Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

Books Journals

An Introduction to Stochastic Modeling

5th Edition
January 2, 2026
Gabriel Lord + 1 more
English

An Introduction to Stochastic Modeling, Fifth Edition bridges the gap between basic probability and an intermediate level course in stochastic processes, serving as the foundation for either a one-semester or two-semester course in stochastic processes for students familiar with elementary probability theory and calculus. The objectives are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide an integrated treatment of theory, applications and practical implementation. A well-regarded resource for many years, the text is an ideal foundation for a broad range of students.

Introduction to Mathematics in Physiology, Medicine, and Health Sciences

1st Edition
January 1, 2026
Dhanjoo N. Ghista + 3 more
English

Introduction to Mathematics in Physiology, Medicine, and Health Sciences provides a quantitative handbook for physiology and biological systems, so researchers, practitioners, and clinicians can have a quantitative foundation, and medicine can incorporate more precise diagnostics. This book’s purpose is to demonstrate how fundamental mathematics can be incorporated into biomedical engineering, physiology, medicine, and health sciences research, application, and clinical practice to make these disciplines more quantitative and computational, and hence more explanatory and informative. The book also provides more quantitative formulation of medical procedures, towards supporting the growing field of precision medicine. The book guides readers though the foundations of mathematics as it is applied to modeling of physiological systems, medicine, biology, and health sciences. Each chapter includes a robust introduction to the mathematical concepts and principles necessary to understand their application to the indicated medical and biological systems, beginning with the fundamental relationships among biological variables in Chapter 2, introduction to basic calculus and rate of change in biomedical variables in Chapter 3, and the principles of linear algebra and vectors applied to medicine in Chapter 4. Chapters 5-7 cover the fundamentals of exponential and logarithmic biomedical functions, maximum and minimum values of a function, and integration applications such as summation, area, and volume. Chapter 8 provides an in-depth look into biomedical applications of Ordinary and Partial Differential Equations, which are important modeling tools for flow and variable systems. Chapter 9 provides extensive coverage of Organ System Analyses, which is the core of the physiological system modeling in the book, with a wide range of applied examples. Chapters 10 and 11 extend the modeling applications to medical devices and signal processing. Each chapter provides in-depth guidance on the mathematical concepts, methodology, and procedures for applying the mathematical formulas and equations to the appropriate biomedical and physiological systems, as well as step-by-step procedures for creating models for a wealth of specific applications.

Functional Analysis: Theory and Applications

1st Edition
January 1, 2026
Ravi P. Agarwal + 2 more
English

An applied understanding of functional analysis is essential for students pursuing research or careers in pure mathematics, applied mathematics, mathematical physics, and engineering, among other disciplines.Function... Analysis: Theory and Applications offers a comprehensive exploration of functional analysis. Authored by esteemed mathematicians with extensive expertise in the field, this book thoroughly introduces fundamental concepts in functional analysis, including Banach spaces, Hilbert spaces, operator theory, nonlinear analysis, linear operators, and normed spaces, and implements these in real-world problems across various scientific and engineering disciplines.The book's rigorous mathematical treatment is combined with worked examples, exercises and solutions, visual aids, application case studies, and future directions across all chapters to reinforce learning, while appendices offer supplementary materials, proofs of theorems, and tables of important results, among other resources.

Graph Theory

1st Edition
January 1, 2026
Sovan Samanta
English
eBook
9 7 8 0 4 4 3 3 3 9 4 2 4

Graph theory is a rapidly evolving and expanding mathematical discipline, with new discoveries, challenges, and techniques emerging every year. Graph Theory: Fundamentals and Applications provides a fully up-to-date and accessible introduction to graph theory, covering both the classical and the modern topics, as well as algorithms and evolving challenges addressed by discipline. Based on the latest syllabi and research trends worldwide, this book includes practical, solved problems that are user friendly to undergraduate, postgraduate, and PhD students, and acts as a key aid in learning the fundamentals and the frontiers of graph theory, as well as developing independent problem-solving and critical thinking skills. This book includes clear instruction in graph representation, basic graph operations, graph connectivity, trees and forests, matching theory, planar graphs and graph drawing, algebraic graph theory, graph traversals, network flows, topological graph theory, and cryptography, among other topics. Each chapter features key term definitions, proofs and algorithms, summary points, and unique exercises to reinforce learning, as well as open problems and research challenges that present unsolved or conjectural problems in graph theory for discussion. Supporting student and instructor sites offer additional exercises, solutions, examples, and case studies in graph theory applications.

An Introduction to Point-Set Topology

1st Edition
January 1, 2026
Shelby Kilmer
English

An Introduction to Point-Set Topology is intended for use in a beginning topology course for undergraduates or as an elective course for graduate students. The book’s style can be thought of as a hybrid between the Texas style (Moore method) of teaching topology and the more traditional styles. In the Texas style the students are given the definitions and the statements of the theorems and then they present their proofs to the class. This type of participation builds students’ confidence and provides them with a deeper understanding of the subject that they will retain longer. This text offers some of the theorems with their proofs and leaves others for the students to prove and present. Those theorems chosen to have their proofs presented in the text keep the course moving forward under the instructors’ guidance and increase student comprehension. An Introduction to Point-Set Topology covers a broad range of topological concepts, including but not limited to, metric spaces, topological spaces, homeomorphisms, connected sets, compact sets, product spaces, Hausdorff spaces, sequences, limits, weak topologies, the axiom of choice, Zorn’s lemma, and Nets. Incorporating both historical references and color graphics, the material keeps readers engaged. The book’s goals include increasing student participation, thus promoting a deeper knowledge through an intuitive understanding of how and why topology was developed in the way that it was. This “instructor-friendly... accessible text is also accompanied by a detailed solutions manual to support both experienced topologists and other mathematicians who would like to teach topology.

