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The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory. The topics covered are many of those included in an introductory Number Theory course for mathematics majors, but the presentation is carefully tailored to meet the needs of elementary education, liberal arts, and other non-mathematical majors. The text covers logic and proofs, as well as major concepts in Number Theory, and contains an abundance of worked examples and exercises to both clearly illustrate concepts and evaluate the students' mastery of the material.
Inhaltsverzeichnis
Introduction.- Conjectures, Proofs and Counterexamples.- Pythagorean Triples.- Prime Numbers.- The Division Algorithm and the Euclidean Algorithm.- Congruences.- Numerical Functions and Special Congruences.- Cryptography.
Zusammenfassung
The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory. The topics covered are many of those included in an introductory Number Theory course for mathematics majors, but the presentation is carefully tailored to meet the needs of elementary education, liberal arts, and other non-mathematical majors. The text covers logic and proofs, as well as major concepts in Number Theory, and contains an abundance of worked examples and exercises to both clearly illustrate concepts and evaluate the students’ mastery of the material.
Zusatztext
“The book under review is a new introductory textbook in number theory. … the book is a fine book. Unique as it is focused to students that are not mathematicians. I do think this can be a trend nowdays to try to write some sophisticated material in a way that non-technical readers can enjoy. And this is a fine example I reccomend it.” (Philosophy, Religion and Science, June, 2016)
“This book is intended for non-math and non-science majors. … Forman and Rash (both, St. Joseph’s Univ.) are commended for approaching this audience with this content, as number theory includes many interesting ideas, such as prime number properties, congruences, key theorems such as Euler’s and Fermat’s, and even public key cryptography. … Summing Up: Recommended. Lower-division undergraduates, two-year technical program students, professionals, and practitioners; general readers.” (J. Johnson, Choice, Vol. 53 (2), October, 2015)
“This material is so fundamental and so well presented that ifI was still teaching college mathematics I would recommend that a course based on this book be required for all potential teachers. For those on the track to teach high school math, this would be the first course in their math sequence. One of the best features of this book is the section that introduces proofs, a topic that terrifies almost every education student and many math students.” (Charles Ashbacher, MAA Reviews, February, 2015)
Bericht
"The book under review is a new introductory textbook in number theory. ... the book is a fine book. Unique as it is focused to students that are not mathematicians. I do think this can be a trend nowdays to try to write some sophisticated material in a way that non-technical readers can enjoy. And this is a fine example I reccomend it." (Philosophy, Religion and Science, June, 2016)
"This book is intended for non-math and non-science majors. ... Forman and Rash (both, St. Joseph's Univ.) are commended for approaching this audience with this content, as number theory includes many interesting ideas, such as prime number properties, congruences, key theorems such as Euler's and Fermat's, and even public key cryptography. ... Summing Up: Recommended. Lower-division undergraduates, two-year technical program students, professionals, and practitioners; general readers." (J. Johnson, Choice, Vol. 53 (2), October, 2015)
"This material is so fundamental and so well presented that ifI was still teaching college mathematics I would recommend that a course based on this book be required for all potential teachers. For those on the track to teach high school math, this would be the first course in their math sequence. One of the best features of this book is the section that introduces proofs, a topic that terrifies almost every education student and many math students." (Charles Ashbacher, MAA Reviews, February, 2015)
