Textbook
Oct 2025
Presents both the analytic and the synthetic viewpoints
Treats conic sections
Includes problems for practice
Part of the book series: Compact Textbooks in Mathematics (CTM)
This is an advanced undergraduate textbook on projective geometry. It provides an introduction to the basic concepts of projective geometry, using first an analytical and later an axiomatic (or synthetic) treatment, before moving on to the more advanced topic of conics. The treatment of both viewpoints, as covered by the first two chapters, aims at offering a broader view of the subject to both students and instructors. However, since the chapters can be read independently from each other, one can choose which viewpoint to focus on.
In addition to analytic geometry, the reader is expected to be familiar with linear algebra and abstract algebra, including the basic properties of groups and fields.
Conference proceedings
Nov 2025
Highlights recent developments in nonlinear, dynamical, and complex systems
Provides an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques
Written by experts in the field
Part of the book series: Springer Proceedings in Complexity (SPCOM)
This proceedings highlights recent developments in nonlinear, dynamical, and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of nonlinear dynamics, chaos, fractals, and their applications in general science and engineering sciences.
The principal aim of CHAOS2024 International Conference is to expand the development of the theories of the applied nonlinear field, the methods, empirical data, and computer techniques as well as the best theoretical achievements of chaotic theory. CHAOS2024 Conference provides a forum for bringing together the various groups working in the area of nonlinear and dynamical systems, chaotic theory, and application to exchange views and report research findings.
Book
Oct 2025
Offers a fresh look at a classical mathematical problem
Outlines Galois theory and why it does not apply to equations of degree greater than four
Presents non-well-known articles from late 19th century outlining how some quintic equations are generally solvable
This monograph explores the well-known problem of the solvability of polynomial equations.
While equations up to the fourth degree are solvable, there are, as demonstrated by Niels Henrik Abel, no general algebraic formulas leading to the solution of equations of fifth or higher degree. Nevertheless, some fifth degree (quintic) equations are indeed solvable. The author describes how Galois theory can be used to identify those quintic equations that can be solved algebraically and then shows how the solutions can be found. This involves shining a light on some little known works dating back to the late 19th century, bringing new life to a classical problem.
This book is a valuable resource for both students and researchers and it constitutes a good basis for a seminar on polynomials and the solvability of equations.
Book
Oct 2025
The state of the art in Baum-Connes, Farrell-Jones and other conjectures
Highly detailed and unified exposition, linking various parts of mathematics
An invaluable reference work by a leading expert
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 78)
This monograph is devoted to the Isomorphism Conjectures formulated by Baum and Connes, and by Farrell and Jones. These conjectures are central to the study of the topological K-theory of reduced group C*-algebras and the algebraic K- and L-theory of group rings. They have far-reaching applications in algebra, geometry, group theory, operator theory, and topology.
The book provides a detailed account of the development of these conjectures, their current status, methods of proof, and their wide-ranging implications. These conjectures are not only powerful tools for concrete computations but also play a crucial role in proving other major conjectures. Among these are the Borel Conjecture on the topological rigidity of aspherical closed manifolds, the (stable) Gromov–Lawson–Rosenberg Conjecture on the existence of Riemannian metrics with positive scalar curvature on closed Spin-manifolds, Kaplansky’s Idempotent Conjecture and the related Kadison Conjecture, the Novikov Conjecture on the homotopy invariance of higher signatures, and conjectures concerning the vanishing of the reduced projective class group and the Whitehead group of torsionfree groups.
Textbook
Sep 2025
Compiles a carefully chosen selection of algebra tests proposed to IMO teams across various countries from 1968 to 2024
Focuses on equations, inequalities, functional equations, mathematical induction, and polynomials
Ideal as a preparation tool for both aspiring students and those passionate about mathematics
Part of the book series: Problem Books in Mathematics (PBM)
This book compiles thoughtfully curated selection tests proposed to IMO (International Mathematical Olympiad) teams across many countries. Offering a blend of original solutions and adaptations by the author, this work is chronologically organized, featuring problems from 1968 to 2024, and provides a unique insight into the evolution of this mathematical contest.
The work starts with a section containing key theories and examples, serving as a quick reference guide. The main inequalities and functional equations are covered, along with topics on mathematical induction and polynomials. This is followed by the problems themselves, covering equations and systems of equations, inequalities, functional equations and inequalities, mathematical induction, and polynomials. A meticulously crafted index helps the reader navigate through the topics with ease. References are provided for further reading and self-study.
Besides serving as an invaluable preparation tool for both aspiring students and those passionate about mathematics alike, this book also complements 'Selection Tests in Number Theory for Mathematical Olympiads,' from the same author, available at Springer.
Textbook
Oct 2025
Gives a concise introduction to spectral graph theory
Introduces abstract graph theory
Provides an overview of the required methods of linear algebra
Part of the book series: Compact Textbooks in Mathematics (CTM)
This book offers an introduction to key topics in spectral graph theory. In spectral graph theory, various properties of graphs are studied using methods from linear algebra, particularly through the eigenvalues and eigenvectors of different matrices that describe the graph structure. Various aspects of graph theory find applications within the field of data science.
In this book, the necessary foundations of abstract graph theory and linear algebra are covered in parallel, making it suitable for students in their early semesters. The book has been tested multiple times in one-semester-long lectures and is therefore well-suited as a basis for a course and a collection of exercises for instructors.
Book
Nov 2025
Includes real-world applications in neural networks, control theory, medical imaging process, and stability analysis
Incorporates computational methods and software-assisted analysis using MATLAB (R) and Python (TM) where appropriate
Presents a research-oriented perspective as well as open problems, research directions, and extensive references
Part of the book series: Synthesis Lectures on Mathematics & Statistics (SLMS)
This book demonstrates the significance, applicability, and widespread nature of fixed point theorems in contexts outside of mathematics, including engineering, computer science, economics, and biological sciences. In the real world, fixed point theory is used to solve problems where stability, balance, or repeated processes are involved, such as predicting economic equilibrium, optimizing traffic flow, ensuring robots move precisely, or stabilizing medical devices like pacemakers. It is also used in artificial intelligence, engineering systems, and biological modeling where stable solutions in complex systems are needed. The authors not only highlight modern hurdles, but also explore how the field has accommodated and grown in response to them. The book provides comprehensive coverage of both the classical underpinnings and the cutting-edge advancements in fixed point theory. Each concept is illustrated with well-crafted, original examples that are carefully chosen to demonstrate both theoretical depth and practical significance. The chapters conclude with open problems and future research directions, encouraging further exploration. This book is designed to serve as both a guide for those entering the field as well as a resource for seasoned researchers looking to deepen their understanding of its modern applications.
Book
Oct 2025
Includes characterizations of difference equations and technical prospectives of discrete-time systems
Provides new insights into the dynamical behaviors of some of the most popular neural networks used in machine learning
Discusses novel technical analyses of discrete-time dynamical systems modeled as difference equations
Part of the book series: Synthesis Lectures on Mathematics & Statistics (SLMS)
This book presents in-depth explanations of well-known and recognized behaviors of neural networks in machine learning. In addition, the author provides novel technical analyses of behaviors of discrete-time dynamical systems modeled as difference equations. These analyses and their outcomes are closely related to models of very well-known neural networks such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) neural networks, which are widely used in machine learning and artificial intelligence (AI) applications. The author also discusses difference equations and their relevance to neural networks, machine learning, and AI.