Mathematics

How does a machine recognize a face?How can AI distinguish speech from noise?Why do modern computer vision systems still rely on mathematical techniques developed decades ago?The answer lies in Fourier and Wavelet Analysis.In Fourier and Wavelet Analysis in Artificial Intelligence, Anshuman Mishra reveals how frequency-domain representations, multi-resolution analysis, and signal-processing techniques continue to shape the future of Machine Learning, Deep Learning, Computer Vision, Speech Recognition, Biomedical AI, and Edge Intelligence.From Fourier Transforms and Fast Fourier Algorithms to Wavelet Scattering Networks and Hybrid CNN Architectures, this book demonstrates how mathematical signal analysis becomes intelligent feature extraction.Discover the mathematics behind perception, representation, and intelligent decision-making.

Can a neural network be viewed as a differential equation?Why does gradient descent behave like a dynamical system?How do biological neurons inspire modern AI architectures?What mathematical principles govern stability, learning, adaptation, and intelligence?In Differential Equations in AI and Neural Dynamics, Anshuman Mishra explores the mathematical framework that underlies modern Artificial Intelligence.From Ordinary Differential Equations and Neural Population Models to Neural ODEs, Stochastic Learning, Reinforcement Learning, and Brain-Inspired Computation, this book reveals how continuous-time mathematics drives intelligent behavior.Discover how equations of change become equations of intelligence.

What do speech recognition systems, computer vision models, autonomous robots, and biomedical AI applications have in common?They all rely on the mathematics of signal transformation.How does a neural network extract meaningful patterns from raw audio?Why are Fourier features becoming increasingly important in machine learning?How can Laplace and Z-Transforms help analyze dynamic systems, sequential data, and intelligent control architectures?In Integral Transforms for Artificial Intelligence, Anshuman Mishra reveals how Fourier, Laplace, and Z-Transform techniques power modern AI systems across machine learning, deep learning, computer vision, speech processing, robotics, and signal analysis.Discover how mathematical transformations convert raw signals into intelligent insights—and how they continue to shape the future of Artificial Intelligence.

Every neural network is a collection of matrix operations.Every convolution is a structured matrix transformation.Every deep learning breakthrough ultimately depends on efficient tensor computations.But how do these mathematical operations actually power intelligent systems?In Matrix Computations for Deep Learning, Anshuman Mishra reveals the mathematical engine behind modern AI. From Singular Value Decomposition and tensor algebra to convolutional neural networks, GPU acceleration, and large-scale machine learning systems, this book provides a complete roadmap for understanding the computational foundations of deep learning.Discover how matrices become intelligence—and how mathematics becomes machine learning.

How should an AI system make decisions when information is incomplete?How can machines quantify uncertainty instead of merely producing predictions?How can intelligent systems continuously update their beliefs as new evidence emerges?The answer lies in Bayesian Mathematics.In Bayesian Mathematics for AI Decision Making, Anshuman Mishra explores the powerful framework that enables modern AI systems to reason probabilistically, model uncertainty, and make rational decisions in complex environments.From Bayesian inference and probabilistic programming to uncertainty-aware deep learning, reinforcement learning, healthcare diagnostics, robotics, and financial forecasting, this book reveals how Bayesian thinking is shaping the next generation of Artificial Intelligence.Learn how uncertainty becomes knowledge—and how probability becomes intelligence.

Every secure communication begins with mathematics.Every modern encryption system relies on number theory.Every intelligent cyber defense increasingly depends on Artificial Intelligence.But what happens when these three worlds converge?In Cryptography, Number Theory, and AI Security, Anshuman Mishra takes readers on a journey from the mathematical foundations of encryption to the cutting-edge frontier of AI-powered cybersecurity.Explore prime numbers, RSA, elliptic curves, blockchain security, machine learning for threat detection, homomorphic encryption, federated learning, adversarial AI, and post-quantum cryptography.Discover how mathematics and machine intelligence work together to secure the digital world.

Prediction is only the beginning.Modern AI systems must explain their predictions, quantify uncertainty, scale to massive datasets, and operate reliably in real-world environments.How do Support Vector Regression models capture nonlinear patterns?How do Bayesian methods estimate uncertainty?How do Gaussian Processes make predictions with confidence intervals?How can complex AI models remain interpretable and trustworthy?In this advanced second volume, Anshuman Mishra explores the cutting-edge regression techniques that power intelligent prediction systems across machine learning, data science, healthcare, finance, robotics, and scientific research.Discover how modern Artificial Intelligence transforms data into reliable, explainable, and scalable predictions.

Every intelligent prediction begins with a simple question:Can we model the relationship between data and outcomes?Regression is the foundation upon which modern predictive analytics, machine learning systems, and countless AI applications are built.From linear regression and regularization techniques to neural network regression, Gaussian processes, explainable AI, and real-world predictive systems, this book provides a complete roadmap for understanding how machines learn to predict.In Linear and Nonlinear Regression in Artificial Intelligence, Anshuman Mishra combines mathematical rigor, practical implementation, and real-world applications to help readers master one of the most powerful tools in Artificial Intelligence.Discover the mathematics behind prediction—and the science behind intelligent decision-making.

