Presents number theory as a computational discipline
Focuses on key examples central to future research
Supports foundational work at the intersection of arithmetic geometry and data science
This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research.
● algebraic varieties over finite fields
● the Chabauty-Coleman method
● modular forms
● rational points on curves of small genus
● S-unit equations and integral points.
Jennifer Balakrishnan is Clare Boothe Luce Associate Professor of Mathematics and Statistics at Boston University. She holds a Ph.D. in Mathematics from the Massachusetts Institute of Technology.
Noam Elkies is Professor of Mathematics at Harvard University. He holds a Ph.D. in Mathematics from Harvard University.
Brendan Hassett is Professor of Mathematics at Brown University and Director of the Institute for Computational and Experimental Research in Mathematics. He holds a Ph.D. in Mathematics from Harvard University.
Bjorn Poonen is Distinguished Professor in Science at the Massachusetts Institute of Technology. He holds a Ph.D. in Mathematics from the University of California at Berkeley.
Andrew Sutherland is Principal Research Scientist at the Massachusetts Institute of Technology. He holds a Ph.D. in Mathematics from the Massachusetts Institute of Technology.
John Voight is Professor of Mathematics at Dartmouth College. He holds a Ph.D. in Mathematics from the University of California at Berkeley.
Series Title : Simons Sym posia
Copyright : 2022
Number of Pages ：X, 589
Number of Illustrations ：12 b/w illustrations, 36 illustrations in colour
Algebraic Geometry, Number Theory, Theory of Computation
This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces.
BISWARANJAN BEHERA is Associate Professor at the Statistics and Mathematics Unit of the Indian Statistical Institute (ISI), Kolkata, India. He received his M.Sc. degree in Mathematics from Sambalpur University, Odisha, India, in 1992, and the Ph.D. degree from the Indian Institute of Technology (IIT) Kanpur, India, in 2001. He was Postdoctoral Fellow at ISI, Kolkata, from 2001?2004. He joined IIT Delhi as Assistant Professor, in 2004. He is working at ISI, Kolkata, since 2010. His research interests are wavelet analysis on the Euclidean spaces, Hardy space and local fields of positive characteristic, and weighted norm inequalities on local fields.
QAISER JAHAN is Assistant Professor at the Indian Institute of Technology (IIT) Mandi, India. She received her M.Sc. degree in Mathematics from the University of Allahabad, India, in 2006, and her Ph.D. from the Indian Statistical Institute, Kolkata, in 2014. After her Ph.D., she worked as Visiting Scientist at ISI, Kolkata, and as Postdoctoral Fellow at IIT Kanpur for two years. After that, she joined the Indian Institute of Science (IISc), Bangalore, as Kothari Postdoctoral Fellow. She has visited a few institutes in abroad for research purposes like the University of Oregon, USA; Philipps University, Germany; and the Institute of Mathematics, the Polish Academy of Sciences. She was awarded the Indo-US WISTEMM fellowship. Her research area is harmonic analysis. In particular, she is working on wavelet analysis, local fields, coorbit spaces, shearlet coorbit spaces, etc. She has written eight research articles in international journals and one conference paper in SampTA 2019.]
Indian Statistical Institute Series
ISBN 9789811678806
333 pages
Springer Nature（2022/03）
Hardcover
9789811669934
The purpose of this book is to explain linear algebra clearly for beginners. In doing so, the author states and explains somewhat advanced topics such as Hermitian products and Jordan normal forms. Starting from the definition of matrices, it is made clear with examples that matrices and matrix operation are abstractions of tables and operations of tables. The author also maintains that systems of linear equations are the starting point of linear algebra, and linear algebra and linear equations are closely connected. The solutions to systems of linear equations are found by solving matrix equations in the row-reduction of matrices, equivalent to the Gauss elimination method of solving systems of linear equations. The row-reductions play important roles in calculation in this book. To calculate row-reductions of matrices, the matrices are arranged vertically, which is seldom seen but is convenient for calculation. Regular matrices and determinants of matrices are defined and explained. Furthermore, the resultants of polynomials are discussed as an application of determinants. Next, abstract vector spaces over a field K are defined. In the book, however, mainly vector spaces are considered over the real number field and the complex number field, in case readers are not familiar with abstract fields. Linear mappings and linear transformations of vector spaces and representation matrices of linear mappings are defined, and the characteristic polynomials and minimal polynomials are explained. The diagonalizations of linear transformations and square matrices are discussed, and inner products are defined on vector spaces over the real number field. Real symmetric matrices are considered as well, with discussion of quadratic forms. Next, there are definitions of Hermitian inner products. Hermitian transformations, unitary transformations, normal transformations and the spectral resolution of normal transformations and matrices are explained. The book ends with Jordan normal forms. It is shown that any transformations of vector spaces over the complex number field have matrices of Jordan normal forms as representation matrices.
