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