New mathematical tables containing the factors, squares, cubes, square roots, cube roots, reciprocals, and hyperbolic logarithms, of all numbers from 1 to 10000; tables of powers and prime numbers; an extensive table of formulæ, or general synopsis of the most important particulars relating to the doctrines of equations, series, fluxions, fluents, &c. &c. &c.

Mode of access: Internet.

RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An Invitation to Additive Prime Number Theory

2000 Mathematics Subject Classification: 11D75, 11D85, 11L20, 11N05, 11N35, 11N36, 11P05, 11P32, 11P55.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

Il canto sospeso de Luigi Nono

This article explains how Nono's Il canto sospeso (1956), for solo voices, choir and orchestra, is structured in a logic of counterbalances for each musical action, overlapping a harmonic or ‘intuitive’ geometry, with a contrasting or ‘anti-intuitive’ plot. Unlike the typical relationships with the golden ratio, found in many musical examples in which it appears ‘naturally’ (see Tatlow 2001), intervals in the prime numbers series here are perceived as ‘counter-rhythm’; as a form of a counterintuitive distribution, or, as Jameson (2003:vii) suggests, as “a very irregular way” of apparent distribution.

Distribution asymptotique du nombre de diviseurs premiers distincts inférieurs ou égaux à m

Le sujet principal de ce mémoire est l'étude de la distribution asymptotique de la fonction f_m qui compte le nombre de diviseurs premiers distincts parmi les nombres premiers $p_1,...,p_m$. Au premier chapitre, nous présentons les sept résultats qui seront démontrés au chapitre 4. Parmi ceux-ci figurent l'analogue du théorème d'Erdos-Kac et un résultat sur les grandes déviations. Au second chapitre, nous définissons les espaces de probabilités qui serviront à calculer les probabilités asymptotiques des événements considérés, et éventuellement à calculer les densités qui leur correspondent. Le troisième chapitre est la partie centrale du mémoire. On y définit la promenade aléatoire qui, une fois normalisée, convergera vers le mouvement brownien. De là, découleront les résultats qui formeront la base des démonstrations de ceux chapitre 1.

Exercise sheet 2

Exercises and solutions in LaTex

Exercise sheet 4 pdf

Exercises and solutions in PDF

Exercise sheet 7 pdf

Exercises and solutions in PDF

Lecture notes pdf

Lecture notes in PDF

Exam 1999 pdf

Exam and solutions in PDF

Exam 2000

Exam and solutions in LaTex

Lecture notes

Lecture notes in LaTex

Exercise sheet 7

Exercises and solutions in LaTex

Exam 1999

Exam and solutions in LaTex