Preface.- 1. Matrices.- 2. Linear Equations.- 3. Determinants.- 4. Vector Spaces.- 5. Linear Mappings.- 6. Inner Product Spaces.- 7. Hermitian Inner Product Spaces.- 8. Jordan Normal Forms.-Notation.- Answers to Exercises.- References.- Index of Theorems.- Index.
Gives complete and comprehensive coverage of major topics in algebra
Contains a rich collection of solved examples and exercises for practice
Discusses applications in numerical methods, analytical geometry, and solving linear system of DE
This book provides a comprehensive knowledge of linear algebra for graduate and undergraduate courses. As a self-contained text, it aims at covering all important areas of the subject, including algebraic structures, matrices and systems of linear equations, vector spaces, linear transformations, dual and inner product spaces, canonical forms of an operator and bilinear and quadratic forms. The last three chapters focus on empowering readers to pursue interdisciplinary applications of linear algebra in numerical methods, analytical geometry and in solving linear system of differential equations. A rich collection of examples and exercises are present at the end of each chapter to enhance the conceptual understanding of readers. Basic knowledge of various notions, such as sets, relations, mappings and so on, has been pre-assumed.
Mohammad Ashraf is Professor at the Department of Mathematics, Aligarh Muslim University, India. He completed his Ph.D. in Mathematics from Aligarh Muslim University, India, in the year 1986 with the thesis entitled “A study of certain commutativity conditions for associative rings”. He also served as Associate Professor at the Department of Mathematics, King Abdulaziz University, KSA, from 1998 to 2004.
His research interests include ring theory/commutativity and structure of rings and near-rings, derivations on rings, near-rings & Banach algebras, differential identities in rings and algebras, applied linear algebra, algebraic coding theory and cryptography. With a teaching experience of around 30 years, Prof. Ashraf has supervised the Ph.D. thesis of 7 students and is currently guiding 6 more. He has published around 161 research articles in journals and conference proceedings of repute. He received the Young Scientist's Award from Indian Science Congress Association in the year 1988 and the I.M.S. Prize from Indian Mathematical Society for the year 1995.
Vincenzo De Filippis is Associate Professor of Algebra at the University of Messina, Italy. He completed his Ph.D. in Mathematics from the University of Messina, Italy, in 1999. He is the member of the Italian Mathematical Society (UMI) and National Society of Algebraic and Geometric Structures and their Applications (GNSAGA). He has published around 100 research articles in reputed journals and conference proceedings.
Mohammad Aslam Siddeeque is Assistant Professor at the Department of Mathematics, Aligarh Muslim University, India. He completed his Ph.D. in Mathematics from Aligarh Muslim University, India, in 2014 with the thesis entitled “On derivations and related mappings in rings and near-rings". His research interest lies in derivations and its various generalizations on rings and near-rings, on which he has published articles in reputed journals.
Copyright : 2022
Number of Pages : XVI, 498
Number of Illustrations : 2 b/w illustrations, 2 illustrations in colour
Topics : Linear Algebra
Highlights new research related to the square of opposition
Examines the theory of the square of opposition through an interdisciplinary lens
Explores the past, present, and future of the field
The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the square of opposition to solve theological problems regarding predestination and theodicy. Other topics covered include:
Hegel’s opposition to diagrams
De Morgan’s unpublished octagon of opposition
turnstile figures of opposition
institutional model-theoretic treatment of oppositions
Lacan’s four formulas of sexuation
the theory of oppositional poly-simplexes
The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts.
