Mathematics

A practical guide to numerical methods for the Cahn–Hilliard equation in alloy design—matrix and spectral schemes, quasi-steady reductions, and matrix exponentials—tested on spinodal benchmarks and illustrated with codes for binary and multicomponent systems.

From Mathematical Foundations to the Future of AIMost deep learning still lives in flat, Euclidean space. Real-world data does not.This 15-chapter university textbook takes you from the basics of topology and geometry to the frontier of Geometric Deep Learning, Topological Data Analysis, equivariant networks, and optimization on manifolds.Clear explanations. Worked examples. Research roadmaps.

AI 越来越会回答、会行动，但下一种真正重要的智能，会不会是"发现"？《当 AI 开始发现》借 AlphaEvolve、自驱实验室、自动证明与世界模型，带你看见智能的一次转向。

The ultimate bridge from high school AP Physics to modern AI. Start with the familiar physics you know, translate it into Python, and use it as a launchpad to build advanced Machine Learning models and neural networks. Includes 100% solved exercises and click-to-run Google Colab labs.

Master PMSM control from first principles to real electric-drive implementation. PMSM² connects electromagnetic theory, FOC, MTPA, field weakening, sensorless estimation, inverter behavior, and BEV calibration in one practical engineering reference.

This textbook accompanies a year-long Discrete Mathematics course for Computer Science and AI students, covering classical topics such as combinatorics, graph theory, probability, logic, and set theory. It emphasizes applications across computer science and complements the standard curriculum with advanced topics in each chapter.

Two people wake with no names, no past, and no way out — only a maze built entirely from the rules of logic, where every proof buys survival and every mistake steals a piece of who they are. Something ancient is watching, something dangerous still loves one of them, and a machine dead for twenty years is starting, impossibly, to wake. Propositional Logic: The Unseen Maze turns the hardest ideas in mathematics into a fight for two people's minds — and asks what's left of you once you've proven everything except who you are.

Review the theory. Work through the examples. Solve the problems. Prepare for your examinations with confidence.Aerodynamics, Turbomachinery & Computational Fluid Dynamics is designed as a practical review and examination-preparation guide for engineering students. It brings together essential concepts, equations, methods, worked examples, solved problems, and numerical exercises to help students quickly revise and apply what they have learned.The book places particular emphasis on step-by-step worked examples and problem solving. Important formulas and principles are followed by applications showing how to approach typical engineering problems, perform calculations, and interpret the results.Use it for systematic revision throughout the semester or intensive preparation before examinations. The worked examples and problems are especially useful for developing speed, accuracy, and confidence in solving numerical and analytical questions.Ideal for students of aerospace engineering, mechanical engineering, aeronautical engineering, and related disciplines, preparing for university examinations, competitive examinations, and technical assessments.

A practical collection of engineering problems for learning, practice, revision, and problem-solving.Strengthen your engineering fundamentals through a wide variety of problems designed to connect theory with practical application. Ideal for engineering students, teachers, and anyone looking for additional practice and reference material.

How do complex phase-separation processes become solvable mathematical models?The Cahn–Hilliard equations lie at the heart of modern phase-field modeling—but their nonlinear, higher-order nature makes them notoriously challenging to solve.Solutions of the Cahn–Hilliard Equations explores analytical, approximate, and numerical approaches for tackling these equations, bringing together mathematical insight and practical solution techniques.A concise reference for researchers, engineers, and postgraduate students working in applied mathematics, computational science, materials modeling, and phase-field methods.Understand the equations. Explore the methods. Solve the problem.Rahul Basu

Build optimization models that remain useful when forecasts are wrong. This practical guide connects uncertainty sets, robust counterparts, duality, budgets of uncertainty, and modern distributionally robust optimization with real operational applications and implementation advice.

Statistics is the language of uncertainty. AI is the science of learning from data. Together, they provide a powerful foundation for modern intelligent systems.Applied Statistics with AI: Hypothesis Testing and Inference for Modern Models is designed for learners who want to understand how statistical methods can be applied to Artificial Intelligence, Machine Learning, Data Science, and modern research.The book begins with essential statistical foundations, including data types, sampling, preprocessing, descriptive statistics, visualization, probability, and probability distributions. It then builds toward statistical inference, covering estimation, Maximum Likelihood Estimation, Bayesian estimation, hypothesis testing, p-values, confidence intervals, Type I and Type II errors, and statistical significance.Readers will learn how classical statistical tests such as t-tests, ANOVA, and Chi-Square tests can be used in AI-related contexts, along with non-parametric methods such as Wilcoxon, Mann-Whitney, Kruskal-Wallis, and Kolmogorov-Smirnov tests.The book then connects statistics directly to Machine Learning through regression, model evaluation, cross-validation, resampling, feature selection, PCA, regularization, A/B testing, and statistical power.Advanced chapters explore Bayesian inference, MCMC, causal inference, uncertainty quantification in deep learning, and confidence estimation in AI predictions. Real-world case studies demonstrate how statistical inference can support applications in healthcare, finance, Natural Language Processing, and Computer Vision.The book also addresses an increasingly important dimension of AI: responsible statistical practice. Readers will explore bias detection, fairness, ethical hypothesis testing, and the responsible interpretation of AI research results.Finally, the book looks ahead to automated statistical inference, AI-driven hypothesis generation, and emerging research challenges.Whether you are a student learning statistics for AI, a researcher evaluating machine learning experiments, a data scientist analyzing evidence, or an AI practitioner seeking stronger statistical foundations, this book provides a structured path from fundamental concepts to modern applications.Understand the data. Test the hypothesis. Quantify uncertainty. Make better AI decisions.

What They Ask: Class-wise MCQs to Build Strong Mathematical Foundations for Class 6th and Class 7thTurn exam fear into exam confidence — one sharp question at a time."What They Ask" brings class-wise MCQ practice for Class 6 and Class 7 Math — numbers, fractions, ratios, geometry, mensuration, data handlingand more. Perfect for students, parents, and teachers preparing for exams.

For nearly a hundred years, math believed it found the edge of its own certainty. Gödel proved some truths can never be proven. Turing proved some questions can never be answered — a permanent wall built into logic.What if it's not structural? What if it's a bug?Both proofs smuggle in a self-referential sentence with no way to be rejected. A third truth-value, and the paradox stops computing.

Class-wise MCQs to Build Strong Mathematical Foundations (I – V). Importent math MCQs for primary school students from class 1 to 5 in odia script