# Aaron Trautwein

Aaron Trautwein specializes in knot theory. Knot theory is a subfield of topology, the area of mathematics that examines shape. In particular, he studies the physical and theoretical properties of harmonic knots and their applications. He has presented numerous talks on his research and wrote the chapter “An Introduction to Harmonic Knots” for the book *Ideal Knots*.

Prof. Trautwein is also active in the scholarship of teaching mathematics. He examines the preparation of future secondary mathematics teachers and how to improve math teaching and learning techniques. He has been the principal or co-principal investigator for a number of grants from various agencies for this work. As part of an interdisciplinary team at Carthage, he was recently awarded a $1.2 million National Science Foundation Noyce Grant.

At Carthage, he has taught a wide array of courses for the Mathematics Department and Western Heritage Program. These courses include applied contemporary mathematics, ethno-mathematics, Calculus I and II, multivariate calculus, geometry, linear and abstract algebra, topology, Western Heritage I and II, and an honors seminar on building and architecture. He was selected as Carthage’s Distinguished Teacher of the Year in 2001.

Prof. Trautwein resides in Kenosha and is active in both the city and college communities. He completed the Leadership Kenosha Training Program, served as Carthage’s United Way Chair and on United Way Community Caring Teams for 15 years, and was a Board Member for the Spanish Center and the Kenosha Area United Way. At Carthage, he has served as the chair of the Faculty Executive Committee, a member of the Academic Senate, and has been the faculty representative to the Alumni Council for the past 20 years.

He earned his B.A. from Washington University, where he majored in mathematics and secondary education and minored in anthropology. At Washington University, he was selected to be a member of Phi Beta Kappa and earned a Missouri Lifetime Secondary School Teaching Certificate. He earned his M.A. in mathematics from St. Louis University and was selected to be a member of Pi Mu Epsilon, the national mathematics honorary. He received the Outstanding Teaching Assistant Award and earned his Ph.D. in mathematics for his thesis titled “Harmonic Knots” from the University of Iowa.

He joined the Carthage faculty in 1995.

- Ph.D. — Mathematics: Topology, University of Iowa
- M.A. — Mathematics, St. Louis University
- B.A. — Mathematics and Secondary Education, Washington University (St. Louis)

- MTH 1030 Applied Mathematics
- MTH 1040 Principles of Modern Mathematics
- MTH 1050 Elementary Statistics
- MTH 1060 Finite Mathematics
- MTH 1070 Functions, Graphs and Analysis
- MTH 1120 Calculus I
- MTH 1220 Calculus II
- MTH 1240 Discrete Structures
- MTH 200T Topics in Mathematics
- MTH 2040 Linear Algebra
- MTH 2080 Modern Geometry
- MTH 2120 Multivariate Calculus
- MTH 3040 Abstract Algebra I
- MTH 3140 Abstract Algebra II
- MTH 3180 Introduction to Topology
- MTH 400T Topics in Mathematics
- MTH 4500 Independent Study
- MTH 4900 Research in Mathematics
- MTH 4990 Senior Thesis Completion

Aaron Trautwein specializes in knot theory. Knot theory is a subfield of topology, the area of mathematics that examines shape. In particular, he studies the physical and theoretical properties of harmonic knots and their applications. He has presented numerous talks on his research and wrote the chapter “An Introduction to Harmonic Knots” for the book *Ideal Knots*.

Prof. Trautwein is also active in the scholarship of teaching mathematics. He examines the preparation of future secondary mathematics teachers and how to improve math teaching and learning techniques. He has been the principal or co-principal investigator for a number of grants from various agencies for this work. As part of an interdisciplinary team at Carthage, he was recently awarded a 1.2 million dollar National Science Foundation Noyce Grant.

“An Introduction to Harmonic Knots” in *Ideal Knots*, World Scientific Publishing, 2000.