Linear Algebra I (MAY121)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAY121
Semester	1
Course Title	Linear Algebra I
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 5, Credits: 7.5)
Course Type	General Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	http://users.uoi.gr/abeligia/LinearAlgebraI/LAI2018/LAI2018.html

Learning Outcomes

Learning outcomes	After finishing the course, the students will be able: to use matrices as a tool in theoretical or numerical computations to compute the rank of a matrix to compute determinants to solve linear systems of equations to understand and use the notion of vector space.
General Competences	The aim of the course is to empower the graduate to analyse and compose basic notions and knowledge of Linear Algebra and advance his creative and productive thinking.

Syllabus

The algebra of (m x n) matrices and applications.
Row echelon forms and reduced row echelon form of a matrix.
Rank of a matrix. Determinants. Invertible matrices.
Linear systems and applications.
Vector spaces. Linear maps.
The space L(E,F) of linear operations.
Subspaces. Bases. Dimension. Rank of a linear operation.
Fundamental equation of dimension and its applications. Matrix of a linear map. Matrix of a change of bases. The isomorphism between linear mapsand matrices. Equivalent matrices. Similar matrices. Determinant of an endomorphism. Sum and direct sum of vector subspaces.

Teaching and Learning Methods - Evaluation

Delivery

Classroom (face-to-face)

Use of Information and Communications Technology

Teaching Material: Teaching material in electronic form available at the home page of the course.
Communication with the students:

Office hours for the students (questions and problem solving).
Email correspondence
Weekly updates of the homepage of the course.

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 analysis of theoretical topics and resolving application problems.

Attached Bibliography

Suggested bibliography:

Introduction to Linear Algebra (Greek), Bozapalidis Symeon, ISBN: 978-960-99293-5-6 (Editor): Charalambos Nik. Aivazis
An Introduction to Linear Algebra, 2012, (Greek) Varsos Dimitris, Deriziwtis Dimitris, Emmanouil Giannis, Maliakas Mixalis, Melas Antonios, Talleli Olympia ISBN: 978-960-6706-36-3 (Editor): “Sofia” Editions
Introduction to LINEAR ALGEBRA, 2006, (Greek) Theodora Theochari, Hara Haralambous, Charilaos Vavatsoulas, ISBN: 960-631-094-9, (Editor): Hara Charalambous