Elementary mathematics from an advanced point of view

[276SM]
a.a. 2025/2026

3° Year of course - Second semester

Frequency Not mandatory

  • 6 CFU
  • 48 hours
  • Italian
  • Trieste
  • Obbligatoria
  • Standard teaching
  • Oral Exam
  • SSD MAT/04
  • Advanced concepts and skills
Curricula: Curr. Didattico
LOGAR ALESSANDRO
CLASS SCHEDULE
EXAM TIMETABLE
Syllabus

To learn the basic concepts introduced in the course

Algebra 1, Algebra 2, Analisi 1

Introduction to set theory (Zermelo Fraenkel). Construction of the natural numbers, integer numbers, rational numbers. Ordered rings, Real numbers: Cantor construction, Dedekind construction,
numbers in decimal notation, Algebraic and trascendent numbers. Continued fractions. Straightedge and compass constructions. Origami constructions.

See the site:
http://www.dmi.units.it/~logar/didattica/matematicheEPSV

Derek Goldrei, Classic Set Theory for guided independent study, Chapman and Hall, 1996.
James M. Henle, An Outline of Set Theory, Problem Books in Mathematics, Springer-Verlag, 1986.
Carl B. Boyer, Storia della matematica, Oscar Mondadori, 1968.
Andras Hajnal, Peter Hamburger, Set Theory, London Mathematical Society, 1999.
Domenico Pagani, Sandro Salsa, Analisi matematica 1, Zanichelli, 2015.
Rodolfo Permutti, Lezioni di algebra.
Aleksandr Khinchin, Continued Fractions, Dover, 1997.
Harold, Davenport, Aritmetica superiore: un'introduzione alla teoria dei numeri, Zanichelli - 1994
Ivan Niven, Numeri razionali e irrazionali, Zanichelli, 1968.
Ian Steward, Galois theory, Chapman and Hall 2003.
Roger C. Alperin, A Mathematical Theory of Origami Constructions and Numbers, New York J. Math.6 (2000) 119–133.
Robert Lang, Origami and geometric constructions
Francesco Defina, Teoria degli Origami: analisi di una teoria assiomatica.
Sundara Row, Geometric exercises in paper folding, Dover Publications, 1966

Introduction to set theory (Zermelo Fraenkel). Construction of the natural numbers, integer numbers, rational numbers. Ordered rings, Real numbers: Cantor construction, Dedekind construction,
numbers in decimal notation, Algebraic and trascendent numbers. Continued fractions. Straightedge and compass constructions. Origami constructions.

See the site:
http://www.dmi.units.it/~logar/didattica/matematicheEPVS

Classroom lectures at the blackboard

more info on the site:
http://www.dmi.units.it/~logar/didattica/matematicheEPVS

oral exam