SECTION                          INSTRUCTOR                  OFFICE                 
     L0101                                   S. Cohen                               TBA
     L0201                                   E. Pujals                              SS4061
     L0202                                   M. Saprykina                         TBA
     L5101                                   R. Stanczak                          NC68A

Course Administrator
 R.Stanczak, office hours : Mon. 3-4, Tue. 3:30-4:30, Fri. 3-4 .

Home page
 http://ccnet.utoronto.ca/20051/mat223h1s

Brief Description
This is the first undergraduate course in linear algebra taken by students from a
variety of disciplines. The course covers: matrix arithmetic and linear systems,
vector space Rn and function spaces, determinants and diagonalization,
orthogonality in Rn and least squares, introduction to linear mappings.
Students will be required to understand all theoretical concepts involved, be
able to solve the standard problems in each section and be able to do simple,
short proofs of particular statements.

Textbook
W.K. Nicholson: Linear Algebra with Applications , 4th edition.

Supplementary Texts
W.K. Nicholson: Partial Solution Manual (for 4th edition)
R. Stanczak: Linear Algebra I, Study Manual  -
                          available at DISCOUNT  TEXTBOOKS , 229 College St.

Tutorials
Every student must be registered in one tutorial section. You may register in one
of the tutorial time slots through ROSI before the end of the second week of
classes. Registration or any changes to your tutorial time after the second
week of classes must be done in person through  R. Stanczak during his
office hours.
By the end of the third week of classes you will be enroled in one of the tutorial
sections. Once your designated tutorial has been posted on the bulletin board
(south-west part of the main floor of Sidney Smith Hall) and on the web site, you
will not be allowed to switch sections.
Tutorials start at the beginning of the 4-th week of classes.
(week beginning Jan.24).. During your tutorials the T.A.will discuss with you
some problems from the list below. Feel free to ask questions about the problems
you have most difficulty with.
There will be 3 quizzes , typically 40  minutes long, each graded out of  20.
Questions given on quizzes will be given out of the list of suggested problems.
In questions where only calculations are required, numbers may be changed.
The best two out of three quizzes will determine your tutorial mark.
You must write your quizzes in the tutorial section in which you are registered,
or your mark will be recorded as zero. There will be no make up quizzes.

Midterm test
There will be one 110 min midterm test common to all students, during the
seventh week of classes. Make sure to see the schedule below for the exact
day/time. If you have a time conflict, contact the course administrator as soon
as possible. Place of the test will be advertised two weeks in advance. There
will be no make up tests.
The test will be graded out of 60 and will consist of two equally weighted parts.
The first part will have 10 simple multiple choice questions in which only your
final answer will count. The second part will consist of  4-5 written questions in
which you have to present your solution in full. In the second part, your mark
will depend on the clarity of your presentation and, of course, on the correctness
of your solution.

Remarking Procedure
Your test/quiz  will  be returned to you in the tutorial section in which you are
REGISTERED as soon as they are marked, usually within one week. If you have
any questions about the marking of the second part of your test, you will have to
return your test to your T.A. within 10 min indicating on the front page which
question you want to be remarked. If you take your paper with you, no one will
look at it again. The same procedure applies to quizzes. You should collect your
test/quiz submitted for remarking from the course administrator within three
weeks otherwise your mark cannot be changed. No test will be remarked unless
the original answers were written in ink.
The answer sheet of the first part of your test will be removed from your paper 
so you are advised to mark your answers by each question also. Contact the
course administrator directly if you want to see your answer sheet anyway.

Missed Term Work
If you miss the test/quiz for a legitimate reason which you can document
(i.e. Doctor's note etc)your grading scheme will be adjusted by increasing the
final exam component of your mark. Basically the mark from your final exam
will replace the "0" on the respective missed piece of term work.
But under no cicumstances can the final exam count for more then 80% of your
final mark. The proof (like doctor's note) should be submitted to the course
administrator not later then 7 days after the test/quiz was written.

