Hands-on mathematics for deep learning : build a solid mathematical foundation for training efficient deep neural networks / Jay Dawani.

Intro
Title Page
Copyright and Credits
About Packt
Contributors
Table of Contents
Preface
Section 1: Essential Mathematics for Deep Learning
Linear Algebra
Comparing scalars and vectors
Linear equations
Solving linear equations in n-dimensions
Solving linear equations using elimination
Matrix operations
Adding matrices
Multiplying matrices
Inverse matrices
Matrix transpose
Permutations
Vector spaces and subspaces
Spaces
Subspaces
Linear maps
Image and kernel
Metric space and normed space
Inner product space

Matrix decompositions
Determinant
Eigenvalues and eigenvectors
Trace
Orthogonal matrices
Diagonalization and symmetric matrices
Singular value decomposition
Cholesky decomposition
Summary
Vector Calculus
Single variable calculus
Derivatives
Sum rule
Power rule
Trigonometric functions
First and second derivatives
Product rule
Quotient rule
Chain rule
Antiderivative
Integrals
The fundamental theorem of calculus
Substitution rule
Areas between curves
Integration by parts
Multivariable calculus
Partial derivatives

Chain rule
Integrals
Vector calculus
Derivatives
Vector fields
Inverse functions
Summary
Probability and Statistics
Understanding the concepts in probability
Classical probability
Sampling with or without replacement
Multinomial coefficient
Stirling's formula
Independence
Discrete distributions
Conditional probability
Random variables
Variance
Multiple random variables
Continuous random variables
Joint distributions
More probability distributions
Normal distribution
Multivariate normal distribution

Bivariate normal distribution
Gamma distribution
Essential concepts in statistics
Estimation
Mean squared error
Sufficiency
Likelihood
Confidence intervals
Bayesian estimation
Hypothesis testing
Simple hypotheses
Composite hypothesis
The multivariate normal theory
Linear models
Hypothesis testing
Summary
Optimization
Understanding optimization and it's different types
Constrained optimization
Unconstrained optimization
Convex optimization
Convex sets
Affine sets
Convex functions
Optimization problems

Non-convex optimization
Exploring the various optimization methods
Least squares
Lagrange multipliers
Newton's method
The secant method
The quasi-Newton method
Game theory
Descent methods
Gradient descent
Stochastic gradient descent
Loss functions
Gradient descent with momentum
The Nesterov's accelerated gradient
Adaptive gradient descent
Simulated annealing
Natural evolution
Exploring population methods
Genetic algorithms
Particle swarm optimization
Summary
Graph Theory
Understanding the basic concepts and terminology