Professors: Dr. Nertila Gjini
e-mail: ngjini@unyt.edu.al
Office Hours: Tuesdays 13:00-14:00

 

Faculty of Law, Arts and Science Department of Computer Sciences

Mathematics and Natural Sciences Teaching Sector

LINEAR ALGEBRA (3 credits)

Fall Semester 2012

Aim and Objectives: The course is intended for undergraduate students majoring in computer science. This course provides an introduction to linear algebra and it’s

application to other disciplines. Students will learn about matrix algebra and its application to the solution of systems of linear equations. They will be introduced to abstract vector spaces and linear transformations, and learn of their application to a variety of problems. Aspects of orthogonality and eigenvalues will be discussed.

Prerequisites: College Algebra.
Teaching Methods: 3 hours per week in the form of lectures.

Main Textbook: Elementary Linear Algebra, Howard Anton, ninth edition, 2005, John Willey & Sons, Inc.

Reference Book:

  •   Linear Algebra, Georgi E. Shilov, Dover Publications, Inc., New York.
  •   Linear Algebra with Applications, 6th edn; Steven J. Leon; Prentice Hall.

    Class Conduct: You are responsible for everything that is announced, presented or discussed in class. The way to avoid any misunderstanding associated with this course is

    to attend class. You are expected to attend class and I do keep attendance records. Please, be courteous during class; both to me and your colleagues. I find late arrivals distracting, which cause a decline in the quality of my lecture. Importantly, it is also disruptive to your colleagues. Please, refrain from talking during class; it is disruptive to your

Address:
Rr.”Medar Shtylla” (ish- “Komuna e Parisit”) Tirana, Albania
Post code 1001

Telephone: +355 4 2441 330/1/2 Fax: +355 4 2441 329

Web site: http://www.unyt.edu.al

UNIVERSITY OF NEW YORK, TIRANA

colleagues and the lecture. I expect the best behavior from all of you. This is what education is all about. Please, consider that the language of instruction is English, so all our conversation into the class must be in this language.
If you feel that you have special learning difficulties, please, make an appointment with Dr. Enila Cenko. Dr. Enila Cenko is trained to help students with learning difficulties. She has offered to provide this service to our students, just as it is offered in all American universities.

Course content:

SYSTEMS OF LINEAR EQUATIONS AND MATRCES

1. Introduction to systems of linear equations 2. Gaussian elimination
3. Matrices and matrix operations
4. Inverses; rules of matrix arithmetic

5. Elementary matrices and a method for finding A-1
6. Further results on systems of equations and invertibility 7. Diagonal, triangular, and symmetric matrices

DETERMINANTS

1. Determinants by cofactor expansion
2. Evaluating determinants by row reduction 3. Properties of the determinant function
4. A combinatorial approach to determinants

VECTORS IN 2-SPACE AND 3-SPACE

1. Introduction to vectors (geometric) 2. Norm of a vector, vector arithmetic 3. Dot product, projections
4. Cross product

5. Lines and planes in 3-space

EUCLIDEAN VECTOR SPACES

1. Euclidean n-space
2. Linear transformations from Rn to Rm
3. Properties of linear transformations from Rn to Rm 4. Linear transformations and polynomials

GENERAL VECTOR SPACES

1. Real vector spaces 2. Subspaces
3. Linear independence

Address:
Rr.”Medar Shtylla” (ish- “Komuna e Parisit”) Tirana, Albania
Post code 1001

Telephone: +355 4 2441 330/1/2 Fax: +355 4 2441 329

Web site: http://www.unyt.edu.al

UNIVERSITY OF NEW YORK, TIRANA

  1. Basis and dimensions
  2. Row space, column space, and nullspace
  3. Rank and nullity

INNER PRODUCT SPACES

1. Inner products
2. Angle and orthogonality in inner product spaces
3. Orthonormal Bases, Gram-Schmidt process; QR-decomposition 4. Best approximation; least squares
5. Change of basis
6. Orthogonal matrices

EIGENVALUES, EIGENVECTORS

1. Eigenvalues and eigenvectors 2. Diagonalization
3. Orthogonal diagonalization

LINEAR RANSFORMATION

1. General linear transformations
2. Kernel and range
3. Inverse linear transformations
4. Matrices of general linear transformations 5. Similarity

6. Isomorphism

Assessment criteria :

Active participation 10% Homework 10% Midterm exam 20% Test 20% Final exam 40%

Exams are closed books. Also, you may use your own calculator and nothing else will be allowed. Mobile phones are strictly not tolerated in the class for any use (including computations). Active participation is meant as the effort and the interest that a student shows in the class, including homework. After each session students are expected to study all the relevant material, read all the associated exercises, identify the difficult points and pose their questions in the next session either directly to me or in the class. Cheating and plagiarism in any form will result immediately in the grade F. Students who are absent more than

Address:
Rr.”Medar Shtylla” (ish- “Komuna e Parisit”) Tirana, Albania
Post code 1001

Telephone: +355 4 2441 330/1/2 Fax: +355 4 2441 329

Web site: http://www.unyt.edu.al

UNIVERSITY OF NEW YORK, TIRANA

20% of the total hours of the semester (i.e. 9 hours) may be required to withdraw from the course.

Grading Scale: Grading scale follows the official UNYT as below:

Letter Grade

Percentage (%)

Generally Accepted Meaning

A

96-100

Outstanding work

A-

90-95

B+

87-89

Good work, distinctly above the average

B

83-86

B-

80-82

C+

77-79

Acceptable work

C

73-76

C-

70-72

D+

67-69

Work that is significantly below average

D

63-66

D-

60-62

F

0-59

Work that does not meet minimum standards for passing the course

Address:
Rr.”Medar Shtylla” (ish- “Komuna e Parisit”) Tirana, Albania
Post code 1001

Telephone: +355 4 2441 330/1/2 Fax: +355 4 2441 329

Web site: http://www.unyt.edu.al