Many of the most recent International Congresses of Mathematics have awarded Fields Medals to researchers in chaotic dynamics and related fields, indicating the importance of these areas. Dynamics has blossomed in the past 50 years, making it useful as a tool for demonstrating techniques to mathematics majors and for developing their general mathematical maturity. It is my hope that this book will provide interested students with an introduction to onedimensional dynamical systems, giving them the tools necessary to succeed in more advanced courses on this topic. The early chapters of this book can be used as a stepping stone from the non-rigorous courses of freshman calculus to the more advanced topics of real analysis and topology.

Towson University is a liberal arts college and is part of the University of Maryland System. In my first years of teaching a course on dynamical systems, I based my lectures on the material of some of the existing textbooks which were then currently available, such as [122], [41], [65] and [32]. Each semester, I found myself changing the course content and exercises (frequently to meet the needs of my students). This led to the production of my own lecture notes (these notes owe a debt to the above mentioned books).

The content of this text arises primarily from lecture notes that I created over many years of teaching senior seminar-type courses to final year students at Towson University, and also from courses in the Towson University Applied Mathematics Graduate Program and the Graduate Program in Mathematics Education. In the senior seminar course, students were taught the basics of one-dimensional dynamics and were required to present a project at completion of the course. The later chapters of this book include many topics from these projects, for example, Sharkovsky's Theorem, as well as topics resulting from the independent study of some of my Master's students. With students in the Master's Program, I was generally able to move quickly through the earlier material and spend more time on advanced topics, the choice of which changed from semester to semester.