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1ERIC EJ1146453: Mathematical Critical Thinking And Curiosity Attitude In Problem Based Learning And Cognitive Conflict Strategy: A Study In Number Theory Course

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This research aims to describe and analyze result of applying Problem-Based Learning and Cognitive Conflict Strategy (PBLCCS) in increasing students' Mathematical Critical Thinking (MCT) ability and Mathematical Curiosity Attitude (MCA). Adopting a quasi-experimental method with pretest-posttest control group design and using mixed method with sequential explanatory strategy, the study involves undergraduate students of Mathematics Education Program at a private university in Riau, Indonesia, academic year 2015/2016 enrolled in Number Theory course. Quantitative data were obtained from essay test and questionnaire whereas qualitative data were from interview and observation. The findings show that; (1) there is a difference between MCT ability taught by PBLCCS and Explicit Direct Instruction (EDI), (2) there is no significant difference between MCA taught by PBLCCS and EDI, (3) students still face obstacles in developing their critical thinking skills when solving mathematical problems.

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2Problem Solving In Mathematics; Elementary Number Theory And Arithmetic

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150 p. 19 cm

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3A Set Of New Smarandache Functions, Sequences And Conjectures In Number Theory

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A set of new Smarandache functions, sequences and conjectures in number theory by Russo, Felice

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4Number Theory

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A set of new Smarandache functions, sequences and conjectures in number theory by Russo, Felice

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5Number Theory Day; Proceedings Of The Conference Held At Rockefeller University, New York, 1976

A set of new Smarandache functions, sequences and conjectures in number theory by Russo, Felice

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6Number Theory And Its History

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A set of new Smarandache functions, sequences and conjectures in number theory by Russo, Felice

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7Number Theory

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A set of new Smarandache functions, sequences and conjectures in number theory by Russo, Felice

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8Wiki - Number Theory Wiki

Number Theory Wiki dumped with WikiTeam tools.

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9Group Properties Of The Residue Classes Of Certain Kronecker Modular Systems And Some Related Generalizations In Number Theory

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Number Theory Wiki dumped with WikiTeam tools.

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10Piaget, Children, And Number : Applying Piaget's Theory To The Teaching Of Elementary Number

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Number Theory Wiki dumped with WikiTeam tools.

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11Noise, Oscillators, And Algebraic Randomness : From Noise In Communication Systems To Number Theory : Lectures Of A School Held In Chapelle Des Bois, France, April 5-10, 1999

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12Number Theory

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13Number Theory

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x, 435 p. 24 cm

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14Number Theory - Andre Weil

Number Theory - Andre Weil- An Approch through History I have no monetary benefits from this work and it is intended for non-commercial uses only 

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15Unsolved Problems In Number Theory

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Number Theory - Andre Weil- An Approch through History I have no monetary benefits from this work and it is intended for non-commercial uses only 

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16Transcendental Number Theory

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Number Theory - Andre Weil- An Approch through History I have no monetary benefits from this work and it is intended for non-commercial uses only 

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17ERIC ED020891: IDEAS FROM NUMBER THEORY.

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THIS BOOKLET, ONE OF A SERIES, HAS BEEN DEVELOPED FOR THE PROJECT, A PROGRAM FOR MATHEMATICALLY UNDERDEVELOPED PUPILS. A PROJECT TEAM, INCLUDING INSERVICE TEACHERS, IS BEING USED TO WRITE AND DEVELOP THE MATERIALS FOR THIS PROGRAM. THE MATERIALS DEVELOPED IN THIS BOOKLET INCLUDE ELEMENTARY IDEAS CONCERNING (1) WHOLE NUMBERS, (2) OPERATIONS WITH SETS, (3) DIVISORS AND MULTIPLES OF A NUMBER, AND (4) ACTIVITIES INVOLVING DIVISORS AND MULTIPLES. ACCOMPANYING THESE BOOKLETS WILL BE A "TEACHING STRATEGY BOOKLET" WHICH WILL INCLUDE A DESCRIPTION OF TEACHER TECHNIQUES, METHODS, SUGGESTED SEQUENCES, ACADEMIC GAMES, AND SUGGESTED VISUAL MATERIALS. (RP)

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18Number Theory And Diophantine Analysis: 151

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"Number Theory and Diophantine Analysis: 151" is an article from The American Mathematical Monthly, Volume 15 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2969925

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19Simple Data Compression By Differential Analysis Using Bit Reduction And Number System Theory

This is a simple algorithm which is based on number theory system and file differential technique. It employs a technique which unlike other is independent of repetition and frequency of character.In the algorithm original file is broken into some small files using differential techniques and then every small file is considered as certain n-base number system where n is the number of different characters in the file. Now the compression is done converting this nbase number system to binary number system. The main concept behind this algorithm is to save the bits by converting the higher number system to lower one. It is a simple compression and decompression process which is free from time complexity.

