Linear Algebra I
Math 261 - Fall 2018
Announcements
The semester is over.
About the course
Linear algebra is a central subject of mathematics which has applications not only in mathematics itself but also in statistics, economics, physics and engineering (just to name a few).
By the end of the course, the students should have a detailed understanding of how to use vectors, matrices and linear transformations to solve fundamental types of problems.
Schedule of Lectures and Office Hours
Lectures: Tuesday and Thursday between 13:40-15:30 in M13.
Attendance will not be taken during the lectures. However, I strongly suggest that you shall attend the lectures regularly.
Office hours: Tuesday between 10:40-12:30 in M141.
If these office hours are not suitable for you, then you shall send me an email to fix an appointment. You may also stop by my office. If I am suitable, I will be happy to answer your questions.
Grading
Your final letter grade will be determined by two midterms and the final exam. The tentative exam dates are as below.
Midterm 1 - November 6 (%30)
Midterm 2 - December 11 (%30)
Final - January 11 (%40)
Textbooks
I will use the following books when I prepare my notes and assign exercise problems:
The first textbook is Friedberg, Insel, Spence - Linear Algebra, 4th edition. It is available in the reserve part of the library with code QA184.F75.
The second textbook is Cemal Koç - Linear Algebra I which is the classical linear algebra book of our department.
Tentative Course Outline
You can find the tentative course outline below. For each week, we will attempt to cover the content of the indicated pages of Friedberg, Insel, Spence - Linear Algebra (4th edition).
(Oct 02, Oct 04) Introduction, Vector Spaces, Subspaces 1--23.
(Oct 09, Oct 11) Linear Combinations and Linear Equations, Linear Dependence and Linear Independence 24--41.
(Oct 16, Oct 18) Bases and Dimension, 42--57.
(Oct 23, Oct 25) Sums and Direct Sums 22, 23, 57, 58 Quotient Spaces 23, 58. (or Cemal Koç 202-214).
(Oct 30, Nov 01) Linear Transformations, Null Spaces and Ranges 64--78.
(Nov 06, Nov 08) The Matrix Representation of a Linear Transformation, Composition of Linear Transformations and Matrix Multiplication 79--98.
(Nov 13, Nov 15) Invertibility and Isomorphisms 99--109.
(Nov 20, Nov 22) The Change of Coordinate Matrix, Dual Spaces 110--126.
(Nov 27, Nov 29) Elementary Matrix Operations and Elementary Matrices, The Rank of a Matrix and Matrix Inverses 147--167.
(Dec 04, Dec 06) Systems of Linear Equations - Theoretical Aspects 168--181.
(Dec 11, Dec 13) Systems of Linear Equations - Computational Aspects 182--197.
(Dec 18, Dec 20) Determinants of Order 2, Determinants of Order n 199--221.
(Dec 25, Dec 27) Properties of Determinants 222--243.
(Jan 01, Jan 03) Some Examples.
Suggested Problems
The following is a list of suggested problems from our textbooks. These questions are from the first textbook, namely Friedberg, Insel, Spence - Linear Algebra, 4th edition.
Section 1.2: 1, 3, 4, 7, 8, 13, 14, 18, 19, 21.
Section 1.3: 1, 3, 5, 6, 8, 9, 11, 12, 15, 18, 19, 22.
Section 1.4: 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15.
Section 1.5: 1, 2, 3, 6, 8, 9, 13, 15, 18.
Section 1.6: 1, 2, 3, 4, 6, 7, 9, 11, 13, 14, 15, 16, 22, 24.
Direct Sums: Questions 24-30 from Sec. 1.3 and 29-34 from Sec. 1.6.
Quotient Spaces: Questions 31 from Sec. 1.3 and 35 from Sec. 1.6.
Section 2.1: 1, 4, 5, 6, 9, 10, 11, 12, 14, 15, 17, 18, 20, 21, 22.
Section 2.2: 1, 2, 3, 5, 9, 10, 13, 14, 16.
Section 2.3: 1, 3, 4, 9, 11, 12, 13, 16, 17.
Section 2.4: 1, 2, 3, 5, 6, 7, 14, 15, 16, 19.
Section 2.5: 1, 3, 4, 5, 7, 10.
Section 2.6: 1, 2, 3, 4, 5, 8.
Section 3.1: 1, 3, 5, 6, 8, 9.
Section 3.2: 1, 3, 4, 5, 6, 7, 11, 14, 19.
Section 3.3: 1, 3, 4, 5, 6, 7, 8, 10.
Section 3.4: 1, 2, 3, 4, 5, 8, 9, 10, 11, 14.
Section 4.1: 1, 2, 4, 7, 9, 11.
Section 4.2: 1, 7, 14, 16, 18, 21, 23, 25.
Section 4.3: 1, 3, 4, 5, 9, 10, 12, 17, 20, 22, 25.
Section 4.4: 1, 4, 6.
Make-up and NA policy:
Only one make-up examination will be offered. The excuse for not attending an examination must be proved with documents. The make-up examination will take place shortly after the final exam. If you have missed both midterms, your letter grade would be NA. If you receive NA, then you can not take the final exam and the makeup.
SageMath
The software SageMath is very simple to learn and
extremely strong to do computations with.