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.
Learning & Teaching
Dr. Ludwig was trained as a point-set topologist and continues work in this field looking at separation and convergence-type problems. In order to include undergraduates in his work, Dr. Ludwig expanded his research to include knot theory, a branch of topology. Since 2005, Dr. Ludwig has worked with nine undergraduate students on seven 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. Dr. Ludwig is happy to advise summer research students in any area of knot theory. 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.
- An infinite family of knots whose mosaic number is realized in non-reduced projections (with Erica Evans (’11) and Joe Paat (’11)), Journal of Knot Theory and its Ramifications, 22:7, 2013
- Linking in straight-edge embeddings of K7 (with Pameila Arbisi (’07)), Journal of Knot Theory and its Ramifications, 19:11, pp. 1431-1447, 2010.
- Dowker Spaces Revisited (with Nyikos and Porter), Tsukuba Journal of Mathematics 34:1, pp. 1-11. 2010
- When graph theory meets knot theory (with Foisy), Contemporary Mathematics 479, pp. 67–85, 2009
Selected student research projects:
- 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.
- 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.
- Colleen Hughes (’06) Linking in straight-edge embeddings of K6, won best presentation at MathFest 2004 and JMM 2005 Poster Session.