Winter Semester: Jan. 2012
Course: MAT 120 A “Linear Algebra I“.
Prereq. MAT 30 or PURE MAT 30 or Equivalent
Course Description: See CUCA Calendar, or
Name: Dr. A. N. (Tom) Tavouktsoglou, PhD
Professor of Mathematics & Chemistry.
Coordinator of the Department of Mathematical and Computing Sciences.
Office: Faculty House F.H.-204 (main level).
Note: Students must phone (780-479-9360) and leave a voice message (or send an
e-mail) ahead of time, if they are unable to present themselves for a test/exam.
Office Hours: M/T/W/R./F: 12:05 – 12:55
Books & Supplies (Available at Concordia University College of Alberta Bookstore):
H. Anton, “Elementary Linear Algebra“, 10th Edition, John Wiley & Sons Inc.
A copy of “Mathematica® – Student Version” appropriate for the student’s own computer is recommended (but not required).
A copy of the Students’ Solutions Manual is on Reserve at the Library.
M/W/F.: 08:00 – 08:50, T: 08:00 – 09:15 in T-103 (Math Lab). Please be punctual!
Additional Bibliography: (optional – do NOT purchase)
D. C. Lay, “Linear Algebra and its Applications“, Addison – Wesley.
S. I. Grossman, “Elementary Linear Algebra“, Saunders College Publishing.
W. K. Nicholson, “Linear Algebra with Applications“, PWS Publishing Co.
G. Schay, “Introduction to Linear Algebra“, Jones and Bartlett Publishers.
G. Williams, “Linear Algebra with Applications“, Jones and Bartlett Publishers.
T. Lawson, “Linear Algebra“,, John Wiley & Sons Inc.
B. Kolman and D. R. Hill, “Introductory Linear Algebra with Applications“, Prentice Hall.
S. Axler, “Linear Algebra Done Right“, 2nd Edition, Verlag.
Many books on the subject are available at the Library. Students may wish to consult one or more of these as alternative sources of information, presentation, style, and for additional problems.
This schedule is tentative and subject to modifications.
Chapter numbers refer to the textbook.
Approximately one week’s notice will be given before each test.
Ch. 1 Systems of Linear Equations and Matrices
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination
1.3 Matrices and Matrix Operations
1.4 Inverses; Algebraic Properties of Matrices
1.5 Elementary Matrices and a method for finding A-1
1.6 More on Linear Systems and Invertible Matrices
1.7 Diagonal, Triangular and Symmetric Matrices
1.8 Application: Applications of Linear Systems (*)
1.9 Application: Leontief Input-Output Models (*)
Ch. 2 Determinants
2.1 Determinants by Cofactor Expansion
2.2 Evaluating Determinants by Row Reduction
2.3 Properties of Determinants; Cramer’s Rule
Test #1. Weight: 20%. Length: 50 min. Date: T.B.A.
Ch. 3 Euclidean Vector Spaces
3.1 Vectors in 2-Space, 3-Space, and n-Space
3.2 Norm, Dot Product, and Distance in Rn
3.4 The Geometry of Linear Systems
3.5 Cross Product
Test #2. Weight: 20%. Length: 50 min. Date: T.B.A.
Ch. 4 General Vector Spaces
4.1 Real Vector Spaces
4.3 Linear Dependence
4.4 Coordinates and Basis
4.6 Change of Basis
4.7 Row Space, Column Space, and Null Space
4.8 Rank, Nullity, and the Fundamental Matrix Spaces
4.9 Matrix Transformations from Rn to Rm
4.10 Properties of Matrix Transformations
4.11 Application: Geometry of Matrix Operations in R2 (*)
4.12 Application: Dynamical Systems and Markov Chains (*)
Ch. 5 Eigenvalues and Eigenvectors
5.1 Eigenvalues and Eigenvectors
Test #3. Weight: 20%. Length: 50 min. Date: T.B.A.
(*) Optional – If time permits
Final Examination (cumulative). Weight: 40%. Length: 2 hours.
Date: as per Final Exam Schedule issued by the Registrar’s Office.
Students should use the math lab outside classroom time as much as possible. The assigned homework includes problems that need to be done on the computer. Tests and exams will also include questions that need to be answered using the computer and Mathematica®.
Students should know how to access their e-mail ”firstname.lastname@example.org‘‘ and to check it regularly. Instructors use it to send course announcements to students.
The instructor regrets that he is unable to answer assignment questions over e-mail.
