Illustrate, using a critical and unitary approach,ÿsome interesting and classical results and notions that are central for teaching mathematics in high school (focussing, principally, on arithmetics, geometry and algebra). The aim of the course is also to give a contribution to teachers training through the investigation on historical, didactic and cultural aspects of these topics.
Curriculum
teacher profile teaching materials
• Ordered Geometry and Sylvester problem.
• Projective Geometry: axioms, Desargues, collineations and
correlations
• Platonic Solids Euler formula. Politops, 4-dimensional space politops.
• Topology of surfaces and graphs 4 colors problem and 6 colors theorem, Heawood theorem.
• Delaunay triangulations.
• Plane curves, local study of singularities, Newton polygons .
2) G. Fisher Plane algebraic curves, AMS Students Mathematical Library V.
15, AMS 2001.
moreover
3) M. Aigner, G. Ziegler, Proofs from THE BOOK, Springer, 1998;
4) S. Rebay, Tecniche di Generazione di Griglia per il Calcolo Scientifico-Triangolazione di Delaunay, slides Univ. Studi di Brescia;
5) B. Sturmfels, Polynomial equations and convex polytopes, American Mathematical Monthly 105 (1998) 907-922.
6) Shuhong Gao, Absolute Irreducibility of Polynomials via Newton Polytopes, J. of Algebra
Fruizione: 20410193 ME410 - MATEMATICHE ELEMENTARI DA UN PUNTO DI VISTA SUPERIORE in Matematica LM-40 SUPINO PAOLA
Programme
• Euclidean Geometry: triangles centers, circle inversion.• Ordered Geometry and Sylvester problem.
• Projective Geometry: axioms, Desargues, collineations and
correlations
• Platonic Solids Euler formula. Politops, 4-dimensional space politops.
• Topology of surfaces and graphs 4 colors problem and 6 colors theorem, Heawood theorem.
• Delaunay triangulations.
• Plane curves, local study of singularities, Newton polygons .
Core Documentation
1) H.S.M. Coxeter Introduction to geometry, Wiley 1970;2) G. Fisher Plane algebraic curves, AMS Students Mathematical Library V.
15, AMS 2001.
moreover
3) M. Aigner, G. Ziegler, Proofs from THE BOOK, Springer, 1998;
4) S. Rebay, Tecniche di Generazione di Griglia per il Calcolo Scientifico-Triangolazione di Delaunay, slides Univ. Studi di Brescia;
5) B. Sturmfels, Polynomial equations and convex polytopes, American Mathematical Monthly 105 (1998) 907-922.
6) Shuhong Gao, Absolute Irreducibility of Polynomials via Newton Polytopes, J. of Algebra
Type of delivery of the course
arguments selected from students proposals will be taken under considerationType of evaluation
oral examination, attending students will be invited to give talks whose evaluation will contribute to the final mark teacher profile teaching materials
• Ordered Geometry and Sylvester problem.
• Projective Geometry: axioms, Desargues, collineations and
correlations
• Platonic Solids Euler formula. Politops, 4-dimensional space politops.
• Topology of surfaces and graphs 4 colors problem and 6 colors theorem, Heawood theorem.
• Delaunay triangulations.
• Plane curves, local study of singularities, Newton polygons .
2) G. Fisher Plane algebraic curves, AMS Students Mathematical Library V.
15, AMS 2001.
moreover
3) M. Aigner, G. Ziegler, Proofs from THE BOOK, Springer, 1998;
4) S. Rebay, Tecniche di Generazione di Griglia per il Calcolo Scientifico-Triangolazione di Delaunay, slides Univ. Studi di Brescia;
5) B. Sturmfels, Polynomial equations and convex polytopes, American Mathematical Monthly 105 (1998) 907-922.
