Benjamin Hutz -- Assistant Professor of Mathematics
Department of Mathematics and Statistics
Office: Ritter Hall 213
Department: 
Department of Mathematics and Statistics
220 N. Grand Blvd.
St. Louis, MO 63103
Tel (314) 977-2444
Email: benjamin (dot) hutz (at) slu.edu
Office Hours:
 MWF: 11:30am-1pm

I receivd my Ph.D. in arithmetic dynamics at Brown University in 2007 under Joseph H. Silverman.  I joined the SLU faculty in the fall of 2015.

Current Teaching

Discrete Mathematics MTH 1660.02 MWF 1:10-2:00pm
Linear Algebra for Engineers MTH 3110.02 MWF 2:10-3:00pm

Number Theory Textbook

    
Title: An Experimental Introduction to Number Theory
Author: Benjamin Hutz
Publisher: American Mathematical Society
Series: Pure and Applied Undergraduate Texts, Volume 31
ISBN: 978-1-4704-3097-9
Website: AMS bookstore

This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems.

The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.

Current Research

My research is in the area of arithmetic dynamics. In particular, I am interested in arithmetic properties of preperiodic points and subvarieties arising from iterating morphisms of projective varieties and associated computational problems. My research brings together methods from number theory, algebraic geometry, dynamical systems, arithmetic geometry, computational number theory, and computational algebraic geometry. Recently I have been heavily involved in improving the computational tools for dynamical systems in the computer algebra system Sage. See the research section of this site for more details.

Student Research

If you are interested in problems in the area of iterated functions (dynamical systems) and developing software in Sage to work on these problems, then stop by my office. I have projects ranging from theoretical problems to computational experimentation to implementation of algorithms. Problems are appropriate for students with mathematical and/or programming (Python or C) backgrounds of all levels.