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20Natural Number Arithmetic In The Theory Of Finite Sets

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We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing lengths and with different closure properties. We give examples of natural number systems incomparable in length; we define hierarchies of natural number systems closed under increasingly powerful functions; and we describe a method by which to construct natural number systems with given closure properties. These natural number systems form natural models for various systems of weak arithmetic.

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21Applications Of The Wulff Construction To The Number Theory

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We apply the geometric construction of solutions of some variational problems of combinatorics to estimate the number of partitions and of plane partitions of an integer.

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22Basic Analytic Number Theory

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We give an informal introduction to the most basic techniques used to evaluate moments on the critical line of the Riemann zeta-function and to find asymptotics for sums of arithmetic functions.

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23Restoration Of Particle Number As A Good Quantum Number In BCS Theory

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As shown in previous work, number projection can be carried out analytically for states defined in a quasi-particle scheme when the states are expressed in a coherent state representation. The wave functions of number-projected states are well-known in the theory of orthogonal polynomials as Schur functions. Moreover, the functions needed in pairing theory are a particularly simple class of Schur functions that are easily constructed by means of recursion relations. It is shown that complete sets of states can be projected from corresponding quasi-particle states and that such states retain many of the properties of the quasi-particle states from which they derive. It is also shown that number projection can be used to construct a complete set of orthogonal states classified by generalized seniority for any nucleus.

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24Theory-of-Mind Development And It‘s Relation To Number Of Siblings And Executive Functions

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This study investigates the relationship between executive functions, the number of siblings, and Theory of Mind (ToM) performance in German preschoolers. Prior research has consistently demonstrated that children with more advanced executive function (EF) skills tend to perform better on ToM tasks (e.g. Fujita et al., 2022). In addition to these cognitive factors, the social environment, particularly the number of siblings has also been shown to influence ToM development positively (Shahaeian et al., 2011). Based on these findings, the present study aims to examine whether executive functions and the number of siblings independently predict children's ToM performance, and whether there is an interaction between these two predictors. Specifically, we hypothesize that both EF and the number of siblings will be positively associated with ToM abilities, and that the effect of EF on ToM may be moderated by sibling count. Children will complete standardized tasks designed to assess their executive functions and Theory of Mind. Demographic information, including the number of siblings, age, and gender, will also be collected.

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25Number Theory Casting A Look At The Mirror

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In this work, we give a purely analytic introduction to the phenomenon of mirror symmetry for quintic threefolds via classical hypergeometric functions and differential equations for them. Starting with a modular map and recent transcendence results for its values, we regard a mirror map $z(q)$ as a concept generalizing the modular one. We give an alternative approach demonstrating the existence of non-linear differential equations for the mirror map, and exploit both an elegant construction of Klemm-Lian-Roan-Yau and the Ax theorem to prove that the Yukawa coupling $K(q)$ does not satisfy any algebraic differential equation of order less than 7 with coefficients from $\mathbb{C}(q)$.

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26Heat Kernel And Number Theory On NC-torus

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The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the number-theoretical aspect of the deformation parameters. The central condition we use is of a Diophantine type. More generally, the importance of number theory is made explicit on a few examples. We apply the results to the spectral action computation and revisit the UV/IR mixing phenomenon for a scalar theory. Although we find non-local counterterms in the NC $\phi^4$ theory on $\T^4$, we show that this theory can be made renormalizable at least at one loop, and may be even beyond.

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27A Dictionary Of Chemistry : Exhibiting The Present State Of The Theory And Practice Of That Science, Its Application To Natural Philosophy, The Processes Of Manufactures, Metallurgy, And Numerous Other Arts Dependant On The Properties And Habitudes Of Bodies, In The Mineral, Vegetable, And Animal Kingdoms ; With A Considerable Number Of Tables, Expressing The Elective Attractions, Specific Gravities, Comparative Heats, Component Parts, Combinations, And Other Affections Of The Objects Of Chemical Research

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The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the number-theoretical aspect of the deformation parameters. The central condition we use is of a Diophantine type. More generally, the importance of number theory is made explicit on a few examples. We apply the results to the spectral action computation and revisit the UV/IR mixing phenomenon for a scalar theory. Although we find non-local counterterms in the NC $\phi^4$ theory on $\T^4$, we show that this theory can be made renormalizable at least at one loop, and may be even beyond.

