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Pseudorandomness In Computer Science and In Additive Combinatorics [chapter]

Luca Trevisan
2010 Bolyai Society Mathematical Studies  
• Define C to be class of functions C A,B (u,v) = 1 iff (u,v) crosses sets (A,B) • Then G is ε-pseudorandom iff G and K |V| are εindistinguishable by C note: domain of functions in C is the set of all  ...  ,N} has size δN, and N > exp(exp(1/δ)), then A must contain a length-3 progression.  ...  • some arguments in additive combinatorics more transparent using language of distributions, adversaries and indistinguishability • arguments in complexity, cleaner and more general using language of functions  ... 
doi:10.1007/978-3-642-14444-8_19 fatcat:akcfnkn4rbfsjnyyylplqxds4y

The Institute for Computational and Experimental Research in Mathematics (ICERM)

Jill Pipher, Sergei Tabachnikov, Homer F. Walker
2016 Notices of the American Mathematical Society  
GirlsGetMath@ICERM participants explore mathematical sciences through hands-on activities, computations, and experimentations.  ...  In addition to providing access to multiple software packages and to high-performance computing through Brown's Center for Computing and Visualization, ICERM staff will also be available for programming  ... 
doi:10.1090/noti1348 fatcat:3atek3myjzer7jsq5uoqblczje

Efficient Computation in Groups and Simplicial Complexes

John C. Stillwell
1983 Transactions of the American Mathematical Society  
Using HNN extensions of the Boone-Britton group, a group E is obtained which simulates Turing machine computation in linear space and cubic time.  ...  Space in E is measured by the length of words, and time by the number of substitutions of defining relators and conjugations by generators required to convert one word to another.  ...  The ability of mathematical systems to simulate computation has often been used to prove unsolvability results.  ... 
doi:10.2307/1999079 fatcat:h5ogcyo7nzguxhjmgughpjxm54

Computability and Noncomputability in Classical Analysis

Marian Boykan Pour-El, Ian Richards
1983 Transactions of the American Mathematical Society  
This paper treats in a systematic way the following question: which basic constructions in real and complex analysis lead from the computable to the noncomputable, and which do not?  ...  Particular attention is paid to those processes which occur in physical applications. The approach to computability is via the standard notion of recursive function from mathematical logic.  ...  In this paper, we find effective uniform continuity playing an especially prominent role in Theorems 1, 4, and 7, and sequential computability in Example 8.  ... 
doi:10.2307/1999038 fatcat:jaam3ha4vbg4fikgixzwxvxism

Nonlinear waves in integrable and nonintegrable systems (Mathematical Modeling and Computation 16) By Jianke Yang

Karima Khusnutdinova
2015 Bulletin of the London Mathematical Society  
(US$ 85.00), ISBN 978-0-898717-05-1 (Society for Industrial and Applied Mathematics, Philadelphia, 2010).  ...  This powerful technique, introduced here in a very simple and instructive example and used in some consequent chapters, allows one to obtain the mathematical 'DNA' of many unmanageable problems -their  ...  Petviashvili, accelerated imaginary-time evolution, squared-operator iteration and Newton conjugate-gradient methods are used for computations of solitary waves.  ... 
doi:10.1112/blms/bdu100 fatcat:ryukenp735b6zmx5edlx2kssim

Efficient computation in groups and simplicial complexes

John C. Stillwell
1983 Transactions of the American Mathematical Society  
Using HNN extensions of the Boone-Britton group, a group E is obtained which simulates Turing machine computation in linear space and cubic time.  ...  Space in E is measured by the length of words, and time by the number of substitutions of defining relators and conjugations by generators required to convert one word to another.  ...  The ability of mathematical systems to simulate computation has often been used to prove unsolvability results.  ... 
doi:10.1090/s0002-9947-1983-0688973-8 fatcat:duladqp3q5fs7arzmhwv33ql4q

Book Review: Computability in analysis and physics

Douglas S. Bridges
1991 Bulletin of the American Mathematical Society  
The distinction between classical and intuitionistic (constructive) logic is significant in several places in recursive mathematics.  ...  In consequence, every theorem of BISH, suitably interpreted, is also a theorem of RUSS and of classical mathematics-, but theorems of constructive mathematics that depend on recursive function theory are  ...  The most mathematically well-understood case is that of one  ... 
doi:10.1090/s0273-0979-1991-15994-x fatcat:prmauqtcwfgcdpn3carivyvjmi

New teaching methods - Using computer technology in physics, mathematics and computer science

