Professors: Dr. Nertila Gjini
email: ngjini@unyt.edu.al
Office Hours: Tuesdays 13:0014:00
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:
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 A1
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 2SPACE AND 3SPACE
1. Introduction to vectors (geometric) 2. Norm of a vector, vector arithmetic 3. Dot product, projections
4. Cross product
5. Lines and planes in 3space
EUCLIDEAN VECTOR SPACES
1. Euclidean nspace
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
INNER PRODUCT SPACES
1. Inner products
2. Angle and orthogonality in inner product spaces
3. Orthonormal Bases, GramSchmidt process; QRdecomposition 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 
96100 
Outstanding work 
A 
9095 

B+ 
8789 
Good work, distinctly above the average 
B 
8386 

B 
8082 

C+ 
7779 
Acceptable work 
C 
7376 

C 
7072 

D+ 
6769 
Work that is significantly below average 
D 
6366 

D 
6062 

F 
059 
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