Even Perfect Numbers—An Update

1981 ◽  
Vol 74 (6) ◽  
pp. 460-463
Author(s):  
Stanley J. Bezuszka
Keyword(s):  
Number Theory ◽  
Problem Solving ◽  
History Of Mathematics ◽  
Independent Study ◽  
History Of ◽  
Perfect Numbers ◽  
Excellent Resource

Do you have students who are computer buffs, always looking for a new problem to program efficiently? Do you have students who do independent study projects? If so, motivate them with this topic that is rich in the history of mathematics and number theory—perfect numbers. They provide an excellent resource for theoretical as well as computerized problem solving.

Ankle Bones, Rogues, and Sexual Freedom for Women

2011 ◽  
pp. 461-468
Author(s):  
Nigel K.L. Pope ◽  
Kevin E. Voges
Keyword(s):  
Information Processing ◽  
Data Analysis ◽  
Problem Solving ◽  
Computational Intelligence ◽  
History Of Mathematics ◽  
Volume Form ◽  
Paper Briefly ◽  
Sexual Freedom ◽  
History Of ◽  
And Control

In this chapter we review the history of mathematics-based approaches to problem solving. The authors suggest that while the ability of analysts to deal with the extremes of data now available is leading to a new leap in the handling of data analysis, information processing, and control systems, that ability remains grounded in the work of early pioneers of statistical thought. Beginning with pre-history, the paper briefly traces developments in analytical thought to the present day, identifying milestones in this development. The techniques developed in studies of computational intelligence, the applications of which are presented in this volume, form the basis for the next great development in analytical thought.

scholarly journals PROGRESSÃO HARMÔNICA E O TRIÂNGULO DE LEIBNIZ

2015 ◽  
Vol 37 ◽  
pp. 426
Author(s):  
David Pinto Martins
Keyword(s):  
Problem Solving ◽  
History Of Mathematics ◽  
Wide Applicability ◽  
History Of ◽  
Problem Solving Strategies

http://dx.doi.org/10.5902/2179460X14661This article intends to address in an elementary way the study of harmonic progressions. To this end, the usage of history of mathematics and problem solving strategies permeated the text. Several problems, some classics and other extracted from mathematical olympiads, were treated to show the wide applicability of this subject. In the end, the triangle of Leibniz and his relationship with the harmonic progressions is studied.

Teaching Mathematics through Historic Environment. A Time-Travel Grounded Pedagogy

2019 ◽  
pp. 380-385
Author(s):  
Marguerite K. Miheso-O´Connor
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
History Of Mathematics ◽  
Time History ◽  
Time Travel ◽  
Teaching Mathematics ◽  
Historical Events ◽  
Long Period ◽  
Present Context ◽  
History Of

Mathematics has been used by generations to make important decisions for a long period of time. History is littered with problem solving events which are results of mathematization of tasks based on available tools in any given generation. While History of mathematics focuses on what each culture contributed to present day conventional mathematics as taught in schools as a subject, Mathematics in a Historic environment focuses on identifying mathematical thinking that exists in all historical events. Historical events when enacted through the Time Travel approach learners get the opportunity to relive past events in the present context. Teaching mathematics in historic environment uses the time travel events that are practised by bridging ages international, to provide a reflective meaningful conceptualization of mathematics is a living subject. The strategy illuminates the centrality of mathematical thinking in all historical events. This paper shares findings from a study carried out on the effectiveness of this approach for teaching mathematics and provides an opportunity to discuss the approach as a viable pedagogic strategy that can be replicated across the curriculum.

scholarly journals The Complexity of Number Theory

2020 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Number Theory ◽  
Infinite Number ◽  
Short Proof ◽  
History Of Mathematics ◽  
Difficult Problem ◽  
Fundamental Question ◽  
Complexity Classes ◽  
History Of ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

The Goldbach's conjecture has been described as the most difficult problem in the history of Mathematics. This conjecture states that every even integer greater than 2 can be written as the sum of two primes. This is known as the strong Goldbach's conjecture. The conjecture that all odd numbers greater than 7 are the sum of three odd primes is known today as the weak Goldbach conjecture. A major complexity classes are L, NL and NSPACE(S(n)) for some S(n). Whether L = NL is a fundamental question that it is as important as it is unresolved. We show if the weak Goldbach's conjecture is true, then the problem PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n). This proof is based on the assumption that if some language belongs to NSPACE(S(n)), then the unary version of that language belongs to NSPACE(S(log n)) and vice versa. However, if PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the strong Goldbach's conjecture is true or this has an infinite number of counterexamples. Since Harald Helfgott proved that the weak Goldbach's conjecture is true, then the strong Goldbach's conjecture is true or this has an infinite number of counterexamples, where the case of infinite number of counterexamples statistically seems to be unlikely. In addition, if PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the Beal's conjecture is true when L = NL. On November 2019, Frank Vega proves that L = NP which also implies that L = NL. In this way, the Beal's conjecture is true and since the Beal's conjecture is a generalization of Fermat's Last Theorem, then this is also a simple and short proof for that Theorem.

scholarly journals The Complexity of Number Theory

2020 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Number Theory ◽  
Infinite Number ◽  
Short Proof ◽  
History Of Mathematics ◽  
Difficult Problem ◽  
Complexity Class ◽  
Fermat's Last Theorem ◽  
History Of ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

The Goldbach's conjecture has been described as the most difficult problem in the history of Mathematics. This conjecture states that every even integer greater than 2 can be written as the sum of two primes. This is known as the strong Goldbach's conjecture. The conjecture that all odd numbers greater than 7 are the sum of three odd primes is known today as the weak Goldbach conjecture. A major complexity class is NSPACE(S(n)) for some S(n). We show if the weak Goldbach's conjecture is true, then the problem PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n). However, if PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the strong Goldbach's conjecture is true or this has an infinite number of counterexamples. Since Harald Helfgott proved that the weak Goldbach's conjecture is true, then the strong Goldbach's conjecture is true or this has an infinite number of counterexamples, where the case of infinite number of counterexamples statistically seems to be unlikely. In addition, if PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the Beal's conjecture is true. Since the Beal's conjecture is a generalization of Fermat's Last Theorem, then this is also a simple and short proof for that Theorem.

History of Mathematics: Number Theory.

Science ◽  
1984 ◽  
Vol 226 (4681) ◽  
pp. 1412-1412
Author(s):  
H. G. DIAMOND
Keyword(s):  
Number Theory ◽  
History Of Mathematics ◽  
History Of
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