Copyright 2025
Paperback
ISBN 9781032596518
294 Pages 229 B/W Illustrations
Published December 2, 2024 by A K Peters/CRC Press
The Four Corners of Mathematics: A Brief History, from Pythagoras to Perelman describes the historical development of the ebig ideasf in mathematics in an accessible and intuitive manner. In delivering this bird's-eye view of the history of mathematics, the author uses engaging diagrams and images to communicate complex concepts while also exploring the details of the main results and methods of high-level mathematics. As such, this book involves some equations and terminology, but the only assumption on the readersf knowledge is A-level or high school mathematics.
Divided into four parts, covering Geometry, Algebra, Calculus and Topology
Presents high-level mathematics in a visual and accessible way with numerous examples and over 250 illustrations
Includes several novel and intuitive proofs of big theorems, so even the nonexpert reader can appreciate them
Sketches of the lives of important contributors, with an emphasis on often overlooked female mathematicians and those who had to struggle.
Part I Geometry. 1. The Beginnings. 2. Non-Euclidean Geometry. 3. Curves,
surfaces, manifolds. 4. Fractal Geometry. Part II. Algebra. 5. The Beginnings.
6. Complex Numbers. 7. Abstract Algebra. 8. Linear Algebra. Part III. Calculus.
9. The Beginnings. 10. The Solar System. 11. Maxima and Minima. 12. PDEfs.
Part IV. Topology. 13. The Beginnings. 14. Degree. 15. Homology. 16. Classification.
Copyright 2025
Paperback
480 Pages 197 B/W Illustrations
March 7, 2025 by Chapman & Hall
Hardback
ISBN 9781032965529
Discrete Mathematics: An Open Introduction, Fourth Edition aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math and computer science majors, especially those who intend to teach middle and high school mathematics. The book began as a set of notes for the Discrete Mathematics course at the University of Northern Colorado. This course serves both as a survey of the topics in discrete math and as the gbridgeh course for math majors.
Uses problem-oriented and inquiry-based methods to teach the concepts.
Suitable for undergraduates in mathematics and computer science.
Large scale restructuring.
Contains more than 750 exercises and examples.
New sections on probability, relations, and discrete structures and their proofs.
0. Introduction and Preliminaries. 0.1. What is Discrete Mathematics?. 0.2. Discrete Structures. 1. Logic and Proofs. 1.1. Mathematical Statements. 1.2. Implications. 1.3. Rules of Logic. 1.4. Proofs. 1.5. Proofs about Discrete Structures. 1.6. Chapter Summary. 2. Graph Theory. 2.1. Problems and Definitions. 2.2. Trees. 2.3. Planar Graphs. 2.4. Euler Trails and Circuits. 2.5. Coloring. 2.6. Relations and Graphs. 2.7. Matching in Bipartite Graphs. 2.8. Chapter Summary. 3. Counting. 3.1. Pascalfs Arithmetical Triangle. 3.2. Combining Outcomes. 3.3. Non-Disjoint Outcomes. 3.4. Combinations and Permutations. 3.5. Counting Multisets. 3.6. Combinatorial Proofs. 3.7. Applications to Probability. 3.8. Advanced Counting Using PIE. 3.9. Chapter Summary. 4. Sequences. 4.1. Describing Sequences. 4.2. Rate of Growth. 4.3. Polynomial Sequences. 4.4. Exponential Sequences. 4.5. Proof by Induction. 4.6. Strong Induction. 4.7. Chapter Summary. 5. Discrete Structures Revisited. 5.1. Sets. 5.2. Functions. 6. Additional Topics. 6.1. Generating Functions. 6.2. Introduction to Number Theory.
Softcover ISBN: 978-1-4704-7215-3
Product Code: CONM/811
Expected availability date: March 20, 2025
Contemporary Mathematics, Volume: 811
2025; Estimated: 287 pp
MSC: Primary 51; 53; 22; 20; 05
This volume contains the proceedings of the International Conference on Geometry, Groups and Mathematical Philosophy, held in honor of Ravindra S. Kulkarni's 80th birthday.
Talks at the conference touched all the areas that intrigued Ravi Kulkarni over the years. Accordingly, the conference was divided into three parts: differential geometry, symmetries arising in geometric and general mathematics, mathematical philosophy and Indian mathematics.
The volume also includes an expanded version of Kulkarni's lecture and a brief autobiography.
