Essentials of Mathematical Methods: Foundations, Principles, and Algorithms
Minimum price
Suggested price

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


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

The Leanpub 45-day 100% Happiness Guarantee

Within 45 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.

See full terms

Do Well. Do Good.

Authors have earned$10,607,028writing, publishing and selling on Leanpub, earning 80% royalties while saving up to 25 million pounds of CO2 and up to 46,000 trees.

Learn more about writing on Leanpub

Free Updates. DRM Free.

If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).

Most Leanpub books are available in PDF (for computers), EPUB (for phones and tablets) and MOBI (for Kindle). The formats that a book includes are shown at the top right corner of this page.

Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.

Learn more about Leanpub's ebook formats and where to read them

Write and Publish on Leanpub

You can use Leanpub to easily write, publish and sell in-progress and completed ebooks and online courses!

Leanpub is a powerful platform for serious authors, combining a simple, elegant writing and publishing workflow with a store focused on selling in-progress ebooks.

Leanpub is a magical typewriter for authors: just write in plain text, and to publish your ebook, just click a button. (Or, if you are producing your ebook your own way, you can even upload your own PDF, EPUB and/or MOBI files and then publish with one click!) It really is that easy.

Learn more about writing on Leanpub