Chapman and Hall/CRC
176 pages | 115 Color Illus.
Introduction to Recognition and Deciphering of Patterns aims to get STEM and non–STEM students acquainted with different patterns, as well as where and when specific patterns arise. In addition, the book seeks to get students to learn how to recognize patterns and distinguish the similarities and differences between them.
Patterns emerge on an every-day basis, such as weather patterns, traffic patterns, behavioural patterns, geometric patterns, linguistic patterns, structural patterns, digital patterns, etc. Recognizing patterns and studying their unique traits is essential for the development and enhancement of our intuitive skills, and in strengthening our analytical skills. Mathematicians often apply patterns to get acquainted with new concepts, but this is a technique that can be applied across many disciplines.
Throughout this book we will encounter assorted patterns that emerge from various geometrical configurations of squares, circles, right triangles and equilateral triangles that either repeat at the same scale or at different scales. The book will also focus on describing linear patterns, geometric patterns, alternating patterns, piece-wise patterns, summation-type patterns and factorial-type patterns analytically. Deciphering the details of these distinct patterns will lead to the proof by induction method. Furthermore, the book will render properties of the Pascal’s Triangle and provide supplemental practice in deciphering specific patterns and verifying them.
The book will adjourn with first order recursive relations: describing sequences as recursive relations, obtaining the general solution by solving an initial value problem and determining the periodic traits.
1. Introduction. 2. Patterns of Geometrical Systems. 3. Sequences and Summations. 4. Pascal's Triangle Identities. 5. First Order Recursive Relations. 6. Periodic Traits