0366.1115 - ANALYTIC GEOMETRY
An undergraduate course
Subject matter:
an analytic and computational description of Euclidian space,
as complete as possible via elementary means.
Prerequisites:
Linear Algebra 2, Calculus 2 (or taken concurrently).
Course requirements:
Weekly exercise-sheet, handed-in every week.
The exercises form an integral part of the course,
account for 20% of the final grade, and form
a prerequisite for the final exam (at least 10
solved sheets).
Course outline
1. Introduction: basic building blocks, axioms and simple results
of the structure of space.
(5) 215-222 (7) 87-101
2. Vectors in space: addition, multiplication by a scalar, linear
dependence.
Vector space: unique representation in a given basis, dimension.
Applications to geometric problems,
(1) 87-92 (5) 1-6 (7) 102-110
3. Scalar, vector and triple products. Coordinates (affine, cartesian).
(1) 93-105 (5) 48-84 (7) 111-143 (does not cover vector product).
4. Straight lines and planes.
(1) 119-139 (7) 144 to end of book, elementary.
5. Linear transformations, orthogonal ones.
(1) 115-118, 180-192
6. Quadrics
(7) 139-170
7. Lines and surfaces in space. Parametric representations.
Ruled and developable surfaces.
8. Projective geometry.
Literature:
(1) A.V. Pogorelov, Analytical Geometry, Mir Pub. 1984
(2) A.V. pogorelov, Geometry, Mir Pub. 1987
Part 1: Analytic Geometry, very simmilar to (1).
(3) M. Berger, Geometry I, II, Springer Verlag 1987
(4) H.S.M. Coxeter, Introduction to Geometry, 2nd Ed. Wiley 1969
In Hebrew:
(5) Analytic Geometry, Amitzur, Akademon, Hebrew University.
pp. 1-84 intuitive approach, 215-236 axiomatic foundations.
(6) Algebra 1, Amitzur, U. Liron, Akademon. pp. 21-45.
(7) Vectors and their use in geometry, Timor, Sabran 1991.