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Università degli Studi di Parma Università degli Studi di Parma
Degree course in
Mathematics
Università degli Studi di Parma
Department of Mathematical, Physical and Computer Sciences

CONTINUED FRACTIONS
cod. 1011679

Academic year 2024/25
2° year of course - First semester
Professor
Alessandro ZACCAGNINI
Academic discipline
Analisi matematica (MAT/05)
Field
A scelta dello studente
Type of training activity
Student's choice
24 hours
of face-to-face activities
3 credits
hub:
course unit
in - - -
lectures timetable
exam calls
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Learning objectives


Basic theory of the continued fractions

Prerequisites

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Course unit content


Basic theory of the continued fractions

Full programme


Euclid's algorithm.
The continued fractions algorithm.
Partial quotients and convergents.
Recurrence relations of order 2.
Finite continued fractions.
Infinite continued fractions and approximation of real numbers.
Periodic continued fractions and Lagrange's theorem.
The continued fraction of Neper's number e

Bibliography


C. D. Olds, Continued Fractions, The Mathematical Association of America, Washington, 1963

G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press, Oxford,, 2008

Teaching methods


Standard lecture

Assessment methods and criteria


Standard oral exams or short lecture by the student

Other information

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2030 agenda goals for sustainable development

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