Books

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.

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.

What if the unpredictable behavior of intelligent systems is not a flaw—but a feature?In Nonlinear Dynamics and Chaos Theory in Artificial Intelligence (VOL-II), Anshuman Mishra explores the fascinating intersection of chaos, complexity, fractals, adaptive intelligence, and machine learning.Discover how chaotic neural networks, nonlinear optimization, fractal learning architectures, autonomous robotics, reinforcement learning, and emergent intelligence are transforming the future of AI.Through mathematical rigor, practical Python implementations, real-world case studies, and cutting-edge research directions, this book reveals how chaos can become a powerful tool for building smarter, more adaptive, and more resilient intelligent systems.For researchers, students, engineers, and AI innovators, this volume opens the door to one of the most exciting frontiers of next-generation artificial intelligence.

What if the unpredictable behavior of AI systems is not a flaw but a consequence of deeper mathematical laws? Explore chaos theory, nonlinear dynamics, fractals, emergence, and complexity to uncover how intelligent systems learn, adapt, self-organize, and evolve in ways that traditional linear models cannot explain.

Explore the advanced world of AI reasoning through SAT and SMT solvers, knowledge representation, intelligent agents, logic programming, formal verification, and neuro-symbolic AI. Learn how modern intelligent systems reason, prove, verify, and explain decisions with mathematical precision.

Discover the mathematical foundations behind intelligent reasoning. Explore propositional logic, predicate logic, theorem proving, SAT and SMT solvers, knowledge representation, formal verification, and AI reasoning systems in one comprehensive guide designed for students, researchers, and AI professionals.

Explore the advanced frontier of Category-Theoretic Artificial Intelligence. Discover how transformers, symbolic reasoning, reinforcement learning, higher categories, topos theory, and compositional learning can be unified through the powerful language of category theory. An essential guide for researchers, AI professionals, and future AGI innovators.