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Here are some of the best presentations of the circle of fifths. Use the circle of fifths to explain key signatures, key relationships and music theory.

A classic introduction to mathematical logic from the perspective of category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Its approach moves always from the particular to the general, following through the steps of the abstraction process until the abstract concept emerges naturally.Beginning with a survey of set theory and its role in mathematics, the text proceeds to definitions…

New scientific paradigms typically consist of an expansion of the conceptual language with which we describe the world. Over the past decade, theoretical physics and quantum information theory have turned to category theory to model and reason about quantum protocols.

This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract…

Let's cook up digestible math lessons on number theory to topology.

The present volume is a collection of seven papers that are either based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at the Be

Dominic Verity presents a gentle introduction to Category Theory, perfect for those who've been playing with Haskell for some time and wanted to know what it's…

Free monoids