Oscar Levin

Contact Information

Education

• 2009, Ph.D. (Mathematics), University of Connecticut.
• 2006, M.A. (Mathematics), University of Connecticut.
• 2004, B.A. (Philosophy), University of Northern Colorado.
• 2004, B.S. (Mathematics), University of Northern Colorado.

Professional/Academic Experience

• 2017-present: Associate Professor, University of Northern Colorado
• 2011-2017: Assistant Professor, University of Northern Colorado.
• 2009-2011: Visiting Assistant Professor, Coastal Carolina University.
• 2005-2009: Graduate Teaching Assistant, University of Connecticut.

Research/Areas of Interest

Teaching

Courses I regularly teach include Discrete Mathematics (MATH 228), and Abstract Algebra I & II (MATH 321 & 322).  I have also taught courses on Calculus, Modern Geometry, Continuous Mathematics, and graduate courses in Logic and Graph Theory.  More information about my teaching activities can be found on my personal website.

Research

I work in an area of mathematical logic known as computability theory (or sometimes as recursion theory). The goal is to understand to what extent "regular" mathematics is or is not algorithmic. I am especially interested in applications to algebra and combinatorics.

I have also collaborated with a number of undergraduate students on research projects both in and out of computability theory.

Open Source Textbooks

I am the author of the widely adopted open source textbook Discrete Mathematics: an Open Introduction, currently in its third edition.  The book is available for free as both a pdf and interactive online ebook.  I have contributed to other open source textbook projects, and am an active member of the OER mathematics community.

Publications/Creative Works

• Levin, O., Markkanen, T. Puzzles of Cardinality, submitted for publication.
• Kenigsberg, M., Levin, O., Prime labelings of infinite graphs, Involve, 12:4 (2019) 633-646.
• Levin, O., McMillan, T., Computing Planarity in Computable Planar Graphs, Graphs and Combinatorics, 32:6 (2016) 2525-2539.
• Levin, O. Computable Dimension for Ordered Fields, Archive for Mathematical Logic, 55:3-4 (2016) 519–534.
• Jura, M., Levin, O., Markkanen, T. A-Computable Graphs. Annals of Pure and Applied Logic 167:3 (2016) 235-246.
• Jura, M., Levin, O., Markkanen, T. Domatic Partitions of Computable Graphs, Archive for Mathematical Logic, 53:1 (January 2014) 137-155.
• Levin, O., Roberts, G. Counting Knights and Knaves, College Mathematics Journal, 44:4 (September 2013) 300-306.
• Kach, A.M., Levin, O., Solomon, D.R., Embeddings of Computable Structures, Notre Dame Journal of Formal Logic, 51:1 (May 2010) 55-68.

See my research page for copies of these papers.

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