Open Problems In Mathematics

Author : John Forbes Nash, Jr.,Michael Th. Rassias
Publisher : Springer
Page : 543 pages
File Size : 50,6 Mb
Release : 2016-07-05
Category : Mathematics
ISBN : 9783319321622

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Open Problems in Mathematics by John Forbes Nash, Jr.,Michael Th. Rassias Pdf

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

Author : Robert Kaplinsky
Publisher : Taylor & Francis
Page : 193 pages
File Size : 42,7 Mb
Release : 2023-10-10
Category : Education
ISBN : 9781003839880

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Open Middle Math by Robert Kaplinsky Pdf

This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.

Author : Stephen Siklos
Publisher : Unknown
Page : 188 pages
File Size : 53,8 Mb
Release : 2019-10-16
Category : Mathematics
ISBN : 1783747765

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Advanced Problems in Mathematics by Stephen Siklos Pdf

This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Author : Çetin Kaya Koç
Publisher : Springer
Page : 439 pages
File Size : 55,8 Mb
Release : 2015-03-25
Category : Computers
ISBN : 9783319106830

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Open Problems in Mathematics and Computational Science by Çetin Kaya Koç Pdf

This book presents interesting, important unsolved problems in the mathematical and computational sciences. The contributing authors are leading researchers in their fields and they explain outstanding challenges in their domains, first by offering basic definitions, explaining the context, and summarizing related algorithms, theorems, and proofs, and then by suggesting creative solutions. The authors feel a strong motivation to excite deep research and discussion in the mathematical and computational sciences community, and the book will be of value to postgraduate students and researchers in the areas of theoretical computer science, discrete mathematics, engineering, and cryptology.

Author : Florentin Smarandache,V. Christianto
Publisher : Infinite Study
Page : 140 pages
File Size : 46,7 Mb
Release : 2006-01-01
Category : Mathematics
ISBN : 9781599730134

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Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and other areas of science by Florentin Smarandache,V. Christianto Pdf

Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation.The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plausible solutions, it is merely to keep the fun of readers in discovering the answers by themselves. Bon voyage!

Author : Richard Guy,R.K. Guy
Publisher : Springer Science & Business Media
Page : 176 pages
File Size : 40,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475717389

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Unsolved Problems in Number Theory by Richard Guy,R.K. Guy Pdf

Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.

Author : Fan Chung,Ron Graham,At&T Labs
Publisher : CRC Press
Page : 155 pages
File Size : 44,8 Mb
Release : 2020-08-26
Category : Mathematics
ISBN : 9781000108668

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Erdös on Graphs by Fan Chung,Ron Graham,At&T Labs Pdf

This book is a tribute to Paul Erdos, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch of problem posers." It examines the legacy of open problems he left to the world after his death in 1996.

Author : Kiyoshi Iseki
Publisher : Unknown
Page : 344 pages
File Size : 45,8 Mb
Release : 2001
Category : Mathematics
ISBN : UOM:39015054186328

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Unsolved Problems on Mathematics for the 21st Century by Kiyoshi Iseki Pdf

Author : Alexandre Borovik,Tony Gardiner
Publisher : Unknown
Page : 398 pages
File Size : 44,5 Mb
Release : 2019-06-11
Category : Mathematics
ISBN : 1783746998

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The Essence of Mathematics Through Elementary Problems by Alexandre Borovik,Tony Gardiner Pdf

Author : Lizhen Ji,Yat Sun Poon,Shing-Tung Yau
Publisher : Unknown
Page : 477 pages
File Size : 46,9 Mb
Release : 2013
Category : Geometry, Differential
ISBN : 1571462783

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Open Problems and Surveys of Contemporary Mathematics by Lizhen Ji,Yat Sun Poon,Shing-Tung Yau Pdf

Author : Teodora-Liliana Radulescu,Vicentiu D. Radulescu,Titu Andreescu
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 40,6 Mb
Release : 2009-06-12
Category : Mathematics
ISBN : 9780387773797

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Problems in Real Analysis by Teodora-Liliana Radulescu,Vicentiu D. Radulescu,Titu Andreescu Pdf

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.

Author : Ji-Xiu Chen
Publisher : World Scientific
Page : 804 pages
File Size : 50,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814304962

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Problems and Solutions in Mathematics by Ji-Xiu Chen Pdf

This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The mathematical problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. While the depth of knowledge involved is not beyond the contents of the textbooks for graduate students, discovering the solution of the problems requires a deep understanding of the mathematical principles plus skilled techniques. For students, this book is a valuable complement to textbooks. Whereas for lecturers teaching graduate school mathematics, it is a helpful reference.

Author : Frans Oort
Publisher : Unknown
Page : 331 pages
File Size : 48,9 Mb
Release : 2019
Category : Arithmetical algebraic geometry
ISBN : 1571463739

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Open Problems in Arithmetic Algebraic Geometry by Frans Oort Pdf

Author : Ian Stewart
Publisher : Profile Books
Page : 340 pages
File Size : 45,7 Mb
Release : 2013-03-07
Category : Mathematics
ISBN : 9781847653512

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The Great Mathematical Problems by Ian Stewart Pdf

There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincar Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

Author : Li M. Chen,Zhixun Su,Bo Jiang
Publisher : Springer
Page : 213 pages
File Size : 44,9 Mb
Release : 2015-12-15
Category : Computers
ISBN : 9783319251271

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Mathematical Problems in Data Science by Li M. Chen,Zhixun Su,Bo Jiang Pdf

This book describes current problems in data science and Big Data. Key topics are data classification, Graph Cut, the Laplacian Matrix, Google Page Rank, efficient algorithms, hardness of problems, different types of big data, geometric data structures, topological data processing, and various learning methods. For unsolved problems such as incomplete data relation and reconstruction, the book includes possible solutions and both statistical and computational methods for data analysis. Initial chapters focus on exploring the properties of incomplete data sets and partial-connectedness among data points or data sets. Discussions also cover the completion problem of Netflix matrix; machine learning method on massive data sets; image segmentation and video search. This book introduces software tools for data science and Big Data such MapReduce, Hadoop, and Spark. This book contains three parts. The first part explores the fundamental tools of data science. It includes basic graph theoretical methods, statistical and AI methods for massive data sets. In second part, chapters focus on the procedural treatment of data science problems including machine learning methods, mathematical image and video processing, topological data analysis, and statistical methods. The final section provides case studies on special topics in variational learning, manifold learning, business and financial data rec overy, geometric search, and computing models. Mathematical Problems in Data Science is a valuable resource for researchers and professionals working in data science, information systems and networks. Advanced-level students studying computer science, electrical engineering and mathematics will also find the content helpful.