𝑞-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra

1986 ◽  
Author(s):  
G. Andrews
Keyword(s):  
Number Theory ◽  
Computer Algebra

Dodgson condensation, alternating signs and square ice

2006 ◽  
Vol 364 (1849) ◽  
pp. 3183-3198 ◽  
Author(s):  
Andrew N.W Hone
Keyword(s):  
Number Theory ◽  
Computer Algebra ◽  
Statistical Physics ◽  
Mathematical Physics ◽  
Algebraic Combinatorics ◽  
General Scientific ◽  
Dodgson Condensation

Starting with the numbers 1,2,7,42,429,7436, what is the next term in the sequence? This question arose in the area of mathematics called algebraic combinatorics, which deals with the precise counting of sets of objects, but it goes back to Lewis Carroll's work on determinants. The resolution of the problem was only achieved at the end of the last century, and with two completely different approaches: the first involved extensive verification by computer algebra and a huge posse of referees, while the second relied on an unexpected connection with the theory of ‘square ice’ in statistical physics. This paper, aimed at a general scientific audience, explains the background to this problem and how subsequent developments are leading to a fruitful interplay between algebraic combinatorics, mathematical physics and number theory.

WAYS OF USE OF COMPUTER ALGEBRA SYSTEMS IN THE TEACHING OF ADVANCED SECTIONS OF MATHEMATICS

2019 ◽  
pp. 50-55
Author(s):  
I. S. Safuanov ◽  
V. A. Chugunov
Keyword(s):  
Number Theory ◽  
Computer Algebra ◽  
Dynamic Geometry ◽  
Abstract Algebra ◽  
Computer Algebra Systems ◽  
Advanced Mathematics ◽  
Genetic Method ◽  
Computer Technologies ◽  
Modes Of Representation ◽  
Derivatives Of

In this article, possible ways of use of computers for the teaching of advanced sections of mathematics that traditionally belong to undergraduate curricula, namely elements of calculus, number theory and abstract algebra are considered. Use of computer technologies can help also to implement such approaches as genetic method and the use of various modes of representation in education. According to cultural-historical theory of L. S. Vygotsky, computer technologies can be considered as the tool for the construction of concepts in the process of learning. The most appropriate for teaching advanced mathematics are such computer algebra systems as Maple, Mathematica, and various systems of dynamic geometry. We will consider the possibilities of Geogebra for the work with functions at the initial stages of undergraduate calculus courses, namely for the work with concepts of limits and derivatives of functions.

scholarly journals Computer algebra systems in the elementary number theory

2013 ◽  
Vol 6 (4(66)) ◽  
pp. 10-13
Author(s):  
Леонід Петрович Бедратюк ◽  
Ганна Іванівна Бедратюк
Keyword(s):  
Number Theory ◽  
Computer Algebra ◽  
Computer Algebra Systems ◽  
Elementary Number Theory ◽  
Elementary Number

scholarly journals Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics

2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Tatiana Bandman ◽  
Shelly Garion ◽  
Boris Kunyavskiĭ
Keyword(s):  
Number Theory ◽  
Dynamical Systems ◽  
Computer Algebra ◽  
Arithmetic Geometry ◽  
Simple Groups ◽  
Arithmetic Dynamics ◽  
Matrix Groups ◽  
The Past ◽  
Word Equations ◽  
Simple Matrix

AbstractWe present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.

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