Morten Brekke, Per Henrik Hogstad
2010 International Journal for Digital Society (IJDS)  
SimVideo is so new that we have not yet developed much content in physics and mathematics, but Per Henrik Hogstad have briefly tried it out in a course given in computer science.  ...  Subsequently I have used parAbel and SimReal in both physics and mathematics courses at my university for approximately 5 years.  ...  Many of these are not the strongest candidates in mathematics and physics.  ... 
doi:10.20533/ijds.2040.2570.2010.0004 fatcat:g5da756p6fftpeqzox3tc4vx44

Computability and noncomputability in classical analysis

Marian Boykan Pour-El, Ian Richards
1983 Transactions of the American Mathematical Society  
This paper treats in a systematic way the following question: which basic constructions in real and complex analysis lead from the computable to the noncomputable, and which do not?  ...  Particular attention is paid to those processes which occur in physical applications. The approach to computability is via the standard notion of recursive function from mathematical logic.  ...  In this paper, we find effective uniform continuity playing an especially prominent role in Theorems 1, 4, and 7, and sequential computability in Example 8.  ... 
doi:10.1090/s0002-9947-1983-0682717-1 fatcat:k6f6twc7h5h4jjavmzpagh5tmy

Book Review: Analog methods in computation and simulation

Francis J. Murray
1955 Bulletin of the American Mathematical Society  
REID Analog methods in computation and simulation. By W. W. Soroka. New York, McGraw-Hill, 1954. 14+390 pp. $7.50 .  ...  In these circumstances mathematics plays a somewhat different role.  ... 
doi:10.1090/s0002-9904-1955-09943-9 fatcat:ucivpqjycffu7hpkoyrbyugn7a

Book Review: Computation and complexity in economic behavior and organization

Stephen J. DeCanio
2003 Bulletin of the American Mathematical Society  
The late emergence of the computational theme in economics may be a consequence of the fact that the notion of computational limits is itself relatively new in mathematics.  ...  Gödel and Turing first discovered limits to what can be proved or computed in the 1930s, and formal theories of computational complexity and algorithmic information only began to emerge in the 1960s [1  ...  Our understanding of social and economic activity will always be limited in (at least) the same ways mathematical knowledge is limited.  ... 
doi:10.1090/s0273-0979-03-00996-0 fatcat:ipyrwpafgzforhto3jjqxtm6hq

Book Review: Computational and algorithmic problems in finite fields

Daqing Wan
1994 Bulletin of the American Mathematical Society  
., for many stimulating suggestions and several colleagues for helpful comments.  ...  Emphasis is on the constructive and computational side of finite fields. However, the treatment of material in both books is from a mathematical point of view.  ...  The area has seen a rapid growth in recent years due to its many new applications and connections with other subjects such as computer science, coding theory, discrete mathematics, algebraic geometry,  ... 
doi:10.1090/s0273-0979-1994-00466-5 fatcat:lpl6spoff5b7hop6pbbrlxhxsa

Formalism and intuition in computability

R. I. Soare
2012 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
of 'inductive' and the founding of Computability in Europe by Cooper and others.  ...  A third wave of intuition has arisen from 1996 to the present with a return to the original meaning of computability in the sense of Turing and Gödel, and a return of 'recursive' to its original meaning  ...  The grant is Computability theory and applications, funded by the Simons Foundation Program for Mathematics and the Physical Sciences.  ... 
doi:10.1098/rsta.2011.0335 pmid:22711859 fatcat:z2ae3dac65dmfmijd2sylefawq

Inherent Presence Of Children In Society "Proposed Criteria And Indicators."

Nermeen Singer, Et. al.
2021 Turkish Journal of Computer and Mathematics Education  
Promote all learning and development outcomes. The results confirm the importance of sensitive practice and responding to children's desires and need to support their real presence in society.  ...  developing children's connection to and participation in their world, improving children's sense of personal happiness, development and improvement of self-confidence in children, and developing and refining  ...  in various forms and for various reasons in many societies.  ... 
doi:10.17762/turcomat.v12i4.627 fatcat:vgux6duv4vecrnzcrkgaldolqi

Book Review: The theory of semirings \RM (with applications in mathematics and theoretical computer science\/\RM )

Hanns J. Weinert
1994 Bulletin of the American Mathematical Society  
Hence interested researchers can access the necessary external papers and books for any required material that is not contained in this book.  ...  The book can serve a reader well in many ways. The methods are explained, with lots of references given.  ...  On the other hand, since semirings and also semimodules over them have become an important tool in applied mathematics and theoretical computer science, semirings appear-sometimes with other names such  ... 
doi:10.1090/s0273-0979-1994-00476-8 fatcat:5uycwirwbvdqzacaxkc7hq4axm
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