Series Title : Studies in Universal Logic
Copyright : 2021
Number of Pages : XIV, 292
Number of Illustrations : 106 b/w illustrations, 193 illustrations in colour
Mathematical Logic and Foundations, Philosophical Logic, Logic, Philosophy
Presents results thanks to generalizations of different works
Provides new applications to various fields
Includes a chapter on Ostrowski inequality
This book provides new contributions to the theory of inequalities for integral and sum, and includes four chapters. In the first chapter, linear inequalities via interpolation polynomials and green functions are discussed. New results related to Popoviciu type linear inequalities via extension of the Montgomery identity, the Taylor formula, Abel-Gontscharoff's interpolation polynomials, Hermite interpolation polynomials and the Fink identity with Green’s functions, are presented. The second chapter is dedicated to Ostrowski’s inequality and results with applications to numerical integration and probability theory. The third chapter deals with results involving functions with nondecreasing increments. Real life applications are discussed, as well as and connection of functions with nondecreasing increments together with many important concepts including arithmetic integral mean, wright convex functions, convex functions, nabla-convex functions, Jensen m-convex functions, m-convex functions, m-nabla-convex functions, k-monotonic functions, absolutely monotonic functions, completely monotonic functions, Laplace transform and exponentially convex functions, by using the finite difference operator of order m. The fourth chapter is mainly based on Popoviciu and Cebysev-Popoviciu type identities and inequalities. In this last chapter, the authors present results by using delta and nabla operators of higher order.
Dr. Nazia Irshad is associated with Dawood University of Engineering and Technology as an Assistant Professor of Mathematics. Her field specialization is in the Mathematical Inequalities and Applications.
Dr. Asif Raza Khan is an Assistant Professor and HEC Approved PhD Supervisor at Department of Mathematics, University of Karachi. His field of research is Mathematical Inequalities and Applications, Convex Analysis, Time Scale and Numerical Integration. He is the author of a monograph entitled “General Linear Inequalities and Positivity: Higher Order Convexity”.
Dr. Faraz Mehmood has a PhD from the University of Karachi. He has been working at Dawood University of Engineering and Technology since November 2009 and presently serving his duties there as an Associate Professor of Mathematics. His field of research is Mathematical Inequalities and Applications, Convex Analysis, Time Scale and Numerical Integration.
Prof. Dr. Josip Pe?ari? is a Croatian mathematician. He has recently retired as a professor of mathematics from the Faculty of Textile Technology at the University of Zagreb, Croatia, and is a full member of the Croatian Academy of Sciences and Arts. He has written and co-authored over 1,500 mathematical publications.
Copyright : 2021
Number of Pages : X, 270
Number of Illustrations : 2 illustrations in colour
Real Functions, Difference and Functional Equations
Contains engaging articles explaining cutting-edge mathematics
Features both contributions with important advances and surveys of new mathematics
Reflects both independent and group research
This volume features contributions from the Women in Commutative Algebra (WICA) workshop held at the Banff International Research Station (BIRS) from October 20-25, 2019, run by the Pacific Institute of Mathematical Sciences (PIMS). The purpose of this meeting was for groups of mathematicians to work on joint research projects in the mathematical field of Commutative Algebra and continue these projects together long-distance after its close. The chapters include both direct results and surveys, with contributions from research groups and individual authors.
The WICA conference was the first of its kind in the large and vibrant area of Commutative Algebra, and this volume is intended to showcase its important results and to encourage further collaboration among marginalized practitioners in the field. It will be of interest to a wide range of researchers, from PhD students to senior experts.
?Claudia Miller is a Professor at Syracuse University and holds a doctoral degree from the University of Illinois at Urbana-Champaign. She is a leading author in homological commutative algebra with connections to algebraic topology and algebraic geometry and has supervised several Ph.D students.
Janet Striuli is an Associate Professor at Fairfield University and holds a doctoral degree from the University of Kansas. Her research interests lie in commutative algebra and its interactions with homological algebra. She has been Program Director at the National Science Foundation.
Emily Witt is an Associate Professor at the University of Kansas and holds a doctoral degree from the University of Michigan. Her research is centered in commutative algebra, though it is motivated by connections with algebraic geometry, representation theory, and singularity theory. She currently holds an NSF CAREER Award.
Series Title : Association for Women in Mathematics Series
Copyright : 2021
Number of Pages : XIV, 200
Number of Illustrations : 19 b/w illustrations, 42 illustrations in colour
Commutative Rings and Algebras, Algebraic Geometry, Number Theory