6) Shuhong Gao, Absolute Irreducibility of Polynomials via Newton Polytopes, J. of Algebra
Fruizione: 20410193 ME410 - MATEMATICHE ELEMENTARI DA UN PUNTO DI VISTA SUPERIORE in Matematica LM-40 SUPINO PAOLA
Programme
• Euclidean Geometry: triangles centers, circle inversion.• Ordered Geometry and Sylvester problem.
• Projective Geometry: axioms, Desargues, collineations and
correlations
• Platonic Solids Euler formula. Politops, 4-dimensional space politops.
• Topology of surfaces and graphs 4 colors problem and 6 colors theorem, Heawood theorem.
• Delaunay triangulations.
• Plane curves, local study of singularities, Newton polygons .
Core Documentation
1) H.S.M. Coxeter Introduction to geometry, Wiley 1970;2) G. Fisher Plane algebraic curves, AMS Students Mathematical Library V.
15, AMS 2001.
moreover
3) M. Aigner, G. Ziegler, Proofs from THE BOOK, Springer, 1998;
4) S. Rebay, Tecniche di Generazione di Griglia per il Calcolo Scientifico-Triangolazione di Delaunay, slides Univ. Studi di Brescia;
5) B. Sturmfels, Polynomial equations and convex polytopes, American Mathematical Monthly 105 (1998) 907-922.
6) Shuhong Gao, Absolute Irreducibility of Polynomials via Newton Polytopes, J. of Algebra
Type of delivery of the course
arguments selected from students proposals will be taken under considerationType of evaluation
oral examination, attending students will be invited to give talks whose evaluation will contribute to the final mark teacher profile teaching materials
• Ordered Geometry and Sylvester problem.
• Projective Geometry: axioms, Desargues, collineations and
correlations
• Platonic Solids Euler formula. Politops, 4-dimensional space politops.
• Topology of surfaces and graphs 4 colors problem and 6 colors theorem, Heawood theorem.
• Delaunay triangulations.
• Plane curves, local study of singularities, Newton polygons .
2) G. Fisher Plane algebraic curves, AMS Students Mathematical Library V.
15, AMS 2001.
moreover
3) M. Aigner, G. Ziegler, Proofs from THE BOOK, Springer, 1998;
4) S. Rebay, Tecniche di Generazione di Griglia per il Calcolo Scientifico-Triangolazione di Delaunay, slides Univ. Studi di Brescia;
5) B. Sturmfels, Polynomial equations and convex polytopes, American Mathematical Monthly 105 (1998) 907-922.
6) Shuhong Gao, Absolute Irreducibility of Polynomials via Newton Polytopes, J. of Algebra
Fruizione: 20410193 ME410 - MATEMATICHE ELEMENTARI DA UN PUNTO DI VISTA SUPERIORE in Matematica LM-40 SUPINO PAOLA
Programme
• Euclidean Geometry: triangles centers, circle inversion.• Ordered Geometry and Sylvester problem.
• Projective Geometry: axioms, Desargues, collineations and
correlations
• Platonic Solids Euler formula. Politops, 4-dimensional space politops.
• Topology of surfaces and graphs 4 colors problem and 6 colors theorem, Heawood theorem.
• Delaunay triangulations.
• Plane curves, local study of singularities, Newton polygons .
Core Documentation
1) H.S.M. Coxeter Introduction to geometry, Wiley 1970;2) G. Fisher Plane algebraic curves, AMS Students Mathematical Library V.
15, AMS 2001.
moreover
3) M. Aigner, G. Ziegler, Proofs from THE BOOK, Springer, 1998;
4) S. Rebay, Tecniche di Generazione di Griglia per il Calcolo Scientifico-Triangolazione di Delaunay, slides Univ. Studi di Brescia;
5) B. Sturmfels, Polynomial equations and convex polytopes, American Mathematical Monthly 105 (1998) 907-922.
6) Shuhong Gao, Absolute Irreducibility of Polynomials via Newton Polytopes, J. of Algebra
Type of delivery of the course
arguments selected from students proposals will be taken under considerationType of evaluation
oral examination, attending students will be invited to give talks whose evaluation will contribute to the final mark