|Office:||Ritter Hall 213|
||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.
|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
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.
While computational data is an important part of this book, the text itself is not tied to any one computational system. Students and instructors are encouraged to use whatever tools they are most comfortable with. It is possible to use this text without computer aided computation, although some exercises will need to be skipped and more work will be needed to generate enough data to make meaningful conjectures.