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“A Dictionary Of Chemistry : Exhibiting The Present State Of The Theory And Practice Of That Science, Its Application To Natural Philosophy, The Processes Of Manufactures, Metallurgy, And Numerous Other Arts Dependant On The Properties And Habitudes Of Bodies, In The Mineral, Vegetable, And Animal Kingdoms ; With A Considerable Number Of Tables, Expressing The Elective Attractions, Specific Gravities, Comparative Heats, Component Parts, Combinations, And Other Affections Of The Objects Of Chemical Research” Subjects and Themes:

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28On The Formulation Of Functional Theory For Pairing With Particle Number Restoration

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The restoration of particle number within Energy Density Functional theory is analyzed. It is shown that the standard method based on configuration mixing leads to a functional of both the projected and non-projected densities. As an alternative that might be advantageous for mass models, nuclear dynamics and thermodynamics, we propose to formulate the functional in terms directly of the one-body and two-body density matrices of the state with good particle number. Our approach does not contain the pathologies recently observed when restoring the particle number in an Energy Density Functional framework based on transition density matrices and can eventually be applied with functionals having arbitrary density dependencies.

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29Some Applications Of W. Rudin's Inequality To Problems Of Combinatorial Number Theory

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In the paper we obtain some new applications of well--known W. Rudin's theorem concerning lacunary series to problems of combinatorial number theory. We generalize a result of M.-C. Chang on L_2 (L)-norm of Fourier coefficients of a set (here L is a dissociated set), and prove a dual version of the theorem. Our main instrument is computing of eigenvalues of some operators.

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30Elements Of Number Theory

In the paper we obtain some new applications of well--known W. Rudin's theorem concerning lacunary series to problems of combinatorial number theory. We generalize a result of M.-C. Chang on L_2 (L)-norm of Fourier coefficients of a set (here L is a dissociated set), and prove a dual version of the theorem. Our main instrument is computing of eigenvalues of some operators.

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31Point Processes In Arbitrary Dimension From Fermionic Gases, Random Matrix Theory, And Number Theory

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It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line. Here we analytically provide exact generalizations of such a point process in d-dimensional Euclidean space for any d, which are special cases of determinantal processes. In particular, we obtain the n-particle correlation functions for any n, which completely specify the point processes. We also demonstrate that spin-polarized fermionic systems have these same n-particle correlation functions in each dimension. The point processes for any d are shown to be hyperuniform. The latter result implies that the pair correlation function tends to unity for large pair distances with a decay rate that is controlled by the power law r^[-(d+1)]. We graphically display one- and two-dimensional realizations of the point processes in order to vividly reveal their "repulsive" nature. Indeed, we show that the point processes can be characterized by an effective "hard-core" diameter that grows like the square root of d. The nearest-neighbor distribution functions for these point processes are also evaluated and rigorously bounded. Among other results, this analysis reveals that the probability of finding a large spherical cavity of radius r in dimension d behaves like a Poisson point process but in dimension d+1 for large r and finite d. We also show that as d increases, the point process behaves effectively like a sphere packing with a coverage fraction of space that is no denser than 1/2^d.

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32Effective Field Theory, Large Number Of Particle Species, And Holography

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An effective quantum field theory (QFT) with a manifest UV/IR connection, so as to be valid for arbitrarily large volumes, can successfully be applied to the cosmological dark energy problem as well as the cosmological constant (CC) problem. Motivated by recent approaches to the hierarchy problem, we develop such a framework with a large number of particle species. When applying to systems on the brink of experiencing a sudden collapse to a black hole, we find that the entropy, unlike the total energy, now becomes an increasing function of the number of field species. An internal consistency of the theory is then used to infer the upper bound on the number of particle species, showing consistency with the holographic Bekenstein-Hawking bound. This may thus serve to fill in a large gap in entropy of any non-black hole configuration of matter and the black holes. In addition, when the bound is saturated the entanglement entropy matches the black hole entropy, thus solving the multiplicity of species problem. In a cosmological setting, the maximum allowable number of species becomes a function of cosmological time, reaching its minimal value in a low-entropy post-reheating epoch.

