Mathematical Foundations of Data Science Using R

Preface
1 Introduction
	1.1 Relationships between mathematical subjects and data science
	1.2 Structure of the book
		1.2.1 Part one
		1.2.2 Part two
		1.2.3 Part three
	1.3 Our motivation for writing this book
	1.4 Examples and listings
	1.5 How to use this book
Part I Introduction to R
	2 Overview of programming paradigms
		2.1 Introduction
		2.2 Imperative programming
		2.3 Functional programming
		2.4 Object-oriented programming
		2.5 Logic programming
		2.6 Other programming paradigms
		2.7 Compiler versus interpreter languages
		2.8 Semantics of programming languages
		2.9 Further reading
		2.10 Summary
	3 Setting up and installing the R program
		3.1 Installing R on Linux
		3.2 Installing R on MAC OS X
		3.3 Installing R on Windows
		3.4 Using R
		3.5 Summary
	4 Installation of R packages
		4.1 Installing packages from CRAN
		4.2 Installing packages from Bioconductor
		4.3 Installing packages from GitHub
		4.4 Installing packages manually
		4.5 Activation of a package in an R session
		4.6 Summary
	5 Introduction to programming in R
		5.1 Basic elements of R
		5.2 Basic programming
		5.3 Data structures
		5.4 Handling character strings
		5.5 Sorting vectors
		5.6 Writing functions
		5.7 Writing and reading data
		5.8 Useful commands
		5.9 Practical usage of R
		5.10 Summary
	6 Creating R packages
		6.1 Requirements
		6.2 R code optimization
		6.3 S3, S4, and RC object-oriented systems
		6.4 Creating an R package based on the S3 class system
		6.5 Checking the package
		6.6 Installation and usage of the package
		6.7 Loading and using a package
		6.8 Summary
Part II Graphics in R
	7 Basic plotting functions
		7.1 Plot
		7.2 Histograms
		7.3 Bar plots
		7.4 Pie charts
		7.5 Dot plots
		7.6 Strip and rug plots
		7.7 Density plots
		7.8 Combining a scatterplot with histograms: the layout function
		7.9 Three-dimensional plots
		7.10 Contour and image plots
		7.11 Summary
	8 Advanced plotting functions: ggplot2
		8.1 Introduction
		8.2 qplot()
		8.3 ggplot()
		8.4 Summary
	9 Visualization of networks
		9.1 Introduction
		9.2 igraph
		9.3 NetBioV
		9.4 Summary
Part III Mathematical basics of data science
	10 Mathematics as a language for science
		10.1 Introduction
		10.2 Numbers and number operations
		10.3 Sets and set operations
		10.4 Boolean logic
		10.5 Sum, product, and Binomial coefficients
		10.6 Further symbols
		10.7 Importance of definitions and theorems
		10.8 Summary
	11 Computability and complexity
		11.1 Introduction
		11.2 A brief history of computer science
		11.3 Turing machines
		11.4 Computability
		11.5 Complexity of algorithms
		11.6 Summary
	12 Linear algebra
		12.1 Vectors and matrices
		12.2 Operations with matrices
		12.3 Special matrices
		12.4 Trace and determinant of a matrix
		12.5 Subspaces, dimension, and rank of a matrix
		12.6 Eigenvalues and eigenvectors of a matrix
		12.7 Matrix norms
		12.8 Matrix factorization
		12.9 Systems of linear equations
		12.10 Exercises
	13 Analysis
		13.1 Introduction
		13.2 Limiting values
		13.3 Differentiation
		13.4 Extrema of a function
		13.5 Taylor series expansion
		13.6 Integrals
		13.7 Polynomial interpolation
		13.8 Root finding methods
		13.9 Further reading
		13.10 Exercises
	14 Differential equations
		14.1 Ordinary differential equations (ODE)
		14.2 Partial differential equations (PDE)
		14.3 Exercises
	15 Dynamical systems
		15.1 Introduction
		15.2 Population growth models
		15.3 The Lotka–Volterra or predator–prey system
		15.4 Cellular automata
		15.5 Random Boolean networks
		15.6 Case studies of dynamical system models with complex attractors
		15.7 Fractals
		15.8 Exercises
	16 Graph theory and network analysis
		16.1 Introduction
		16.2 Basic types of networks
		16.3 Quantitative network measures
		16.4 Graph algorithms
		16.5 Network models and graph classes
		16.6 Further reading
		16.7 Summary
		16.8 Exercises
	17 Probability theory
		17.1 Events and sample space
		17.2 Set theory
		17.3 Definition of probability
		17.4 Conditional probability
		17.5 Conditional probability and independence
		17.6 Random variables and their distribution function
		17.7 Discrete and continuous distributions
		17.8 Expectation values and moments
		17.9 Bivariate distributions
		17.10 Multivariate distributions
		17.11 Important discrete distributions
		17.12 Important continuous distributions
		17.13 Bayes’ theorem
		17.14 Information theory
		17.15 Law of large numbers
		17.16 Central limit theorem
		17.17 Concentration inequalities
		17.18 Further reading
		17.19 Summary
		17.20 Exercises
	18 Optimization
		18.1 Introduction
		18.2 Formulation of an optimization problem
		18.3 Unconstrained optimization problems
		18.4 Constrained optimization problems
		18.5 Some applications in statistical machine learning
		18.6 Further reading
		18.7 Summary
		18.8 Exercises
Bibliography
Subject Index