Pascal S Triangle Importance
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Numeral Systems With Irrational Bases For Mission-critical Applications
This volume is the result of the author's many-years of research in this field. These results were presented in the author's two books, Introduction to the Algorithmic Measurement Theory (Moscow, Soviet Radio, 1977), and Codes of the Golden Proportion (Moscow, Radio and Communications, 1984), which had not been translated into English and are therefore not known to English-speaking audience. This volume sets forth new informational and arithmetical fundamentals of computer and measurement systems based on Fibonacci p-codes and codes of the golden p-proportions, and also on Bergman's system and 'golden' ternary mirror-symmetrical arithmetic. The book presents some new historical hypotheses concerning the origin of the Egyptian calendar and the Babylonian numeral system with base 60 (dodecahedral hypothesis), as well as about the origin of the Mayan's calendar and their numeral system with base 20 (icosahedral hypothesis). The book is intended for the college and university level. The book will also be of interest to all researchers, who use the golden ratio and Fibonacci numbers in their subject areas, and to all readers who are interested to the history of mathematics.
The Mad Math Manual
After studying and teaching math and science over the years I realized that many good opportunities for learning and teaching important and essential things were missing from the resources that were available. Included in this book are many exercises, techniques and insights that strengthen a learner’s mathematical and logical abilities which are simply not to be found anywhere else. Also included are things which I have learned from different, disparate places that, for the student’s convenience, have all been gathered into one place and which I attempted to explain in simpler terms than what is currently available. Afterall, it is hard enough to learn these concepts let alone have to shift through all of the data to find what really pertains to one’s study. Some of the material presented are things which I myself found to be the most confusing. In this regard I hope that the manual can be a great resource for students trying to learn more about math and science as well as the workings of nature. Even though it is unlikely a reader will be able to understand all of the material presented on their own and without the presence of a teacher, having another resource in which the material and concepts are presented in a unique and simpler way is highly useful. Generally, when people learn about math and science, they are usually not satisfied by the answer that their teacher or textbook has to give on why nature settled on a certain constant or equation. It’s mind boggling to me how many people fail to acknowledge the relatedness of many physical constants as well as the logic behind some of the greatest discoveries, and in effect are missing out on a lot of the beauty behind science and the workings of nature.
Hands-On Combinatorics
Author: Brian Hopkins
language: en
Publisher: American Mathematical Society
Release Date: 2025-01-29
This book provides an active-learning approach to combinatorial reasoning and proof through a thoughtful sequence of low threshold, high ceiling activities. A novel feature is its narrative format, with much of the text written from the perspective of a student working through the material with peers. Furthermore, each chapter includes detailed notes for the instructor such as additional scaffolding, extensions, and notation for more advanced students. The exposition is complemented by over 300 colorful illustrations. The main focus of the book is the study of integer compositions with forays into graph theory and recreational mathematics. Befitting the constructive nature of the book, compositions are represented by trains made up of cars. By physically constructing these objects, students become proficient in hands-on verifications of numerous identities. Developed by a recipient of the MAA's Haimo Award for Distinguished Teaching and used in several teacher professional development workshops and college courses, the book has very modest prerequisites. In particular, no prior experience with symbolic formalism is presumed, allowing this material to be used in multiple classroom settings, from enrichment activities for secondary school students through undergraduate classes in discrete mathematics. The structure of the book also makes it conducive to self-study. Get ready to “build some trains” and explore the enlightening world of combinatorial proofs! Hands-On Combinatorics is a wonderful book, cleverly designed for readers of all mathematical levels. With eye-catching illustrations, Brian Hopkins creates beautiful bijections and clever combinatorial arguments with binomial coefficients, Fibonacci numbers, and beyond. —Arthur T. Benjamin, Harvey Mudd College, co-author of Proofs That Really Count