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33On Twisted Virasoro Operators And Number Theory

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We explore some axioms of divergent series and their relations with conformal field theory. As a consequence we obtain another way of calculating $L(0,\chi)$ and $L(-1,\chi)$ for $\chi$ being a Dirichlet character. We hope this discussion is also of interest to physicists doing renormalization theory for a reason indicated in the Introduction section. We introduce a twist of the oscillator representation of the Virasoro algebra by a group of Dirichlet characters and use this to give a 'physical interpretation' of why the values of certain divergent series should be given by special L values. Furthermore, we use this to show that some fractional powers which are crucial for some infinite products to have peculiar modular transformation properties are expressed explicitly by certain linear combinations of $L(-1, \chi)$'s for appropriately chosen $\chi$'s, and can be understood physically as a kind of 'vacuum Casimir engergy' in our settings. We also note a relation between field theory and our twisted operators. Lastly we give an attempt to reinterpret Tate's thesis by a sort of conformal field theory on a number field.

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34Non-Standard Limit Theorems In Number Theory

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We present a limit theorem describing the behavior of a probabilistic model for square-free numbers. The limiting distribution has a density that comes from the Dickman-De Bruijn function and is constant on the interval $[0,1]$. We also provide estimates concerning the error term in the limit theorem.

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35The Trace Of Modular Forms And Its Application To Number Theory

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We provide a generalization of an algebraic linear combination for the trace of certain elliptic modular forms, and through specializing the expression at a suitable pair consisting of an elliptic curve over algebraic number fields and its a certain cyclic subgroup with finite order, show a formula between distinct algebraic number fields, the one related to modular forms and the other related to elliptic curves.

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36Pi And The AGM : A Study In Analytic Number Theory And Computational Complexity

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We provide a generalization of an algebraic linear combination for the trace of certain elliptic modular forms, and through specializing the expression at a suitable pair consisting of an elliptic curve over algebraic number fields and its a certain cyclic subgroup with finite order, show a formula between distinct algebraic number fields, the one related to modular forms and the other related to elliptic curves.

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37Theory And Testing Of Uniform Random Number Generators.

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Two structural tests for random number generators of the Lehmer congruential type are discussed. They are known now to be essentially equivalent but are formulated incorrectly and the computational algorithms to implement the tests are unnecessarily complicated. New algorithms for these tests will be sketched.

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38Topics In Number Theory - First Edition

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This is a copy of the PDF version of the first edition of the book "Topics in Number Theory" (TNT) by Masum Billal and Amir Parvardi uploaded to Internet Archive by the authors. There is an AoPS forum dedicated to TNT in which anyone can ask questions regarding the book. 

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39Foundations Of Algebra And Number Theory

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xiii, 142 p. 23 cm

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40Multiple-base Number System : Theory And Applications

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xiii, 142 p. 23 cm

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41Number In Preschool And Kindergarten : Educational Implications Of Piaget's Theory

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xiii, 142 p. 23 cm

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42Number Theory

xiii, 142 p. 23 cm

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43Number Theory; An Introduction To Proof

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xiii, 142 p. 23 cm

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44Number Theory : Proceedings Of The 4th Matscience Conference Held At Ootacamund, India, January 5-10, 1984

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xiii, 142 p. 23 cm

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45202 (Number Theory)

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"202 (Number Theory)" is an article from The American Mathematical Monthly, Volume 26 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2973834

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46Field Engineering. A Hand-book Of The Theory And Practice Of Railway Surveying, Location, And Construction, Designed For The Class-room, Field, And Office, And Containing A Large Number Of Useful Tables, Original And Selected

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"202 (Number Theory)" is an article from The American Mathematical Monthly, Volume 26 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2973834

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47Analytic Number Theory- 18.785- Dirichlet Characters And Dirichlet L-Series

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In this unit, we introduce some special multiplicative functions, the Dirichlet characters, and study their corresponding Dirichlet series. We will use these in a subsequent unit to prove Dirichlet�s theorem on primes in arithmetic progressions, and the prime number theorem in arithmetic progressions.

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48Analytic Number Theory- 18.785- Introduction To Large Sieve Inequalities

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In this unit, we consider a relatively simple example of a large sieve inequality, of the sort introduced by Linnik. This is a setup for the multiplicative large sieve inequality we will need for Bombieri-Vinogradov.

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49Symmetry Of Physical Laws. Part 2 : Q-number Theory Of Space-time Inversions And Charge-conjugation Q-number Theory Of Space-time Inversions And Charge-conjugation.

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1 v. (var. pag.) ; 28 cm

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50Analytic Number Theory

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1 v. (var. pag.) ; 28 cm

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