PDF Linear Algebra MTH4213-3 Jamoum University College

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Course Title: Advanced Linear Algebra Course Code: MTH4213-3

Program: BSc. In Mathematics Department: Mathematics

College: Jamoum University College

Institution: Umm Al-Qura University

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3 H. Course Identification

1. Credit hours: 3 2. Course type

a. ^University College Department Others

b. Required ^Elective

3. Level/year at which this course is offered: Eleventh level/fourth year 4. Pre-requisites for this course (if any): Linear algebra 2

5. Co-requisites for this course (if any): Non

6. Mode of Instruction (mark all that apply)

No Mode of Instruction Contact Hours Percentage

1 Traditional classroom 0 0

2 Blended 0 0

3 E-learning Three hours/week %100

4 Distance learning 0 0

5 Other 0 0

7. Contact Hours (based on academic semester)

No Activity Contact Hours

1 Lecture 30

2 Laboratory/Studio 0

3 Tutorial 10

4 Others (specify) 0

Total 40

B. Course Objectives and Learning Outcomes

1. Course Description

Linear Algebra is an area of mathematics that deals with the properties and applications of vectors, matrices, and other related mathematical structures. Interestingly, these topics readily lend themselves to a very rigorous study of the underlying mathematical theory, as well as to a broadly applications-oriented study of concepts, methods, and algorithms. This course will place roughly equal emphasis on theory and applications.

Main topics we will cover are included in this advance course in linear algebra. The course description are as follows: Revisions of: Caley Hamilton theorem, Characteristic polynomials, minimum polynomials and the spectral of a linear transformation. Then more theory of

diagonalizations and quadratic forms. Then the exponential of a square matrix and the

relationship between determinant of exponential of a square matrix and the exponential of the trace of the same matrix. Main objective is to deliver the notion of tensor product of two matrices (Kronecker product). Tensor product of two vector spaces. Modules as a generalization of vector spaces. One main objective is the notion of Modules over principal ideal domains.

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This course will provide a common mathematical advanced foundations related to theory of linear algebra for students in all of the programs, drawing upon the full range of undergraduate courses in mathematics. In addition, it will permit students to build upon and share knowledge already acquired while pointing out areas in which additional study may be needed. In addition, it will develop the communication skills and understanding of the process of doing mathematics necessary for graduate-level study.

3. Course Learning Outcomes

CLOs Aligned

PLOs 1 Knowledge and Understanding: by the end of this course, the

student is expected to be able to

1.1 Definition and properties of the matrix exponential and its determinant 1.2 Describe the tensor product of two matrices.

1.3 Describe the tensor product of vector spaces and its basic properties.

1.4 Outline modules, submodules, quotients, and direct sum of modules 2 Skills: by the end of this course, the student is expected to be able to 2.1 Demonstrate accurate and efficient use of advanced algebraic

techniques

2.2 Calculate the matrix exponential and its determinant.

2.3 Perform tensor product.

2.4 Distinguish between vector spaces and modules.

3 Values: by the end of this course, the student is expected to be able to

3.1 Analyze quantitative data verbally, graphically, symbolically and numerically

3.2 Communicate quantitative data verbally, graphically, symbolically and numerically

3.3 Integrate appropriately technology into mathematical processes 3.4 Generalize mathematical concepts in problem-solving through

integration of new material and modeling

C. Course Content

No List of Topics Contact

Hours 1 Some revisions of: Caley Hamilton theorem, Characteristic polynomials,

minimum polynomials and the spectral of a linear transformation. 6

2 More Theory of diagonalizations and quadratic forms. 3

3

The exponential of a square matrix and the relationship between

determinant of exponential of a square matrix and the exponential of the trace of the same matrix.

3

4 Tensor product of two matrices (Kronecker product). 2

5 Tensor product of two vector spaces. 6

6 Modules as a generalization of vector spaces. 6

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7 Modules over principal ideal domains. 6

Total 30

D. Teaching and Assessment

1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods

Code Course Learning Outcomes Teaching Strategies Assessment Methods 1.0 Knowledge and Understanding

1.1 Definition and properties of the matrix exponential and its determinant

Lecture and Tutorials Exams, quizzes 1.2 Describe the tensor product of two

matrices.

