Position Type
Faculty
Service
- Present
Specialization
knot theory, pedagogy
Biography

Lew Ludwig joined the Denison faculty in 2002.  Prior to this, he had visiting positions at Miami University and Kenyon College.  He earned his doctorate at Ohio University under his advisor A. V. Arhangelskii, a Master’s Degree in Mathematics at Miami University and a Master’s in Education from the College of Mount St. Joseph.  Dr. Ludwig has taught a variety of classes at Denison including FYS 102, Math 121, Math 122, Math 123, Math 124, Math 231, Math 210, Math 321/322 and Math 400 Knot Theory.  He also teaches Math 215 Technically Speaking.  In recent years, Dr. Ludwig has adopted the “flip classroom” format where students engage in the material before coming to class.  In 2013, he was awarded the Distinguished Teaching Award from the Ohio Section of the Mathematical Association of America.

Degree(s)
B.S., B.A., M.E., College of Mount St. Joseph; M.S., Miami University; Ph.D., Ohio University

Learning & Teaching

Courses
  • FYS 102/HNRS 132 - The Art of Mathematical Thinking
  • MATH 115 - Mathematical Methods for the Physical and Social Sciences
  • MATH 130 - Essentials of Calculus
  • MATH 135 - Single Variable Calculus
  • MATH 145 - Multi-variable Calculus
  • MATH 213 - Linear Algebra and Differential Equations
  • MATH 300 - Introductions to Proofs
  • MATH 395 - Technical Communication I
  • MATH 415 - Operations Research
  • MATH 440 - Advanced Analysis
  • MATH 451 - Senior Research
  • MATH 471 - Advanced Mathematical Topics - Knot Theory
  • MATH 495 - Technical Communications II
Academic Positions
  • 2020 - present Director of the Center for Learning and Teaching
  • 2015 - present Full Professor
  • 2016-2018 Chair of Mathematics and Computer Science
  • 2008-2015 Associate Professor
  • 2002-2008 Assistant Professor

Research

Professor Ludwig conducts research in the mathematical field of knot theory. He is happy to consider summer research students in any area of knot theory.
Details

Professor Ludwig was trained as a point-set topologist and worked on separation and convergence-type problems. In order to include undergraduates in his work, Professor Ludwig expanded his research to include knot theory, a branch of topology. Since 2005, he has worked with eleven undergraduate students on nine different research projects. Combined, his students have won 11 national awards with cash prizes totaling over $1000, for the quality of their work and presentations. He and his students have been very successful with the two hands-on topics of stick knots and knot mosaics, producing four peer-reviewed publications.

In the area of point-set topology, Professor Ludwig worked on alpha-normal and beta-normal spaces, a generalization of normal spaces. He has also considered kappa-Frechet-Urysohn spaces, a type of convergence property. In knot theory, Professor Ludwig has worked on intrinsic knotting and linking in straight-edge embeddings of complete graphs. He also conducted research on knot mosaics, an equivalent knot representation developed by Lomonaco and Kauffman.

Works

Publications

Research publications:

  • Colin Adams (Editor), Erica Flapan (Editor), Allison Henrich (Editor), Louis H. Kauffman (Editor), Lewis D. Ludwig (Editor), The Concise Encyclopedia of Knot Theory published December 29, 2020 by Chapman and Hall/CRC. Authored Chapter 1 and 5.
  • Ludwig, Lewis D.; Paat, Joseph S. ’11; Lee, Hwa Jeong; Peiffer, Amanda ‘16, Knot Mosaic Tabulation, 11 (2018), no. 1, 13-26.
  • Flapan, Erica et al., From Molecules to the Universe: An Introduction to Topology, American Mathematical Society (December 22, 2015). Coauthored Chapters 4 and 11.
  • Ludwig, Lewis D.; Evans, Erica L. ‘11; Paat, Joseph S. ‘11, An infinite family of knots whose mosaic number is realized in non-reduced projections, J. Knot Theory Ramifications 22 (2013) no. 7, 11 pp.
  • Arbisi, Pamela ‘07; Ludwig, Lewis D., Linking in Straight-edge embeddings of K7, J. Knot Theory Ramifications, 19 (2010), no. 11, 1431-1447 .

Pedagogical publications:

  • Ludwig, Lewis D., Why I learned the Rubik’s Cube: Seeing the expert blindspot, MAA Focus, April—May, 2022, 11—14.
  • Ludwig, Lewis D., The one question calculus final, MAA Focus, Aug-Sep, 2019, 16—17.
  • Ludwig, Lewis, D., MAA Instructional Practices Guide Project Leadership Team: Martha L. Abell, Linda Braddy, Doug Ensley, Lewis Ludwig, Hortensia Soto, Notes (89) 2016, MAA Press.
  • Ludwig, Lewis D., “Introduction to Proofs Over-Easy: A Low-Cost Alternative to the Flipped Classroom.” Beyond Lecture: Techniques to Improve Proof-Student Writing Across the Curriculum edited by Rachel Schwell, Aliza Steurer, and Jennifer F. Vasquez, Notes (85) 2016, MAA Press, 213-219.

Service

Professional Memberships
  • Contracted by the American Mathematical Society to develop a hands- on activity in knot theory for the two-day USA Science and Engineering Festival in Washington, D.C. which drew over 150,000 attendees.

Other

Grants & Funding

Over $500,000 in NSF funding including:

  • Co-PI and Project Team coordinator for the MAA Instructional Practices Guide Project – a guide to evidence-based instructional practices in undergraduate mathematics. The Guide had over 20,000 unique downloads as of January, 2020.
  • Creator, co-organizer and host of the Undergraduate Knot Theory Conference 2009, 2012, 2016, 2019. Each a was 3-day national conference with 95-110 participants ranging from undergraduates, graduate students, and undergraduate faculty, to leading researchers in the field. A total of 135 scholarly presentations.
  • Creator of NSF funded Technically Speaking which trains STEM students how to give technical talks to a non-technical audience.
Honors & Awards
  • Distinguished Teaching Award, Ohio Section of the MAA, 2012-2013
  • Nancy Eshelman Brickman Endowed Professor, named teaching chair of the faculty at Denison University, 2014-19
Student Collaborations

Selected student research projects:

  • Joseph Paat ‘11 and Amanda Peiffer ‘16, Knot Mosaic Tabulation.
  • Joseph Paat ‘11 and Erica Evans ‘11, An infinite family of knots whose mosaic number is realized in non-reduced projections, won best presentation at MathFest 2010 and JMM 2011 Poster Session.
  • Joseph Paat ‘11 and Jacob Shapiro ‘10, Tabulating knot mosaics, won best presentation at JMM 2010 Poster Session.
  • Sam Behrend ‘09, Linking in straight-edge embeddings of K9, won best presentation at MathFest 2008 and JMM 2009 Poster Session.
  • Rachel Grotheer ‘08, Linking in straight-edge embeddings of K8, won best presentation at MathFest 2007 and JMM 2008 Poster Session.
  • Pamela Arbisis ‘07, Linking in Straight-edge embeddings of K7
  • Colleen Hughes ‘06, Linking in straight-edge embeddings of K6, won best presentation at MathFest 2004 and JMM 2005 Poster Session.

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