Ravindra S. Kulkarni ? My pursuit of truth through mathematics
Ravindra S. Kulkarni ? Philosophy of mathematics ? four issues
Ara Basmajian and Robert Suzzi Valli ? Counting cusp excursions of reciprocal geodesics
W. Barrera, A. Cano, J. P. Navarrete and J. Seade ? Elementary groups in PSL(3,C)
Po-Ning Chen, Mu-Tao Wang, Ye-Kai Wang and Shing-Tung Yau ? Quasilocal mass and angular momentum
S. G. Dani ? Geodesics on the modular surface and continued fraction expansions of their endpoints
Allan L. Edmonds ? Finite group actions on 1-complexes and homology
William M. Goldman ? Affine structures on surfaces and the twisted cubic cone
Kriti Goel, Vivek Mukundan, Sudeshna Roy and J. K. Verma ? Computing mixed multiplicities, mixed volumes and sectional Milnor numbers
Parul Gupta, Yashpreet Kaur and Anupam Singh ? Differential central simple algebras
Vikas S. Jadhav ? z
-Classes and rational conjugacy classes
A. D. Mednykh, I. A. Mednykh and I. N. Yudin ? On Jacobian group and complexity of the ¢
-graph
Rohit Parikh ? Groups, communication and coordination
Nitin Nitsure ? Curvature and torsion via quadrilateral gaps
Soham Swadhin Pradhan ? Schur index and extensions of Witt-Bermanfs theorems
M. A. Sofi ? Nonlinear retracts and the geometry of Banach spaces
Jagmohan Tanti ? Computations for invariant bilinear forms under an invertible linear transformation: an expository article
Bankteshwar Tiwari ? A comparative overview of Riemannian and Finsler geometry
Devendra Tiwari and Harshavardhan Reddy ? Revisiting Kulkarnifs topological proof of Millingtonfs theorem
Mukut Mani Tripathi ? Kulkarni-Nomizu tensor fields
Graduate students and research mathematicians interested in relations between geometry and groups.
Softcover ISBN: 978-1-4704-7534-5
Product Code: CONM/812
Expected availability date: March 16, 2025
Contemporary Mathematics, Volume: 812
2025; 341 pp
MSC: Primary 20
This volume contains the proceedings of the AMS Special Session on Ends and Boundaries of Groups, held in honor of Michael Mihalik's 70th birthday, on April 15?16, 2023, at the University of Cincinnati, Cincinnati, Ohio.
The papers cover current topics in geometric group theory and related topology. Four survey papers discuss hyperbolic actions, CAT(0) groups, Thompson-type groups and Z
-set boundaries. Other papers cover new material related to hyperbolic groups, Poincare Duality groups, outer automorphism groups, right angled Artin groups, and mapping class groups. Several papers present new results on ends of spaces and related group theory. A notable addition, intended for readers interested in the interplay of topology and group theory, is a self-contained detailed exposition of Z
-sets and their role in geometric group theory.
Yael Algom-Kfir and Mladen Bestvina ? Groups of proper homotopy equivalences of graphs and Nielsen Realization
Fredric D. Ancel ? Z-sets in ANRs
Liam Axon and Jack Calcut ? The End Sum of Surfaces
Sahana H. Balasubramanya ? A survey on classifying hyperbolic actions of groups
Martin R. Bridson, Dawid Kielak and Monika Kudlinska ? Stallingsfs Fibring Theorem and PD3
-pairs
Noah Caplinger and Dan Margalit ? Totally Symmetric Sets
M. Cardenas, F. F. Lasheras and A. Quintero ? Proper 2
-equivalences and amalgams over virtually free groups
Alexander Dranishnikov and Satyanath Howladar ? On Gromovfs conjecture for right-angled Artin groups
Jerzy Dydak, Yuankui Ma and Hussain Rashed ? Ends of large scale groups
Daniel S. Farley ? The expansion set construction of classifying spaces for generalized Thompson groups
Talia Fernos ? Le Conte de la Mesure sur les Complexes Cubiques CAT(0)
Craig R. Guilbault and Daniel Gulbrandsen ? A generalized theory of expansions and collapses with applications to Z
-compactification
G. Christopher Hruska and Kim Ruane ? Hyperbolic groups and local connectivity
Nir Lazarovich and Emily Stark ? Failure of quasi-isometric rigidity for infinite-ended groups
Rylee Alanza Lyman ? One-endedness of outer automorphism groups of free products of finite and cyclic groups
Molly A. Moran ? A brief survey of Z
-boundaries
Graduate students and research mathematicians interested in topology and infinite groups.
