scholarly journals Postcards from the Edge, or Snapshots of the Theory of Generalised Moonshine

2002 ◽  
Vol 45 (4) ◽  
pp. 606-622
Author(s):  
Terry Gannon
Keyword(s):  
Number Theory ◽  
Gauss Sums ◽  
Quadratic Reciprocity ◽  
The Impact

AbstractWe begin by reviewing Monstrous Moonshine. The impact of Moonshine on algebra has been profound, but so far it has had little to teach number theory. We introduce (using ‘postcards’) a much larger context in which Monstrous Moonshine naturally sits. This context suggests Moonshine should indeed have consequences for number theory. We provide some humble examples of this: new generalisations of Gauss sums and quadratic reciprocity.

scholarly journals Pengembangan Game Puzzle Sebagai Edugame Berbasis Android Untuk Meningkatkan Kemampuan Berpikir Matematika Siswa SD

2019 ◽  
Vol 3 (1) ◽  
pp. 74
Author(s):  
Baiq Olatul Aini ◽  
Khaerunnisa Cantika Ayu ◽  
Siswati Siswati
Keyword(s):  
Number Theory ◽  
Data Analysis ◽  
Student Learning ◽  
Learning Outcomes ◽  
Student Learning Outcomes ◽  
Average Score ◽  
Class Iii ◽  
Research Instrument ◽  
The Impact

Abstrak: Pada aplikasi game puzzle ini berisi materi teori bilangan, aljabar, bangun datar dan bangun ruang. Pada game ini terdapat 15 level dan dibuat dari Appsgeyser. Penelitian ini bertujuan untuk meningkatkan kemampuan berpikir melalui minat belajar siswa di SD kelas III, IV, V dan VI. Dampak dari media pembelajaran edugame ini adalah media pembelajaran berpengaruh pada kemampuan berpikir siswa. Instrument penelitian yang digunakan adalah pedoman angket dan observasi. Berdasarkan hasil analisis data, diperoleh hasil validasi dari ahli media dengan skor rata-rata 73,649% dalam kriteria layak, sedangkan respon dari pengguna rata-rata sebesar 80,335% dalam kreteria menarik. Abstract: In this puzzle game application contains material in number theory, algebra, wake up flat and build space. In this game there are 15 levels and are made from Appsgeyser. This study aims to increase students' interest in learning at SD class III, IV, V, and VI. The impact of edugame learning media is learning media influencing student learning outcomes. The research instrument used was the questionnaire and observation guidelines. Based on the results of data analysis, the results of validation from media experts were obtained with an average score of 73,649% in eligible criteria, while the response from users on average was 80,335% in the criteria interesting.

Using decomposition groups to prove theorems about quadratic residues

2020 ◽  
Vol 1 (1) ◽  
pp. 12-20
Author(s):  
Tomas Perutka
Keyword(s):  
Field Theory ◽  
Number Theory ◽  
Class Field Theory ◽  
Legendre Symbol ◽  
Quadratic Reciprocity ◽  
Class Field ◽  
Reciprocity Laws ◽  
Reciprocity Law ◽  
Quadratic Residues ◽  
Cyclotomic Extensions

In this text we elaborate on the modern viewpoint of the quadratic reciprocity law via methods of alge- braic number theory and class field theory. We present original short and simple proofs of so called addi- tional quadratic reciprocity laws and of the multiplicativity of the Legendre symbol using decompositon groups of primes in quadratic and cyclotomic extensions of Q.

Gauss Sums and Orthogonal Polynomials

1997 ◽  
Vol 12 (01) ◽  
pp. 289-294 ◽  
Author(s):  
A. S. Zhedanov
Keyword(s):  
Number Theory ◽  
Weight Function ◽  
Orthogonal Polynomials ◽  
Hermite Polynomials ◽  
Gauss Sums ◽  
Gauss Sum ◽  
The Real ◽  
Root Of Unity ◽  
Szegő Polynomials

It is shown that q-Hermite polynomials for q a root of unity are orthogonal on finite numbers of points of the real axes. The (complex) weight function coincides with a special type of the Gauss sums in number theory. The same Gauss sum plays the role of the weight function for the Stiltjes–Wigert and Rogers–Szegö polynomials leading to the orthogonality on the regular N-gons.

scholarly journals ASSOCIATION AMONG MATHEMATICAL CRITICAL THINKING SKILL, COMMUNICATION, AND CURIOSITY ATTITUDE AS THE IMPACT OF PROBLEM-BASED LEARNING AND COGNITIVE CONFLICT STRATEGY (PBLCCS) IN NUMBER THEORY COURSE

2018 ◽  
Vol 7 (1) ◽  
pp. 15 ◽  
Author(s):  
Zetriuslita Zetriuslita ◽  
Wahyudin Wahyudin ◽  
Jarnawi Afgani Dahlan
Keyword(s):  
Number Theory ◽  
Critical Thinking ◽  
Communication Skill ◽  
Problem Based Learning ◽  
Cognitive Conflict ◽  
Thinking Skill ◽  
Critical Thinking Skill ◽  
Mathematical Communication ◽  
The Impact ◽  
Conflict Strategy

This research aims to find out the association amongMathematical Critical Thinking (MCT) ability, Mathematical Communication, and Mathematical Curiosity Attitude (MCA) as the impact of applying Problem-Based Learning Cognitive Conflict Strategy(PBLCCS) in Number Theory course. The research method is correlative study. The instruments include a test for mathematical critical thinking skill and communication, and questionnaire to obtain the scores of mathematical curiosity attitude. The findings show that: 1) there is no association between critical thinking skill and mathematical curiosity attitude as the impact of applying problem-based learning cognitive conflict strategy, 2) there is no association between mathematical communication and curiosity attitude as the impact of applying problem-based learning and cognitive conflict strategy, and 3) the impact of applying problem-based learning cognitive conflict strategy is more influential in developing critical thinkingskillthan communication skill and curiosity.

Computational Cryptography

2021 ◽  
Keyword(s):  
Number Theory ◽  
Lattice Reduction ◽  
Reduction Algorithm ◽  
65Th Birthday ◽  
Integer Factorization ◽  
Cryptographic Keys ◽  
Mathematical Problems ◽  
The Impact ◽  
Selection Of ◽  
Scientific Achievements

The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra–Lenstra–Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.

Formation of Lunar Craters and Bright Rays as a Result of Meteorite Impacts

1962 ◽  
Vol 14 ◽  
pp. 415-418
Author(s):  
K. P. Stanyukovich ◽  
V. A. Bronshten
Keyword(s):  
Explosive Charge ◽  
The Moon ◽  
Meteorite Impacts ◽  
The Earth ◽  
Lunar Craters ◽  
The Impact

The phenomena accompanying the impact of large meteorites on the surface of the Moon or of the Earth can be examined on the basis of the theory of explosive phenomena if we assume that, instead of an exploding meteorite moving inside the rock, we have an explosive charge (equivalent in energy), situated at a certain distance under the surface.

The Geosciences Applied to Lunar Exploration

1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green
Keyword(s):  
Lunar Surface ◽  
Probable Mechanism ◽  
Point Of View ◽  
Lunar Exploration ◽  
Geological Model ◽  
Apply Geophysics ◽  
Surface Features ◽  
The Impact

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.

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