Lecture and Tutorials Exams, quizzes 1.3 Describe the tensor product of vector

spaces and its basic properties.

Lecture and Tutorials Exams, quizzes 1.4 Outline modules, submodules,

quotients, and direct sum of modules

Lecture and Tutorials Exams, quizzes

2.0 Skills

2.1 Demonstrate accurate and efficient use of advanced algebraic techniques

Lecture/Individual or group work

Exams, quizzes, Homework 2.2 Calculate the matrix exponential and

its determinant

Exams, quizzes, Homework 2.3 Perform tensor product.

.

Exams, quizzes, Homework 2.4 Distinguish between vector spaces and

modules.

Exams, quizzes, Homework

3.0 Values

3.1 Analyze quantitative data verbally, graphically, symbolically and numerically

Exams, quizzes, research essays 3.2 Communicate quantitative data

verbally, graphically, symbolically and numerically

Exams, quizzes, research essays 3.3 Integrate appropriately technology

into mathematical processes

Exams, quizzes, research essays 3.4 Generalize mathematical concepts in

problem-solving through integration of new material and modeling

Exams, quizzes, research essays 2. Assessment Tasks for Students

# Assessment task* Week Due Percentage of Total

Assessment Score

1 Midterm Exam 6th %25

2 Quizes and homeworks During semester %25

3 Final exam End of semester %50

*Assessment task (i.e., written test, oral test, oral presentation, group project, essay, etc.)

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6 E. Student Academic Counseling and Support

Arrangements for availability of faculty and teaching staff for individual student consultations and academic advice:

All faculty members are required to be in their offices outside teaching hours. Each member allocates at least 4 hours per week to give academic advice to students and to better explain the concepts seen during the lectures.

Students are required to complete the homework problems. Students are welcome to work together on homework. However, each student must turn in his or her own assignments, and no copying from another student’s work is permitted. Deadline extensions for homework will not be given. Students are encouraged to discuss with professor about homework problems.

F. Learning Resources and Facilities

1.Learning Resources

Required Textbooks

• Roman, Steven, S. Axler, and F. W. Gehring. Advanced linear algebra. Vol. 3. New York: Springer, 2005.

• Hoffman, Kenneth. Linear algebra. Englewood Cliffs, NJ, Prentice-Hall, 1971.

Essential References Materials

• Weintraub, Steven H. A Guide to Advanced Linear Algebra. No.

44. MAA, 2011.

• G. Strang, Introduction to Linear Algebra. 5^th Edition. Wellesley, MA: Wellesley-Cambridge Press, 2016.

Electronic Materials https://en.wikipedia.org/wiki/Linear_algebra

Other Learning Materials

Computing data for matrices such eigenvalues and eigenvectors using computer packages.

2. Facilities Required

Item Resources

Accommodation

(Classrooms, laboratories, demonstration rooms/labs, etc.)

Large classrooms that can accommodate more than 30 students or Online via Blackboard if the administration approved Online Teaching for this Course

Technology Resources

(AV, data show, Smart Board, software,

etc.) Data Show, Smart Board

Other Resources

(Specify, e.g. if specific laboratory equipment is required, list requirements or

attach a list)

Blackboard

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7 G. Course Quality Evaluation

Evaluation

Areas/Issues Evaluators Evaluation Methods Effectiveness of teaching and

assessment 

Students Direct

Quality of learning resources Students Direct Extent of achievement of

course learning outcomes

Faculty Member Direct

Evaluation areas (e.g., Effectiveness of teaching and assessment, Extent of achievement of course learning outcomes, Quality of learning resources, etc.)

Evaluators (Students, Faculty, Program Leaders, Peer Reviewer, Others (specify) Assessment Methods (Direct, Indirect)

H. Specification Approval Data

Council / Committee Council of the Mathematics Department Reference No.

Date