education
BS, State University of New York at Binghamton; MS, Ph.D., Lehigh University
585-475-2514
Areas of Expertise
Graph Theory
Combinatorics
Social Networks
Functional Connectivity of the Brain
Mathematical Modeling
Select Scholarship
Journal Paper
Merchant-Borna, K., et al. "Novel Method of Weighting Cumulative Helmet Impacts Improves Correlation with Brain White Matter Changes After One Football Season of Sub-concussive Head Blows." Annals of Biomedical Engineering 44. 12 (2016): 3679-3692. Print.
Vargas, R., et al. "Refining the Clustering Coefficient for Analysis of Social and Neural Network Data." Social Network Analysis and Mining (Springer) 6. 49 (2016): 1-8. Print.
Swart, B., et al. "Extrema Property of the k-ranking of Directed Paths and Cycles." AKCE Int. J. Graphs Comb. 13. (2016): 38-53. Print.
Richter, Peter, et al. "Rank Numbers for Bent Ladders." Discussiones Mathematicae Graph Theory 34. (2014): 309-329. Print.
Lind, Joy and Darren A, Narayan. "Detecting Controversial Articles in Wikipedia." Bulletin of the Institute of Combinatorics and Its Applications 70. (2014): 57-68. Print.
Ek, Bryan, Caitlin VerSchneider, and Darren A. Narayan. "Efficiency of Star-like Networks and the Atlanta Subway Network." Physica A 392. (2013): 5481-5489. Print.
Bileschi, Maxwell, et al. "A Characterization of Optimal k-rankings of Paths and Cycles." Bulletin of the Institute of Combinatorics and Its Applications 67. (2013): 17-26. Print.
Lind, Joy and Darren A. Narayan. "Spanning Trees and Hierarchical Networks." Bulletin of the Institute of Combinatorics and Its Applications 67. 1 (2013): 119-127. Print.
Lind, Joy and Darren A. Narayan. "Page Ranking by Internet Search Engines." Bulletin of the Institute of Combinatorics and Its Applications 67. 1 (2013): 94-98. Print.
Lind, Joy and Darren A. Narayan. "Optimal Matching of Approvers to Access Requests." Bulletin of the Institute of Combinatorics and Its Applications 67. 1 (2013): 99-103. Print.
Dorff, Michael and Darren A. Narayan. "Obtaining Funding and Support for Undergraduate Research." PRIMUS 23. (2013): 776-784. Print.
Ek, Bryan, et al. "Real World Graph Efficiency." Bulletin of the Institute of Combinatorics and Its Applications 69. September (2013): 47-59. Print.
Lind, Joy and Darren A. Narayan. "Real World Graph Efficiency." Bulletin of the Institute of Combinatorics and Its Applications 69. September (2013): 14-24. Print.
Cahill, Nathan D., Joy Lind, and Darren A. Narayan. "Measuring Brain Connectivity." Bulletin of the Institute of Combinatorics and Its Applications 69. September (2013): 68-78. Print.
Kostyuk, Victor and Darren A. Narayan. "Maximum Minimal K-rankings of Cycles." Ars Combinatoria 111. (2013): 13-31. Print.
Jamison, Robert E. and Darren A. Narayan. "Max-Optimal and Sum-Optimal Labelings of Graphs." Information Processing Letters (Elsevier Science) 112. 1-2 (2012): 26-31. Print.
Invited Keynote/Presentation
Narayan, Darren A. "Graph Theory Methods for Analyzing Social and Neural Network Data." Data Science Seminar, Department of Mathematics. College of William and Mary. Williamsburg, VA. 2 Mar. 2016. Guest Lecture.
Narayan, Darren A. "Stem Real World Applications of Mathematics." SIAM Conference on Applied Mathematics Education. Society for Industrial and Applied Mathematics. Philadelphia, PA. 30 Sep. 2016. Conference Presentation.
Narayan, Darren A. "STEM Real World Applications of Mathematics,." Careers in Mathematics Speaker Series. Department of Mathematics, Brigham Young University. Provo, UT. 28 Oct. 2016. Guest Lecture.
Narayan, Darren A. "STEM Real World Applications of Mathematics." Joint Mathematics Meetings MAA Poster Session on Projects Supported by the NSF Division of Undergraduate Education. Mathematical Association of America. Seattle, WA. 7 Jan. 2016. Conference Presentation.
Narayan, Darren A. and Roger Vargas. "Temporal Graph Theory and Functional Connectivity in the Human Brain." Joint Mathematics Meetings, AMS Session on Combinatorics and Graph Theory, V. American Mathematical Society. Seattle, WA. 9 Jan. 2016. Conference Presentation.
Narayan, Darren A. "Graph Theory Metrics for Analyzing Functional MRI Data and Brain Connectivity." Joint Mathematics Meetings. Mathematical Association of America. Seattle, WA. 9 Jan. 2016. Conference Presentation.