Handbook of MRI Pulse Sequences

2nd Edition
December 1, 2025
Xiaohong Joe Zhou + 4 more
English
Hardback
9 7 8 0 3 2 3 9 1 5 9 7 7
eBook
9 7 8 0 3 2 3 9 1 5 9 8 4

Handbook of MRI Pulse Sequences, Second Edition includes 92 self-contained sections, with each section focusing on a single subject. A new section on detailing the advanced pulse sequence techniques covers a variety of basic and advanced image reconstruction methods. The extensive topic coverage and cross-referencing makes this book ideal for beginners learning the building blocks of MRI pulse sequence design, as well as for experienced professionals who are seeking deeper knowledge of a particular technique.This book is among the most important medical imaging techniques available today. Each of these scanners is capable of running many different "pulse sequences." These sequences are governed by physics and engineering principles and implemented by software programs that control the MRI hardware.

Synthetic Media, Deepfakes, and Cyber Deception

1st Edition
October 1, 2025
Cameron H. Malin + 2 more
English
Paperback
9 7 8 0 4 4 3 2 3 8 8 7 1
eBook
9 7 8 0 4 4 3 2 3 8 8 8 8

Synthetic Media, Deepfakes, and Cyber Deception: Attacks, Analysis, and Defenses introduces the only analytical Synthetic Media Analysis Framework (SMAF) to help describe cyber threats and help security professionals anticipate and analyze attacks. This framework encompasses seven dimensions: Credibility, Control, Medium, Interactivity, Familiarity, Intended Target, and Evocation. Synthetic media is a broad term that encompasses the artificial manipulation, modification, and production of information, covering a spectrum from audio-video deepfakes to text-based chatbots. Synthetic media provides cyber attackers and scammers with a game-changing advantage over traditional ROSE attacks because they have the potential to convincingly impersonate close associates through text, imagery, voice, and video.This burgeoning threat has yet to be meaningfully addressed through any written treatment on the topic. The book is co-authored by three cyber influence and deception experts who have gained deep knowledge and experience on the topic through diverse, true operational pathways and backgrounds. The diversity and perspectives of the author team makes the content in the book the broadest and deepest treatment of synthetic media attacks available to readers.

Machine Learning Solutions for Inverse Problems: Part A

1st Edition
Volume 26
October 1, 2025
Andreas Hauptmann + 3 more
English

Machine Learning Solutions for Inverse Problems: Part A, Volume 26 in the Handbook of Numerical Analysis, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Data-Driven Approaches for Generalized Lasso Problems, Implicit Regularization of the Deep Inverse Prior via (Inertial) Gradient Flow, Generalized Hardness of Approximation, Hallucinations, and Trustworthiness in Machine Learning for Inverse Problems, Energy-Based Models for Inverse Imaging Problems, Regularization Theory of Stochastic Iterative Methods for Solving Inverse Problems, and more.Other sections cover Advances in Identifying Differential Equations from Noisy Data Observations, The Complete Electrode Model for Electrical Impedance Tomography: A Comparative Study of Deep Learning and Analytical Methods, Learned Iterative Schemes: Neural Network Architectures for Operator Learning, Jacobian-Free Backpropagation for Unfolded Schemes with Convergence Guarantees, and Operator Learning Meets Inverse Problems: A Probabilistic Perspective

Recent Developments in Theory and Applications of Fractional Order Systems

1st Edition
September 1, 2025
Mehmet Yavuz + 2 more
English
Paperback
9 7 8 0 4 4 3 2 3 9 5 2 6
eBook
9 7 8 0 4 4 3 2 3 9 5 3 3

Recent Developments in Theory and Applications of Fractional Order Systems presents a rigorous and thorough analysis of various aspects of Fractional Calculus. The book provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines. The authors present each computational modeling concept with a definition, methods, theorems, and observations followed by typical application problems and step-by-step solutions. Each topic is covered in detail, followed typically by several meticulously worked out examples and a problem set containing many additional related problems.In addition, the book discusses recent developments and the latest research on Fractional Calculus and its applications, demonstrating important applications in Engineering, Computer Science, Management, Social Science, and the Humanities.

Statistics in Industry and Government

1st Edition
Volume 53
September 1, 2025
Ravindra Khattree + 2 more
English
Hardback
9 7 8 0 4 4 3 3 1 4 2 2 3
eBook
9 7 8 0 4 4 3 3 1 4 2 3 0

Statistics plays a central role in industrial quality control and high-class quality maintenance in products. Statistical designs and data collection are central also in government planning and program implementation. These two important aspects of statistical theory and applications will be of focus of this volume. We aim to cover as many applications that use statistics as an underlying tool in bringing the best quality products and industrial designs. Indian Statistical Institute played an important role in developing quality control measures during the 1940s-70s due to C.R. Rao and those methods helped to train several statistical industries and engineers across the world, for example, Genichi Taguchi of Japan, etc who revolutionized industrial quality in Japan. There are several such examples.

Related subjects

Mathematics and applied mathematics

Statistics and probability

Life Sciences

Physical Sciences & Engineering

Social Sciences & Humanities

Health