Mark Hunacek's Books

Introduction to Number Theory

By: Mark Hunacek

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Introduction to Number Theory covers the essential content of an introductory number theory course including divisibility and prime factorization, congruences, and quadratic reciprocity. The instructor may also choose from a collection of additional topics. Aligning with the trend toward smaller, essential texts in mathematics, the author strives for clarity of exposition. Proof techniques and proofs are presented slowly and clearly. The book employs a versatile approach to the use of algebraic ideas. Instructors who wish to put this material into a broader context may do so, though the author introduces these concepts in a non-essential way. A final chapter discusses algebraic systems (like the Gaussian integers) presuming no previous exposure to abstract algebra. Studying general systems helps students to realize unique factorization into primes is a more subtle idea than may at first appear; students will find this chapter interesting, fun and quite accessible. Applications of number theory include several sections on cryptography and other applications to further interest instructors and students alike.

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Page Count

165

Publisher

CRC Press

Published Date

ISBN 10

1000833836

ISBN 13

9781000833836

Quantitative Literacy Through Games and Gambling

By: Mark Hunacek

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Quantitative Literacy Through Games and Gambling

By: Mark Hunacek

This book was developed to address a need. Quantitative Literacy courses have been established in the mathematics curriculum for decades now. The students in these courses typically dislike and fear mathematics, and the result is often a class populated by many students who are unmotivated and uninterested in the material. This book is a text for such a course; however, it is focused on a single idea that most students seem to already have some intrinsic interest in and is written at an accessible level. It covers the basic ideas of discrete probability and shows how these ideas can be applied to familiar games (roulette, poker, blackjack, etc.). The gambling material is interweaved through the book and introduced as soon as the necessary mathematics has been developed. Throughout, mathematical formalism and symbolism have been avoided, and numerous examples are provided. The book starts with a simple definition of probability, goes through some basic concepts like combining events and expected value, and then discusses some elementary mathematical aspects of various games. Roulette is introduced very early on, as is the game of craps, which requires some knowledge of conditional probability. Other games like poker, blackjack, and lotteries, whose study requires some rudimentary combinatorics, come shortly thereafter. The book ends with a brief introduction to zero-sum games, with some attention paid to the use of these ideas in studying bluffing. In addition to discussion of these traditional games, the author motivates probability by talking about a few applications in legal proceedings that illustrate how mathematics has been misused in the courtroom. There is also a discussion of the Monty Hall problem, a nonintuitive result in probability that has an interesting and colorful history. Hopefully, students studying from this text will find that mathematics is not as horrible as they have always thought and offers some interesting applications in the real world. This should perhaps be the goal of any quantitative literacy course.

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Page Count

120

Publisher

CRC Press

Published Date

ISBN 10

1040131212

ISBN 13

9781040131213

Fundamentals of Abstract Algebra

By: Mark J. DeBonis

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Fundamentals of Abstract Algebra

By: Mark J. DeBonis

Fundamentals of Abstract Algebra is a primary textbook for a one year first course in Abstract Algebra, but it has much more to offer besides this. The book is full of opportunities for further, deeper reading, including explorations of interesting applications and more advanced topics, such as Galois theory. Replete with exercises and examples, the book is geared towards careful pedagogy and accessibility, and requires only minimal prerequisites. The book includes a primer on some basic mathematical concepts that will be useful for readers to understand, and in this sense the book is self-contained. Features Self-contained treatments of all topics Everything required for a one-year first course in Abstract Algebra, and could also be used as supplementary reading for a second course Copious exercises and examples Mark DeBonis received his PhD in Mathematics from the University of California, Irvine, USA. He began his career as a theoretical mathematician in the field of group theory and model theory, but in later years switched to applied mathematics, in particular to machine learning. He spent some time working for the US Department of Energy at Los Alamos National Lab as well as the US Department of Defense at the Defense Intelligence Agency, both as an applied mathematician of machine learning. He held a position as Associate Professor of Mathematics at Manhattan College in New York City, but later left to pursue research working for the US Department of Energy at Sandia National Laboratory as a Principal Data Analyst. His research interests include machine learning, statistics and computational algebra.

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Page Count

351

Publisher

CRC Press

Published Date

ISBN 10

1040009336

ISBN 13

9781040009338

Book's by Mark Hunacek

Introduction to Number Theory

Introduction to Number Theory

Quantitative Literacy Through Games and Gambling

Quantitative Literacy Through Games and Gambling

Fundamentals of Abstract Algebra

Fundamentals of Abstract Algebra

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