Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.

Horizons Math Kindergarten builds the foundation for the method of study that is used all the way through the Horizons Math program. Every concept follows a deliberate pattern of introduction and gradual development. Each lesson begins with a new concept or an expansion of a previously covered concept. This introduction starts a cycle of repetition and review that students will experience as they work through the lessons. Horizons Math Kindergarten lays a foundation for order and exactness. The daily practice in the student books teaches the recognition and printing of the numerals 0 to 100. Simple addition and subtraction from 0 to 10 are taught. the addition-subtraction concept is extended through 99 with the aid of counters and the number line. Counting through 100 is presented by 1's, 10's, 5's, 2's, 3's, and 4's. Principles of place value, measurement, calendar use, telling time, graphing, comparisons, and money concepts are also introduced.

Exquisite expositions of mathematics taken from the first ten years of the Math Horizons magazine.

"Math Horizons celebrates the people and ideas that are mathematics. Containing the editors' selection from the first ten years of the magazine's existence, this volume features exquisite expositions of mathematics accessible at the level of an undergraduate or advanced high school student"--Back cover.

'This delightful book connects mathematical concepts in a dozen areas to magic tricks. Expositions of the mathematics precede description and analysis of the tricks. The expositions are too short for in-depth learning; the intent is to give sophomores a taste of the content and ideas of later mathematics courses. Each chapter features exercises on the mathematics, and students can have fun practicing the tricks.'Mathematics MagazineTeixeira and Park present over 60 different magic tricks while introducing students to high-level math areas. Readers will learn really interesting ideas that will better prepare them for future courses and help them finding areas they might want to study deeper. And as a 'side effect' students will learn amazing magic tricks, century-old secrets, and details from famous magicians and mathematicians.The material was written to quickly present key concepts in several mathematical areas in direct way. Little or no proficiency in math is assumed. In fact, students do not require any Calculus knowledge. And since chapters are almost independent from each other, this book also work as introduction to several other courses.Topics covered include mathematical proofs, probability, abstract algebra, linear algebra, mathematical computing, number theory, coding theory, geometry, topology, real analysis, numerical analysis and history of math.