Department of Mathematics
Department of Mathematics
GC University, Lahore
Course Title:
Algebra III (16 Weeks)
Course Code:
MATH-3201Course Length:
Semester
Credits:
3 hrs
Course description: This is the course in abstract linear
algebra. The majority of follow up courses in both pure and applied
mathematics assume the material covered in this course.Contents:
Vector spaces; sums and direct sums of subspaces of a finite
dimensional vector space, Dimension theorem, linear transformation,
null space, image space of linear transformation, rank and nullity
of a linear transformation, relation between rank, nullity and
dimension of domain of a linear transformation, matrix of linear
transformation, change of basis, inner product spaces, projection
of a vector along another vector, norm of a vector, Cauchy Schwartz
inequality, Orthogonal and orthonormal basis, similar matrices and
diagonalization of a matrix, Hom(V,W), dimension and basis of
Hom(V,W), dual space and dual basis, annihilators.Prerequisite
Course(s): Algebra IICourse goals and performance objectives:
Goal I:Conceptual and practical understanding of modes of
learning,
problem solving and creative Inquiry
(20% of Scheduled Learning Activities)
Obj.:Ability to understand Elementary Concepts of Vector spaces;
sums and direct sums of subspaces of a finite dimensional vector
spaceGoal II:Information gathering, reasoning and synthesizing
abilities.
(25% of scheduled learning activities)
Obj.:Ability to understand Dimension theorem, linear
transformation, null space, image space of linear transformation,
rank and nullity of a linear transformation, relation between rank,
nullity and dimension of domain of a linear transformationGoal
III:Knowledge and understanding
(30% of scheduled learning activities)
Obj.:Ability to understand matrix of linear transformation,
change of basis, inner product spaces, projection of a vector along
another vector, norm of a vector, Cauchy Schwartz inequalityGoal
IV:Reflective, creative and critical dispositions.
(25% of scheduled learning activities)
Obj. :Orthogonal and orthonormal basis, similar matrices and
diagonalization of a matrix, Hom(V, W), dimension and basis of
Hom(V,W), dual space and dual basis, annihilators.Teaching Learning
Strategies:
The formal lectures in the class room by the teacher will be
accompanied by class room discussion. So the students are expected
to participate in the class room discussion. Class room activities
may include problem solving techniques related with the subject
matter. Students are required to present a term paper in
consultation with the class teacher focusing on the issues of a
topic or problems related to the text. Invited lectures by the
expert in the field may also be arranged and students must attend
these lectures.
Time Management Matrix:
Goal 01:
20% - 08 Lectures
Goal 02:
25% - 10 Lectures
Goal 03:
30% - 12 Lectures
Goal 04:
25% - 10 Lectures
Total:
100% - 40 Lectures
Assessment Strategies:
The assessment for curse in a semester will be carried out on
the basis of following criteria:
Semester Work
40% - 40 Marks
Final Examination 60% - 60 Marks
Total:
100% - 100 Marks
Semester work includes Quizzes/ Term papers/ projects given by
the instructor to the students.
Guidance for term paper:
The students are required to submit term paper in time. The term
paper should not merely be descriptive, must include the
backgrounds, motivation, application and related problems. Term
papers will be assessed on the basis of ones analytical, logical
thinking and comprehension of the subject. Web based material
should be discouraged.
Recommended Texts:
1. Axle S J, Linear algebra Done Right, Undergraduate Texts in
Mathematics, 1996,
Springer, New York.2. Birkhoff G, Maclane S, A survey of Modern
Algebra (4th edition), AKP.3. Classics Perry WL, Elementary Linear
Algebra, 1988, McGraw-Hill, New York. PAGE 1
