Math Without Numbers
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Math Without Numbers
An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.
Mathematics without Numbers
Geoffrey Hellman presents a detailed interpretation of mathematics as the investigation of structural possibilities, as opposed to absolute, Platonic objects. After dealing with the natural numbers and analysis, he extends his approach to set theory, and shows how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world.
Math Without Numbers
Author: William S. Veatch
language: en
Publisher: Createspace Independent Publishing Platform
Release Date: 2016-11-09
Math Without Numbers - The Mathematics of Ideas. Volume 1 - Foundations. This Volume 1 in the "Math Without Numbers" series explores the nature of Ideas, from both a practical and an abstract mathematical point of view. The book demonstrates that mathematics can explain "how" we think, but cannot tell us "what" to think or how to act. The author applies principles of Set Theory to Ideas, and illustrates how Ideas form structures that are well-known in the field of Mathematics, including Partitions/Equivalence Classes, Groups, Boolean Algebras, Rings, Lattices, and Topologies. The book touches on Logic, Argumentation, and Debate, which are topics that will be explored in detail in Volumes 2 and 3. The discussion is original and accessible, and includes material appropriate for anyone with a background in basic high school math, as well as more advanced material for those looking for a challenge. The book begins at an introductory level, but proceeds to discuss more complex material for those interested in making language more precise and unambiguous. Much of the focus is on Lattices and Boolean Algebras/Rings, as applied to Ideas rather than numbers. There are many similarities to the relatively new field of mathematics called Formal Concept Analysis, although Math Without Numbers focuses on building a foundation in Set Theory and Logic. This book is intended for anyone interested in Set Theory, the Philosophy of Mathematics, the Philosophy of Language, Critical Thinking, Logic, and/or Artificial Intelligence. Those who like solving word puzzles will enjoy the Math Without Numbers series, which attempts to solve one of the greatest puzzles of all time: the Mathematics of Ideas.