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An Introduction to Mathematical Reasoning
This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.
The Presence in the Midst
How do we make sense of and respond to our experience of the world around us? How do we discern well together? By considering profound questions such as free will and the place of life in the universe, Peter J. Eccles casts an illuminating and engaging light on a key element of Quaker practice. He emphasises the profound importance of discernment to Quaker experience: "The quality of the experience when we come together in meeting for worship depends on each one of us. The Presence in the Midst is always with us, ready to sustain and support us. It calls on each of us to rise above our weakness and live out our true self."--Publisher's description.
An Introduction to Mathematical Reasoning
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. Over 250 problems include questions to interest and challenge the most able student as well as plenty of routine exercises to help familiarize the reader with the basic ideas.
The Tools of Mathematical Reasoning
This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.
Homotopy of Operads and Grothendieck-Teichmuller Groups
The Grothendieck–Teichmüller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of homotopy automorphisms associated to the operad of little 2-discs, which is an object used to model commutative homotopy structures in topology. This volume gives a comprehensive survey on the algebraic aspects of this subject. The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck–Teichmüller group from the viewpoint o...
From Categories to Homotopy Theory
Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.
Convex Optimization & Euclidean Distance Geometry
Convex Analysis is the calculus of inequalities while Convex Optimization is its application. Analysis is inherently the domain of the mathematician while Optimization belongs to the engineer. In layman’s terms, the mathematical science of Optimization is the study of how to make a good choice when confronted with conflicting requirements. The qualifier Convex means: when an optimal solution is found, then it is guaranteed to be a best solution; there is no better choice. Any Convex Optimization problem has geometric interpretation. Conversely, recent advances in geometry and in graph theory hold Convex Optimization within their proofs’ core. This book is about Convex Optimization, convex geometry (with particular attention to distance geometry), and nonconvex, combinatorial, and geometrical problems that can be relaxed or transformed into convex problems. A virtual flood of new applications follows by epiphany that many problems, presumed nonconvex, can be so transformed. International Edition III
An Introduction to Mathematical Reasoning
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.
