Essentials of Mathematical Methods: Foundations, Principles, and Algorithms
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Essentials of Mathematical Methods: Foundations, Principles, and Algorithms

About the Book

Today, mathematical methods, models, and computational algorithms are playing increasingly significant roles in addressing major challenges arising from scientific research and technological development. Although many novel methods and algorithms, such as deep learning and artificial intelligence, are emerging and reshaping various areas at an unprecedented pace, their core ideas and working mechanisms are inherently related to and deeply rooted in some essential mathematical foundations and principles. By performing an in-depth survey on the underlying foundations, principles, and algorithms, this book aims to navigate the vast landscape of mathematical methods widely used in diverse domains.  

This book starts with a survey of mathematical foundations, including essential concepts and theorems in real analysis, linear algebra, etc. Then it covers a broad spectrum of applied mathematical methods, ranging from traditional ones such as optimizations and dynamics modeling, to state-of-the-art such as machine learning, deep learning, and reinforcement learning. The emphasis is placed on methods regarding statistical modeling, stochastic and dynamical system modeling, optimal decision making, and statistical learning. For each part, this book organizes fundamental definitions, theorems, methods, and algorithms in a logical, self-explanatory way. 

About the Author

YUGUANG YANG
YUGUANG YANG

PhD and MS from Johns Hopkins University. Passionate about artificial intelligence and mathematical modeling for applied science, engineering, and industrial applications.

Table of Contents

  • Mathematical Foundations
    • Sets, Sequences and Series
    • Metric Space and Topological Space
    • Advanced Calculus
    • Linear Algebra and Matrix Analysis
    • Basic Functional Analysis
  • Mathematical Optimization Methods
    • Unconstrained Nonlinear Optimization
    • Constrained Nonlinear Optimization
    • Linear Optimization
    • Convex Analysis and Convex Optimization
    • Basic Game Theory
  • Classical Statistical Methods
    • Theory of Probability
    • Statistical Distributions
    • Statistical Estimation Theory
    • Multivariate Statistical Methods
    • Linear Regression Analysis
    • Monte Carlo Methods
  • Dynamics Modeling Methods
    • Models and estimation in linear dynamical systems
    • Stochastic Process
    • Stochastic Calculus
    • Markov Chain and Random Walk
    • Time Series Analysis
  • Statistical Learning Methods
    • Supervised Learning Principles and Methods
    • Linear Models for Regression
    • Linear Models for Classification
    • Generative Models
    • K Nearest Neighbors
    • Tree Methods
    • Ensemble and Boosting Methods
    • Unsupervised Statistical Learning
    • Neural Network and Deep Learning
  • Optimal Control and Reinforcement Learning Methods
    • Classical Optimal Control Theory
    • Reinforcement Learning

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