1st Edition - May 1, 2025
Language: English
Paperback ISBN: 9780443301346
9 7 8 - 0 - 4 4 3 - 3 0 1 3 4 - 6
Integral Manifolds for Impulsive Differential Problems with Applications offers readers a comprehensive resource on integral manifolds for different classes of differential equations which will be of prime importance to researchers in applied mathematics, engineering, and physics. The book offers a highly application-oriented approach, reviewing the qualitative properties of integral manifolds which have significant practical applications in emerging areas such as optimal control, biology, mechanics, medicine, biotechnologies, electronics, and economics. For applied scientists, this will be an important introduction to the qualitative theory of impulsive and fractional equations which will be key in their initial steps towards adopting results and methods in their
1: Basic Theory
2: Integral Manifolds and Impulsive Differential Equations
2.1. Integral Manifolds and Impulsive Differential Equations
2.1.1. Integral Manifolds and Perturbations of the Linear Part of Impulsive Differential Equations
2.1.2. Integral Manifolds and Singularly Perturbed Impulsive Differential Equations
2.2. Affinity Integral Manifolds for Linear Singularly Perturbed Systems of Impulsive Differential Equations
2.3. Integral Manifolds of Impulsive Differential Equations Defined on Torus
3. Impulsive Differential Systems and Stability of Manifolds
3.1. Stability of Integral Manifolds
3.1.1. Integral Manifolds and Principle of the Reduction for Impulsive Differential Equations
3.1.2 Integral Manifolds and Principle of the Reduction for Singularly Impulsive Differential Equations
3.1.3. Integral Manifolds and Boundedness of the Solutions of Impulsive Functional Differential Equations
3.1.4. Integral Manifolds and Asymptotic Stability of Sets for Impulsive Functional Differential Equations
3.2. Stability of Moving Integral Manifolds
3.2.1. Stability of Moving Integral Manifolds for Impulsive Differential Equations
3.2.2. Stability of Moving Conditionally Integral Manifolds for Impulsive Differential Equations
3.2.3. Stability of Moving Integral Manifolds for Impulsive Integro-Differential Equations
3.2.4. Stability of Moving Integral Manifolds for Impulsive Differential-Difference Equations
3.3. Stability of H-Manifolds
3.3.1. Practical Stability with Respect to h-Manifolds for Impulsive Functional Differential Equations with Variable Impulsive Perturbations
3.3.2 Impulsive Control Functional Differential Systems of Fractional Order: Stability with Respect to h-Manifolds
4. Applications
4.1. Integral Manifolds and Impulsive Neural Networks
4.1.1. Integral Manifolds and Impulsive Neural Networks with Time-varying Delays
4.1.2. Stability with Respect to H-manifolds of Cohen-Grossberg Neural Networks with Time-varying Delay and Variable Impulsive Perturbations
4.2. Integral Manifolds and Mathematical Models in Biology
4.2.1. Integral Manifolds and Kolmogorov Systems of Fractional Impulsive Differential Equations
4.2.2. Impulsive Lasota-Wazewska Equations of Fractional Order with Time-varying Delays: Integral Manifolds
4.3. Solow-type Models and Stability with respect to Manifolds
4.4 Reaction-Diffusion Impulsive Neural Networks and Stability with Respect to Manifolds
4.4.1. Stability of Sets Criteria for Impulsive Cohen ?Grossberg Delayed Neural Networks with Reaction ?Diffusion Terms
4.4.2. Global Stability of Integral Manifolds for Reaction ?Diffusion Cohen?Grossberg-type Delayed Neural Networks with Variable Impulsive Perturbations
4.4.3. Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach
4.4.4. h-Manifolds Stability for Impulsive Delayed SIR Epidemic Model
4.4.5 Impulsive Control of Reaction-Diffusion Impulsive Fractional Order Neural Networks with Time-varying Delays and Stability with Respect to Integral Manifolds
4.4.6. Reaction-Diffusion Impulsive Fractional-order Bidirectional Neural Networks with Distributed Delays: Mittag-Leffler Stability along Manifolds