Università Roma Tre

Mathematics for Elementary School teachers
SFP 2016/7
prof. Paola Supino



SETS and NUMBERS
0. set up for set language
1. functions between sets, graphs
2. relations between sets, order and equivalence relations, partitions.
3. very elementary elements of logics
4. numbers in Ancient Rome, the abacus and the arabic numbers
5. Counting and cardinality of sets, cartesian product, the sets of subsets, Cantor diagonal argument
6. Peano axioms
7. Ordering numbers
8. well--ordering principle
9. Building the integers, operations and properties
10. Euclidean division theorem, basis representation theorem for numbers
11. The GCD and Euclid algorithm, Bezout identity
12. Linear Diophantine equations
13. divisibility between natural numbers.
14. Prime numbers, their infinitness, Eratosthenes, unique factorization theorem, other theorems and famous conjectures
18. modular arithmetic
19. building rational numbers, operations and properties
20. Order and density of rational numbers
21. Cardinality of rational numbers
22. decimal representation of rational numbers, base 10 and base 3 numbers representation
23. Irrationality of square root of 2, and of a prime
24. Real numbers

EUCLIDEAN GEOMETRY
25. The origin: the Elements of Euclid
26. From Euclid to Hilbert
27. the first book of Elements I, some proofs
33. Pitagora theorem
35. When the V postulate fails: spherical and other geometries
36. Il book of Euclid geometric algebra
37. VI book and Thales
38. convex subsets and polygons, regular polygons
39. equivalence in geometry: Isoperimetry and equi-extension problems,
40. solid shapes in space
41. Euler formula
42. analytic geometry: points and lines in cartesian plane distance, circle.
43. Euclidean plane isometries.

the student can refer to any source she/he desire