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

Preface

Part I: Data Processing

Chapter 1: Introduction & Overview

Chapter 2: Perspectives on Data

Chapter 3: Dynamic Distributed Dimensional Data Model

Chapter 4: Associative Array Intuition: Music

Chapter 5: Associative Array Intuition: Art

Chapter 6: Manipulating Graphs with Matrices

Chapter 7: Graph Analysis and Machine Learning Systems

Part II: Data Foundations

Chapter 8: Abstract Algebra: Overview

Chapter 9: Abstract Algebra: Definitions

Chapter 10: Associative Array Definition and Matrix Properties

Chapter 11: Graph Construction and Structure

Chapter 12: Survey of Common Transformations

Part III: Data Processing

Chapter 13: Maps and Bases

Chapter 14: Linear Systems

Chapter 15: Eigenvalues and Eigenvectors

Chapter 16: Higher Dimensions