Analytic Geometry (MAY223)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAY223
Semester	2
Course Title	Analytic Geometry
Independent Teaching Activities	Lectures, laboratory exercises (Weekly Teaching Hours: 5, Credits: 7.5)
Course Type	General Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek, English
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	-

Learning Outcomes

Learning outcomes

It is an introductory course on geometry. The aim is to study problems in geometry using rectangular coordinates and tools based on Linear Algebra. On completion of the course the student should be familiar with basic notions in geometry like the one of isometry. Furthermore, the student should have a background to allow him to attain more advanced courses on geometry, calculus of several variables and others.

General Competences

Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism

Syllabus

Axioms of Euclidean geometry (plane and space) and proofs of basic propositions. Cartesian model, vectors, linear independence, bases, coordinates and applications. Inner product, cross product, area, volume and determinants. Lines and planes. Geometric transformations (parallel transports, rotations, reflections), isometries and the notion of congruence. Transformation of area and volume under linear transformations. Curves and surfaces of 2nd degree and their classification. Curves, surfaces and parametrizations.

Teaching and Learning Methods - Evaluation

Delivery	Classroom (face-to-face)
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures (13X5) 65 Working independently 100 Exercises-Homeworks 22.5 Course total 187.5
Student Performance Evaluation	Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems.

Attached Bibliography

• Thomas F. Banchoff και John Wermer, Η Γραμμική Άλγεβρα μέσω Γεωμετρίας, Εκδόσεις Leader Books, Σειρά Πανεπιστήμιακα Μαθηματικά Κείμενα, Αθήνα, 2009.