Copyright 2024
Hardback
ISBN 9781032453835
ISBN 9781032453842
130 Pages 100 Color & 229 B/W Illustrations
November 9, 2023 by A K Peters/CRC Press
Design Techniques for Origami Tessellations is both a collection of origami tessellations and a manual to design them.
This book begins by explaining general design methods, the history and definitions of origami tessellations, and the geometric features of flat origami, before moving on to introduce a brand-new design method: the "twist-based design method." This method generates base parts that connect "twist patterns” (that can be folded with a twist) without using a lattice. Therefore, it can generate base parts such as regular pentagons, which cannot be generated with more conventional methods, and can generate new origami tessellations connected to them.
No proofs or formulas in the text and minimal jargon.
Suitable for readers with a roughly middle school to high school level of mathematical background.
Web application implementing the method described in this book is available, allowing the readers to design their own patterns.
0. Origami and Traditional Tessellation Patterns. 0.1. Background of Origami Tessellations. 0.2 Crease Patterns. 0.3 Basic Geometry of Flat-Foldable Crease Patterns. 0.4 Folded State of Crease Patterns. 0.5 Patterns for Twist-Folding. 0.6 Tessellations. 0.7. Tips for Making Beautiful Folds. 1.Folding on Square Grid. 1.1. Square Twist-Patterns. 1.2. Isosceles Right Triangle Twist Pattern. 1.3. Checker Base. 1.4. Changing folded shape. 1.5. Crease patterns as connectable tile. Appendix 1: Pixel Arts Composed of Origami Tessellation. 2. Folding on Equilateral Triangle Grid. 2.1. Equilateral Triangle Twist-Patterns. 2.2. Regular Hexagon Twist-Patterns. 2.3. Right Triangle Twist-Patterns. Column 1: Grid and Twist Pattern. 3. Connecting Triangle Twist Patterns. 3.1. Creating Triangle Twist Patterns. 3.2. Connecting Triangle Twist Patterns. 3.3. Design for Regular Polygon Patterns. Column 02: How to use Triangle Twist Pattern Maker. Appendix 2: Changing Length of Pleat Base. 4.Connecting of Different Base Parts. 4.1. Connectable Side of Boundary. 4.2. Regular Tessellations. 4.3. Tessellation with Equilateral Polygons. 4.4. Combining Crease Patterns Having Different Guide Sides. Appendix 3: Condition that Boundaries are Folded into Similar Shape. 5. Generating Aesthetic Origami Tessellations. 5.1. Origami Tessellations Regarding as Positive-Negative Pattern. 5.2. Parallel Moving Faces by Flat Folding. 5.3. Design for Origami Tessellations Regarding as Positive-Negative Pattern. Appendix 4: Deformation of crease pattern using pleat bases. 6. Folding Bellows. 6.1. Folding Parallel Lines. 6.2. Bent Bellows. 6.3. Periodic Bellows. 6.4. Bending Irregular Bellows. Column 03: Origami Tessellation Design Software “Tess”. 7. Application of Twist Pattern Design Method. 7.1. Reconstructing Guide from Given Origami Tessellation. 7.2. Fractal Origami Tessellations and Guides. 7.3. Guide with Gaps. Column 4: Connecting 3D Origami Arts and Origami Tessellations.
Softcover ISBN: 978-1-4704-7176-7
Product Code: MBK/150
Aspiring and Inspiring is a collection of essays from successful women and gender minority mathematicians on what it takes to build a career in mathematics. The individual essays are intended to advise, encourage, and inspire mathematicians throughout different stages of their careers. Themes emerge as these prominent individuals describe how they managed to persist and rise to positions of leadership in a field which can still be forbidding to many. We read, repeatedly, that individual mentorship matters, that networks of support can be critical, and that finding fulfillment can mean formulating one's own definition of success. Those who aspire to leadership in the field will find much useful advice here.
The cumulative power of the collection carries a strong impact. The glass
ceiling is very real in mathematics and is the result of cultural and sociological
factors at work in our community. The book makes clear that we won't achieve
equality of opportunity merely by exhorting those who are often excluded
to change their behaviors and their goals. The need for systemic cultural
change is vividly, at times painfully, evident in these stories. As Dr.
