Mathematics of Big Data

Mathematics of Big Data: Spreadsheets, Databases, Matrices, and Graphs

Jeremy Kepner (MIT) and Hayden Jananthan (Vanderbilt)

This book will be available from MIT Press in 2017

In the meantime, please see the related MIT Open Course Ware (OCW) class with many code examples: Signal Processing on Databases

Table of Contents


Part I: Applications and Practice

Chapter 1: Introduction and Overview

Chapter 2: Perspectives on Data

Chapter 3: Dynamic Distributed Dimensional Data Model

Chapter 4: Associative Arrays and Musical Metadata

Chapter 5: Associative Arrays and Abstract Art

Chapter 6: Manipulating Graphs with Matrices

Chapter 7: Graph Analysis and Machine Learning Systems

Part II: Mathematical Foundations

Chapter 8: Visualizing the Algebra of Associative Arrays

Chapter 9: Defining the Algebra of Associative Arrays

Chapter 10: Structural Properties of Associative Arrays

Chapter 11: Graph Construction and Graphical Patterns

Chapter 12: Survey of Common Transformations

Part III: Linear Systems

Chapter 13: Maps and Bases

Chapter 14: Linearity of Associative Arrays

Chapter 15: Eigenvalues and Eigenvectors

Chapter 16: Higher Dimensions