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

The main aim of this book is to make the advanced mathematical background accessible to someone with a programming background. This book will equip the readers with not only deep learning architectures but the mathematics behind them. With this book, you will understand the relevant mathematics that...

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Main Author: Dawani, Jay (Author) Electronic eBook English Birmingham : Packt Publishing, 2020. CONNECT CONNECT
• Intro
• Title Page
• Contributors
• 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
• 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