A Readable Introduction to Real Mathematics

This book is a comprehensive introduction to real mathematics, suitable for undergraduate courses or independent study. It presents sophisticated mathematical ideas in an elementary and friendly fashion, with a large number of exercises of varying difficulty. The sole prerequisite is high school algebra, and the book covers topics such as mathematical induction, modular arithmetic, the Fundamental Theorem of Arithmetic, Fermat's Little Theorem, RSA encryption, the Euclidean algorithm, rational and irrational numbers, complex numbers, cardinality, Euclidean plane geometry, constructibility, infinite series, and higher dimensional spaces. The book is praised for its clear and engaging style, and is recommended for a wide variety of courses and students of mathematics and other subjects.

Format: Paperback / softback
Length: 218 pages
Publication date: 28 July 2021
Publisher: Springer Nature Switzerland AG

This text is designed for an undergraduate course or for independent study, presenting sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some designed to help reinforce basic concepts and others challenging virtually all readers. The sole prerequisite for reading this text is high school algebra. Topics covered include:

Mathematical induction
Modular arithmetic
The Fundamental Theorem of Arithmetic
Fermat's Little Theorem
RSA encryption
The Euclidean algorithm
Rational and irrational numbers
Complex numbers
Cardinality
Euclidean plane geometry
Constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)
Infinite series
Higher dimensional spaces

This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book.

From the reviews of the first edition:

"It is carefully written in a precise but readable and engaging style... I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences." (Nick Lord, The Mathematical Gazette, Vol. 100 {PHONE})

"The book is an introduction to real mathematics and is very readable. ... The book is indeed a joy to read, and would be an excellent text for an 'appreciation of mathematics course, among other possibilities." (G.A. Heuer, Mathematical Re.

Weight: 367g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030807313
Edition number: 2nd ed. 2018