Erica Graham says in her powerful and moving essay, we need “a different
kind of academy”, and we'll only get it by working for it. We can start
by reading this book and recognizing the kind of academy we currently have
Graduate students and researchers interested in professional advancement.
Preface
Chapter 1. A path to success: Enabled by guardians, connectors and taking adventurous steps (Jacqueline M. Dewar)
Chapter 2. Trust yourself! (Alicia Dickenstein)
Chapter 3. The fight within (Maria Emelianenko)
Chapter 4. Intersectionality as impetus and impediment (Erica J. Graham)
Chapter 5. Find your passion, get organized & cultivate support systems (Allison Henrich)
Chapter 6. Tenure: The rules of the game (Rhonda J. Hughes)
Chapter 7. Make yourself valuable (Jacqueline Jensen-Vallin)
Chapter 8. It’s a wonderful life! - Reflections on the career of a mathematician (Luise-Charlotte Kappe)
Chapter 9. Success is a relative term (Kathryn Leonard)
Chapter 10. Multifaceting: Shattering your own glass ceiling (Perla Myers)
Chapter 11. Positioning yourself to crack the glass ceiling (Catherine A. Roberts)
Chapter 12. I am not your typical role model (or do not follow my steps) (Ivelisse M. Rubio)
Chapter 13. How I became a department head (Irena Swanson)
Chapter 14. Around the glass ceiling (Karen Uhlenbeck)
Chapter 15. The professional advancement of women mathematicians (Shanise Walker)
Chapter 16. Branch cuts: Writing, editing, and ramified complexities (Ursula Whitcher)
Chapter 17. Reach as you climb: Searching for purpose and meaning in academia (Cynthia Wyels)
Credits
Softcover ISBN: 978-1-4704-7147-7
Product Code: CONM/788
Contemporary Mathematics, Volume: 788; 2023; 237 pp
MSC: Primary 32; 35; 37; 47; 53; 58; 76; 82; 83;
This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13?17, 2021, at the Independent University of Moscow and Moscow State University, Moscow, Russia.
The papers are devoted to various interrelations of nonlinear PDEs with geometry and integrable systems. The topics discussed are: gravitational and electromagnetic fields in General Relativity, nonlocal geometry of PDEs, Legendre foliated cocycles on contact manifolds, presymplectic gauge PDEs and Lagrangian BV formalism, jet geometry and high-order phase transitions, bi-Hamiltonian structures of KdV type, bundles of Weyl structures, Lax representations via twisted extensions of Lie algebras, energy functionals and normal forms of knots, and differential invariants of inviscid flows.
The companion volume (Contemporary Mathematics, Volume 789) is devoted
to Algebraic and Cohomological Aspects of PDEs
Graduate students and research mathematicians interested in modern theory of partial differential equation and its relations with differential geometry, integrable systems, fluid mechanics, and field theory.
Fatemeh Ahangari - Geometric analysis of metric Legendre foliated cocycles on contact manifolds via SODE structure
Dmitri V. Alekseevsky, Alessio Marrani and Andrea Spiro - Special Vinberg cones, invariant admissible cubics and special real manifolds
Andreas ?ap and Jan Slovak - Bundles of Weyl structures and invariant calculus for parabolic geometries
Vladimir N. Chetverikov - Coverings and pseudosymmetries of differential equations
Anna Duyunova - Differential invariants of inviscid flows in pipes
Maxim Grigoriev - Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles
G. F. Helminck and E. A. Panasenko - Minimal realizations of the KP hierarchy, its strict version and their reductions
Josef Jany?ka and Marco Modugno - Minimal coupling of gravitational and electromagnetic fields in General Relativity
Paolo Lorenzoni and Raffaele Vitolo - Projective-geometric aspects of bi-Hamiltonian structures of KdV type
Valentin V. Lychagin - Measurement of random operators, jet geometry and high-order phase transitions
Gianni Manno, Jan Schumm and Andreas Vollmer - Metrics admitting projective and c-projective vector fields
Oleg I. Morozov - Lax representations via twisted extensions of infinite-dimensional Lie algebras: some new results
A. B. Sossinsky - Energy functionals and normal forms of knots and plane curves
*
Softcover ISBN: 978-1-4704-7051-7
Product Code: MBK/149
2023; 241 pp
MSC: Primary 00; 01; 03; 11; 53; 62; 68; 76; 81; 97;
This book is a collection of essays written by a distinguished mathematician with a very long and successful career as a researcher and educator working in many areas of pure and applied mathematics. The author writes about everything he found exciting about math, its history, and its connections with art, and about how to explain it when so many smart people (and children) are turned off by it. The three longest essays touch upon the foundations of mathematics, upon quantum mechanics and Schrodinger's cat phenomena, and upon whether robots will ever have consciousness. Each of these essays includes some unpublished material. The author also touches upon his involvement with and feelings about issues in the larger world. The author's main goal when preparing the book was to convey how much he loves math and its sister fields.
