Title: The Foundations of Geometry
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- exposé
- cours - matière potentielle : lectures on euclidean geometry
- hilbert as a course of lectures on euclidean geometry
- criterion for the possibility of a geometrical construction by means
- demonstration for plane geometry by aid of the axioms of congruence
- geometry by david hilbert
- means of the theorems
- axioms
- geometry
- straight line
- space
- points
FUNDAMENTALS
Program
Introduction to matrix algebra Symmetry in nature and in human life
BASIC CONCEPTS
Affine spaces vs. vector spaces Mappings: affine and Euclidean; isometries and symmetry operations Sets; homomorphisms, isomorphisms, automorphisms Introduction to group theory: abstract groups, subgroups, cosets
CRYSTALLOGRAPHY IN DIRECT SPACE
Periodic structure of the crystalline matter Crystal lattice vs. crystal pattern and crystal structure Symmetry directions in a lattice Unit cells: primitive cells, multiple cells, conventional cells in 2D and 3D Crystal families Symmetry groups and types of symmetry in direct space omorphological symmetry osymmetry of physical properties osymmetry of lattices osymmetry of the unit cell content osymmetry of crystallographic patterns oHermannMauguin symbols for point groups lattice systems Crystal systems Stereographic projection and the morphology of crystals Types of crystallographic point groups through the stereographic projection Generation of space groups. Symmetry operations with and without a glide component. HermannMauguin symbols for space groups Orthogonal projections of space groups. General and special positions, sitesymmetry groups, crystallographic orbits Introduction to crystallographic calculations through matrix algebra. Abstract groups, subgroups, cosets Short introduction to the subgroups and supergroups of space groups Exercises on the space group diagrams from Volume A of theInternational Tables for Crystallography
PHYSICS OF DIFFRACTION AND CRYSTALLOGRAPHIC IN RECIPROCAL SPACE
Interaction of Xrays with crystalline matter