Narayan, Darren A. "Refining the Clustering Coefficient for Analysis of Social and Neural Network Data." Applied Mathematics Colloquium. Department of Mathematics, University of North Carolina. Chapel Hill, NC. 15 Apr. 2016. Guest Lecture.
Narayan, Darren A. "STEM Real World Applications of Mathematics." Fall MAA Seaway Section Meeting. Mathematical Association of America. Rochester, NY. 22 Oct. 2016. Conference Presentation.
Narayan, Darren. "Panel: Undergraduate Research in Mathematics." Joint Mathematics Meetings. Mathematical Association of America. San Antonio, TX. 11 Jan. 2015. Conference Presentation.
Narayan, Darren. "STEM Real World Applications of Mathematics." Joint Mathematics Meetings. MAA - NSF-DUE Poster Session. San Antonio, TX. 11 Jan. 2015. Conference Presentation.
Narayan, Darren. "Modeling Functional Connectivity of the Brains of Athletes." Joint Mathematics Meetings. Mathematical Association of America. San Antonio, TX. 11 Jan. 2015. Conference Presentation.
Narayan, Darren. "Realizing the Full Potential of Online Instructional Systems." Joint Mathematics Meetings. Mathematical Association of America. San Antonio, TX. 11 Jan. 2015. Conference Presentation.
Narayan, Darren A. "Finding Funding and Support for Building an Undergraduate Research Program." 2012 Trends in Undergraduate Research in the Mathematical Sciences Conference. Mathematical Association of America. Chicago, IL. 28 Oct. 2012. Conference Presentation.
Narayan, Darren A. "Efficiency of Graphs." Fall Eastern Section Meeting, American Mathematical Society. Rochester Institute of Technology. Rochester, NY. 23 Sep. 2012. Conference Presentation.
Published Article
Narayan, D. A. et al. “Representation numbers for complete graphs minus a disjoint union of graphs.” Journal of Combinatorical Mathematicsand Combinatorial Computing, 72 (2010),173-180. Print. *
Narayan, Darren A. et al. “Minimal k-rankings of prism graphs”, Involve, 3:2 (2010): 183-190. Print. " É *
Narayan, Darren A. et al. “Greedy algorithms for generalized rankings of graphs.” Information ProcessingLetters, 110 (2010): 979-985. Print. " É *
Narayan, Darren A.“Maximum Flow in Fiber-Optic Networks.”Bulletin of the Institute of Combinatoricsand Its Applications, 60 (September 2010):91-96. Print. É *
Adams, Sarah, R. Gillman, D. Narayan.”Balancing the R with the E in REU Programs.” Resources for Undergraduate Research, 6 (2010): n.p. Web. É
Formal Presentation
Narayan, Darren. “Mathematical Quips, Quotes, Rumors, andHumorous Tales” Spring 2010 Meeting of the Seaway Section of the Mathematical Association of America. Oswego, NY. April 2010. Presentation.
Narayan, Darren A. “Intermediate Ordered Colorings of Graphs.”AMS Session on Discrete Mathematics, VI,Joint Mathematics Meetings. San Francisco,CA. January 2010. Presentation.
Currently Teaching
MATH-190
Discrete Mathematics for Computing
3 Credits
This course introduces students to ideas and techniques from discrete mathematics that are widely used in Computer Science. Students will learn about the fundamentals of propositional and predicate calculus, set theory, relations, recursive structures and counting. This course will help increase students’ mathematical sophistication and their ability to handle abstract problems.
MATH-200
Discrete Mathematics and Introduction to Proofs
3 Credits
This course prepares students for professions that use mathematics in daily practice, and for mathematics courses beyond the introductory level where it is essential to communicate effectively in the language of mathematics. It covers various methods of mathematical proof, starting with basic techniques in propositional and predicate calculus and set theory, and then moving to applications in advanced mathematics.
MATH-351
Graph Theory
3 Credits
This course covers the theory of graphs and networks for both directed and undirected graphs. Topics include graph isomorphism, Eulerian and Hamiltonian graphs, matching, covers, connectivity, coloring, and planarity. There is an emphasis on applications to real world problems and on graph algorithms such as those for spanning trees, shortest paths, and network flows.
MATH-361
Combinatorics
3 Credits
This course introduces the mathematical theory of enumeration of discrete structures. Topics include enumeration, combinatorial proofs, recursion, inclusion-exclusion, and generating functions.
MATH-790
Research & Thesis
0 - 9 Credits
Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.
MATH-799
MATH GRADUATE Independent Study
1 - 3 Credits
Independent Study
In the News
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February 3, 2023
![Group of students and faculty pose for photo at the REU site.]()
RIT’s longest-running NSF Research Experiences for Undergraduates program renewed for fifth time
The National Science Foundation is providing RIT new funding to continue a long-running mathematical sciences research program for undergraduate students from across the country. The NSF awarded RIT nearly $325,000 to continue to serve as a Research Experiences for Undergraduates (REU) site in extremal graph theories and dynamical systems for the next three summers.
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April 9, 2024
Narayan presents mathematics paper