Description
Book Synopsis: Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic. In this book, the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory.
Among the topics covered in this accessible, carefully designed introduction are:
- Multiplicativity-divisibility, including the fundamental theorem of arithmetic
- Combinatorial and computational number theory
- Congruences, arithmetic functions, primitive roots and prime numbers
Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory), and geometric number theory. Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated.
Dover is widely recognized for a magnificent mathematics list featuring such world-class theorists as Paul J. Cohen (Set Theory and the Continuum Hypothesis), Alfred Tarski (Undecidable Theories), Gary Chartrand (Introductory Graph Theory), Hermann Weyl (The Concept of a Riemann Surface), Shlomo Sternberg (Dynamical Systems), and multiple works by C. R. Wylie in geometry, plus Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.
Details
Are you interested in exploring the fascinating world of number theory? Look no further than "Number Theory" by Dover Books on Mathematics. Whether you're a math major or a liberal arts student, this exceptional undergraduate text is specifically designed to accommodate both. With its combinatorial approach, it covers the basics while also providing a captivating introduction to more advanced concepts like partitions, multiplicativity-divisibility, quadratic congruences, and additivity. Don't miss out on the opportunity to delve into this captivating subject!
At Dover Books, we understand that not all undergraduates have the same level of familiarity with number theory. That's why "Number Theory" offers a more basic introduction, ensuring that students in education and the liberal arts can grasp the fundamental principles. Through a carefully designed, accessible format, the author seamlessly integrates topics like multiplicativity-divisibility, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots, and prime numbers. This comprehensive approach leaves no stone unturned!
One of the standout features of this book is its emphasis on practical applications and numerical examples in number theory. By providing exercises that involve constructing numerical tables with or without a computer, students are able to develop their understanding and intuition. These concrete examples not only make the theorems more intuitive but also demonstrate the role of computers in obtaining and analyzing complex data. Get ready to see number theory come to life!
Dover Books is renowned for its exceptional mathematics list, featuring prestigious theorists such as Paul J. Cohen, Alfred Tarski, Gary Chartrand, Hermann Weyl, Shlomo Sternberg, and C. R. Wylie. With "Number Theory" as a valuable addition to our collection, we continue to provide students and enthusiasts with the highest quality mathematical resources. Don't miss out on your chance to explore the captivating world of number theory. Get your copy of "Number Theory" today and embark on an incredible mathematical journey!
Click here to get your copy of "Number Theory" now and discover the beauty and significance of number theory!
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