Undergraduate students interested in mathematics in science and society.
The Math Behind the Cover
Preface: Confessions of a Polymath
Part 1. Opening More Eyes to Mathematics
Chapter 1. How to Get Middle School Students to Love Formulas & Triangles
i. Algebra
ii. Geometry
Chapter 2. Explaining Grothendieck to Non-mathematicians
i. Nature magazine vs. rings & schemes
ii. A geologist vs. ??? & topoi
Chapter 3. Are Mathematical Formulas Beautiful?
i. Equations as art
ii. Equations reflected in MRI scans and mathematical tribes
Part 2. The History of Mathematics
Chapter 4. Pythagoras’s Rule
i. Its discovery
ii. How did it spread and was it rediscovered?
Chapter 5. The Checkered History of Algebra
i. Babylon
ii. Greece
iii. China
iv. India
v. Early modern Europe
vi. Today
Chapter 6. Multi-cultural Math History in Five Slides
Chapter 7. “Modern” Art/“Modern” Math and the Zeitgeist
i. Beauty and power through randomness
ii. When did abstract, non-figurative art & math start?
iii. Brave new worlds
iv. Full-blown abstraction
Interlude: Intelligent Design in Orion?
Part 3. AI, Neuroscience, and Consciousness
Chapter 8. Parse Trees Are Ubiquitous in Thinking
i. Language
ii. Vision
iii. Actions and plans
iv. The big picture
Chapter 9. Linking Deep Learning and Cortical Functions
i. Neural nets
ii. Tokens vs. distributed data
iii. Transformers and context
iv. Context in the brain
v. What is missing?
Chapter 10. Does/Can Human Consciousness Exist in Animals and Robots?
i. What do neuroscientists say about consciousness?
ii. Consciousness in animals
iii. We need emotions #$@*&!
iv. What do physicists say about consciousness?
v. The philosopher and the sage
Part 4. And Now, Some Bits of Real Math
Chapter 11. Finding the Rhythms of the Primes
Chapter 12. Spaces of Shapes and Rogue Waves
i. Nonlinear gravity waves
ii. Shape spaces
iii. Zakharov’s Hamiltonian
Chapter 13. An Applied Mathematician’s Foundations of Math
i. A warm-up: Arithmetic
ii. Being conservative with second-order arithmetic
iii. The standard foundation: ZFC
iv. The applied perspective
Part 5. Coming to Terms with the Quantum
Chapter 14. Quantum Theory and the Mysterious Collapse
i. Background: Measurements and ‘Copenhagen’
ii. AMU sets
iii. Constraints on macroscopic variables
iv. Molecules
v. Fields
vi. DNA
vii. Bohr bubbles and speculations
Chapter 15. Path Integrals and Quantum Computing
Part 6. Nothing Is Simple in the Real World
Chapter 16. Wake Up!
i. Springer and Klaus Peters
ii. The impact of the internet
Chapter 17. One World or Many?
i. My own experiences
ii. Russia and Shafarevich
iii. India and castes
Chapter 18. Spinoza: Euclid, Ethics, Time
i. Spinoza and substances
ii. A short history of dualism and substances
iii. Spinoza’s Ethics
iv. Relations to various religions and to modern science
Chapter 19. Thoughts on the Future
i. The population explosion
ii. The consequences of this explosion
iii. A safety valve?
iv. Love those robots
v. Playing God with the genome
vi. Unknowns
Figure Credits
Author’s Bibliography
Bibliography
Softcover ISBN: 978-1-4704-7355-6
Product Code: CONM/789
Contemporary Mathematics Volume: 789;
2023; 223 pp
MSC: Primary 13; 14; 34; 35; 46; 53; 55; 58; 68; 81;
This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13?17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia.