Cellular Telephone Policy:
All cellular telephones should be de-activated upon enrty into any classroom or lab. A cellular phone may be left on, only with the express permission of the instructor. Permission MUST be obtained before the class commences. During tests, cellular phones must be de-activated, placed in the student’s bag, and the bag left at the front of the class.
Tests/Exams may not be missed. There are NO MAKE-UP TESTS.
Students must inform the instructor ahead of time by telephone (leave a message at 780-479-9360) or by e-mail (email@example.com), if unable to present themselves for a test due to illness or other serious extenuating circumstances.
Students must contact the instructor in person as soon as possible after a missed test. At that time, they should present a physician’s note or other appropriate proof of the reason the test was missed. In this case, the weight of the missed test will be added to the final exam.
A missed test is considered non-excused, if either rule 2 or 3 above has not been adhered to. The missed test in this case is assigned a grade of zero.
All tests/exams are closed book.
Use of calculators is NOT permitted. Use of Mathematica® is permitted and/or required.
All Concordia University College of Alberta rules and regulations apply; in particular the ones regarding Academic Honesty. See CUCA Calendar.
Each lecture commences with a brief, point-form review of material covered in the previous lecture.
Question period: to clarify and explain concepts further, and to solve homework problems.
Theoretical presentation and treatment of new material.
How to Do Well:
Do not skip classes. Attend regularly. If you miss a class due to illness, obtain the notes and do the homework as soon as possible.
Try to read ahead by one lecture.
In class, pay attention, scrutinize every sentence or statement, never be embarrassed to ask.
Look up your notes as soon as possible after a lecture.
Study systematically, using pencil and paper; do not simply read.
Study notes and textbook carefully. Make sure that you have understood a concept well, before proceeding to the next one. Test your understanding of the concept by mentally defining it or pretending to explain it to someone else; be clear, concise and precise.
After studying solved examples, whether from your textbook or notes, make sure that you can solve the same problems independently.
Try the homework problems after you have done steps 6 and 7 above.
If a particular problem gives you trouble, leave it for a while, and come back to it at a later time (or next day). If still unsuccessful, ask in class. If questions still persist, discuss them with your colleagues, and seek help from your professor.
Use the math lab on a regular basis for your homework and for computer practice.
Working in small groups often helps, provided the group participants are all willing to actively contribute to the work and discussions, and they are not simply passive recipients of work done by others.
Remember… Question time is all the time! Ask!
Study regularly. Do not “fall behind”. Every topic is built on the previous one.
Do not cram before exams. Exams are designed to test your understanding of the material and your competence in the course according to established criteria and standards; they are also meant to rank students according to their performance in the course. They are not meant to trick or fool them.
Review often. Reviewing enhances the understanding, aids learning and builds up confidence.
Enjoy the course! I wish you well!
The weights of tests/exams are indicated under “Syllabus/Tests/Exams” above.
Tests/exams are marked out of 100.
The final weighted average is calculated as a percentage and reported on the alpha grading scale as follows:
98 – 100
95 – 97
90 – 94
85 – 89
80 – 84
75 – 79
70 – 74
65 – 69
60 – 64
55 – 59
00 – 49
The Bell curve will NOT be applied. Students know their standing in the course at any point in time as a result of their marks in the tests. Marks are not scaled.
Assignments are given on a regular basis. However, they are not collected or graded. It is the responsibility of the individual student to do his/her homework.
All final marks will be reported on the Four-Point Grading Scale as follows (also see Calendar):
Four-Point Grading Scale
Grade Point Value
When difficulties arise:
If you feel you need help, do not hesitate to seek it. Here is a list of people who can assist you in various circumstances…
About the course… Contact your professor, Dr. A. N. (Tom) Tavouktsoglou, F.H.-204, Tel. 780-479-9360, firstname.lastname@example.org
General academic or personal… Contact the Associate Vice President of Student and Enrollment Services, Dr. Jonathan Strand, email@example.com
Psychological, Personal… Contact the Campus Counselling Psychologist, Barbara Van Ingen, firstname.lastname@example.org
Spiritual, Pastoral… Contact the Campus Chaplain, Rev. Dr. Garry Dombrosky email@example.com
Career Counseling… Contact our campus career practitioner, Ms. Doreen Kooy,
Assistance in writing… Make an appointment by contacting Student and Enrollment Services.
Dr. Vladimir Pitchko, Associate Professor of Chemistry, Chair of the Science Division,
F.H. – 305, Tel.: 780-379-9376, firstname.lastname@example.org