Artificial Intelligence does not learn in certainty.It learns through uncertainty, exploration, randomness, and adaptation.How does AlphaGo evaluate millions of possible moves?How do reinforcement learning agents discover optimal strategies?How do diffusion models generate realistic images?How do autonomous robots navigate uncertain environments?The answer lies in stochastic processes.In this advanced second volume, Anshuman Mishra explores the mathematical foundations behind reinforcement learning, probabilistic deep learning, robotics, generative AI, and emerging stochastic algorithms that are shaping the future of intelligent systems.Discover how randomness becomes learning—and how uncertainty becomes intelligence.

Artificial Intelligence is often described as learning from data.But beneath every learning algorithm lies something even more fundamental:Probability, randomness, and uncertainty.From Hidden Markov Models and stochastic gradient descent to Monte Carlo methods and reinforcement learning, modern AI systems depend on stochastic processes to make predictions, learn from experience, and adapt to changing environments.In Stochastic Processes in Artificial Intelligence, Anshuman Mishra provides a structured and accessible journey through the mathematical foundations that power intelligent systems.Discover how uncertainty becomes intelligence—and why stochastic thinking is essential for the future of Artificial Intelligence.

Every intelligent system faces a fundamental challenge:How do you find the best solution when there are millions—or even trillions—of possibilities?From A* search and heuristic optimization to neural architecture search, hyperparameter tuning, constraint satisfaction, and quantum optimization, modern AI depends on sophisticated strategies for navigating combinatorial search spaces.In this advanced second volume, Anshuman Mishra explores the powerful algorithms that enable intelligent systems to search smarter, optimize faster, and scale beyond brute force computation.Discover how combinatorial thinking drives machine learning, optimization, quantum AI, and the future of intelligent decision-making.The future of AI belongs to those who understand combinatorial complexity.

Artificial Intelligence is not merely about data, learning, or neural networks—it is fundamentally about exploring vast spaces of possibilities.Every search algorithm, planning system, optimization framework, recommendation engine, and machine learning model faces a common challenge: navigating an enormous combinatorial universe of potential solutions.In Combinatorial Thinking in Artificial Intelligence, Anshuman Mishra reveals the mathematical foundations that drive modern AI systems. Through permutations, combinations, graph theory, probability, search strategies, and optimization techniques, readers learn how intelligent systems reason, search, and make decisions in complex environments.If you want to understand why AI algorithms work—not just how to implement them—this book provides the missing mathematical perspective.Discover the combinatorial engine behind intelligence.

Can Hidden Markov Models predict financial market regimes?How are genes discovered from DNA sequences?How do robots determine their location in uncertain environments?Can probabilistic AI still compete with Transformers and Deep Learning?Volume-3 of Hidden Markov Models and AI answers these questions through real-world applications, Python implementations, industrial case studies, advanced projects, and future AI research.Explore how Hidden Markov Models are used in bioinformatics, cybersecurity, finance, robotics, autonomous systems, anomaly detection, and scientific discovery. Learn to build HMM systems from scratch, work with professional AI libraries, and understand the evolving relationship between probabilistic models and deep learning.This volume is designed for readers who want to move beyond theory and develop practical expertise in modern sequential artificial intelligence.

How do voice assistants understand speech?How does a chatbot track conversation context?How can machines identify speakers, translate languages, recognize named entities, and process sequential information?The answer lies in sequence modeling.In Volume-2 of Hidden Markov Models and AI, readers move beyond theory into practical applications of Hidden Markov Models in speech recognition, natural language processing, machine translation, speaker verification, conversational AI, and intelligent decision-making systems.Learn how modern AI systems transform speech signals and language sequences into meaningful intelligence using probabilistic models that continue to influence today's most advanced technologies.Whether you are an AI student, NLP researcher, speech engineer, or machine learning professional, this volume provides the practical knowledge required to master sequential learning systems.

Artificial Intelligence is not only about neural networks and transformers. Behind many of the world's most influential AI systems lies a powerful probabilistic framework known as the Hidden Markov Model (HMM).From speech recognition and natural language processing to robotics, cybersecurity, finance, and bioinformatics, HMMs remain one of the most important sequence modeling techniques ever developed.This book takes readers on a complete journey through Markov Chains, probabilistic reasoning, Hidden Markov Models, Forward-Backward algorithms, Viterbi decoding, Baum-Welch training, and advanced HMM architectures.Designed for students, researchers, and AI professionals, the book combines rigorous mathematics with practical applications, making complex concepts accessible and immediately useful.If you want to truly understand how intelligent systems model uncertainty, learn from temporal patterns, and reason about hidden information, this book provides the foundation.