The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frolicher structures in the formal Kadomtsev?Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras.
The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.
Graduate students and research mathematicians interested in the modern theory of partial differential equation in the wide context of commutative and noncommutative algebra and cohomology theories.
Luca Amata and Francesco Oliveri - Automatic determination of optimal systems of Lie subalgebras: The package SymboLie
Orest D. Artemovych, Denis L. Blackmore, Rados?aw A. Kycia and Anatolij K. Prykarpatski - New Dubrovin-type integrability theory applications of differential rings
I. A. Bobrova and V. V. Sokolov - Non-abelian Painleve systems with generalized Okamoto integral
Alexei Bocharov - Mathematical etudes on quantum computation
Dimitry Gurevich and Pavel Saponov - Quantum vector fields via quantum doubles and their applications
Hovhannes M. Khudaverdian - Non-linear homomorphisms of algebras of functions are induced by thick morphisms
H. M. Khudaverdian and Th. Th. Voronov - On the Buchstaber?Rees theory of “Frobenius n
-homomorphisms” and its generalization
Jacob Kryczka - Differential calculus over graded commutative algebras and vector bundles with inner structures
Fabrizio Pugliese, Giovanni Sparano and Luca Vitagliano - Vinogradov’s cohomological geometry of partial differential equations
Jean-Pierre Magnot, Enrique G. Reyes and Vladimir Rubtsov - Frolicher structures, diffieties, and a formal KP hierarchy
G. Sharygin - Quasi-derivations on Ugln
and the argument shift method
Piergiulio Tempesta and Giorgio Tondo - Polarization of generalized Nijenhuis torsions
Hardcover ISBN: 978-1-4704-7428-7
Product Code: GSM/235
Softcover ISBN: 978-1-4704-7523-9
Product Code: GSM/235.S
Graduate Studies in Mathematics Volume: 235;
2023; 339 pp
MSC: Primary 53; 58; 57; 30;
Ricci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifold's topology and geometry is a desirable outcome. Upon closer examination, these singularities often reveal intriguing structures known as Ricci solitons.
This introductory book focuses on Ricci solitons, shedding light on their role in understanding singularity formation in Ricci flow and formulating surgery-based Ricci flow, which holds potential applications in topology. Notably successful in dimension 3, the book narrows its scope to low dimensions: 2 and 3, where the theory of Ricci solitons is well established. A comprehensive discussion of this theory is provided, while also establishing the groundwork for exploring Ricci solitons in higher dimensions.
A particularly exciting area of study involves the potential applications of Ricci flow in comprehending the topology of 4-dimensional smooth manifolds. Geared towards graduate students who have completed a one-semester course on Riemannian geometry, this book serves as an ideal resource for related courses or seminars centered on Ricci solitons.
Graduate students and researchers interested in Ricci flow and Ricci solitons.
Ricci flow singularity formation
The Ricci soliton equation
The 2
-dimensional classification
Estimates for shrinking Ricci solitons
Classification of 3
-dimensional shrinkers
The Bryant soliton
Expanding and steady GRS and the flying wing
Brendle’s theorem on the uniqueness of 3
-dimensional steadies
Geometric preliminaries
Analytic preliminaries
Softcover ISBN: 978-1-4704-7345-7
Product Code: SURV/274
Mathematical Surveys and Monographs Volume: 274;
2023; 491 pp
MSC: Primary 65; 62; Secondary 78; 94; 86;
The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas.
Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.
Graduate students and researchers interested in sampling theory and inverse problems.
Introductory remarks
Constituents of the univariate antenna problem
Regularization tools
Functional and Fourier analytic auxiliaries
Regularization methodologies
Matricial methodologies of resolution
Compact operator methodologies of resolution
Example realizations light: Univariate differentiation
Reconstruction and regularization methods
Regularization examples
Regularization methodologies in geotechnology
Sampling tools
Lattice point and special function theoretic auxiliaries
Sampling methodologies
Sampling over continuously connected pointsets
Sampling over discretely given pointsets
Polyharmonic finite bandwidth sampling
Polyharmonic infinite bandwidth sampling
Polymetaharmonic finite bandwidth sampling
Polymetaharmonic infinite bandwidth sampling
Sampling examples
Sampling methodologies in technology
Concluding remarks
Recovery as interconnecting whole