Grading Scheme
The format of the final exam will be similar to the format of the midterm test and
will be graded out of  100. Your final grade will be determined as follows
                      Tutorials (quizzes)                     - 20%
                      Midterm Test                           -  30%
                      Final Exam                                - 50%
 
 

                   SCHEDULE AND SUGGESTED PROBLEMS
You should solve, at the very minimum, the problems on the list below. To
prepare well for the test and the final exam you should solve the problems
from the Linear Algebra I , Study Manual. Your instructor may be slightly
ahead or behindthis schedule but the topics covered on the quizzes and the
test will be the same for all students.

WEEK  1 (beginning Jan.03) Lecture: Matrices (p.29-42),
                                                             Systems of Linear Equations.
2.1 # 3, 5, 9(b), 10, 13, 14, 15, 17, 18, 19
2.2 # 1, 2(b), 4, 5, 6
1.1 # 1(b), 2(d), 4, 6, 8(b), 11, 12, 16
1.2 # 1, 3(d), 5(a)(e)(g), 7(b), 8(a)(d), 9(c)(d)(e)(f), 11(e), 12, 13, 15, 21

WEEK 2 (beginning Jan.10) Lecture: Matrices and Systems  (cont.)
1.3 # 1, 2(b), 2(d), 3, 4, 5, 6, 8
2.2 # 8(b), 9, 10(a), 11, 12, 13, 14, 17, 20, 25, 26, 28, 33, 34, 35, 36, 37

WEEK 3 (beginning Jan.17) Lecture: The Inverse and Elementary Matrices
2.3 # 4, 5, 9, 10, 12, 16, 22, 25, 27, 29, 31, 32, 33, 34, 35, 36, 37, 38(a), 38(b), 40
2.4 # 1, 2, 3, 6(b), 7(b), 8, 13, 18

WEEK 4 (beginning Jan.24, tutorials start)  Lecture: Vector Space Rn.
4.1 # 4, 9, 10, 11, 13, 16, 18
5.1 #1, 2, 3, 4, 5, 6

WEEK 5 (beginning Jan.31, QUIZ#1 - covers 1.1-3, 2.1-3) Lecture: Bases,
                                                                                                            Dimension.
5.1 # 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26
INSERT A  - all exercises
NOTE: Skip the second part of proof in Ex.17(sec.5.1), as in the vector space
             structure the only operations defined are  (a) addition of vectors
                                                               (b) multiplication of a vector by a scalar
 

WEEK 6 (beginning Feb.07) Lecture: Rank. Introduction to Euclidean n-space
5.2 # 1, 2, 3, 4, 5, 7, 10, 11, 12, 13, 14, 16, 17
4.2 # 7, 10, 14, 15, 16, 23, 25, 29      4.3 # 6(a)(b), 9, 11   
7.1 # 1, 3(d), 4, 5(b), 6,  7, 8
NOTE: In section 5.2 read pages 197 to 201 only plus Theorem 5 and example 5
Remark: Sections 4.2 and 4.3 (pages 165,166 only) are for self study as the
               topics there should be familiar to you from a high school. Instructors
               may (at their discretion) cover parts of those sections.

R E A D I N G   W E E K

WEEK 7 (beginning  Feb.21)   Lecture: Gram-Schmidt algorithm, Projections.
7.1 # 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 23, 27 , 29, 30, 31

WEEK 8 (beginning Feb.28)   Lecture: Least Squares.
                                                               Introduction to Linear Transformations.
7.8 # 1, 5, 7(a)          4.4 # 1(d), 2(b), 3
Note: You do not need to read section 4.4
5.4 # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 22, 23

WEEK 9 (beginning Mar.07) Lecture: Linear Transformations (cont).
                                                               The Determinant.
INSERT B - all exercises.
3.1 # 1, 6, 7, 10, 11, 12, 13, 14, 18, 24

WEEK 10  (beginning Mar.14, QUIZ #2- covers 7.1, 7.8, 4.4, 5.4)
                                               Lecture: The Determinant (cont.)
3.2 # 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 17, 18, 21, 22, 23, 24, 25, 28, 30

WEEK 11 (beginning Mar.21) Lecture: Eigenvalue Problem, Diagonalization.
(skip the subsections: Linear Dynamical Systems, Complex Eigenvalues,
Symmetric Matrices)  
3.3 # 1, 3, 4, 6, 8, 9, 11, 12, 13, 14, 16, 17, 20, 21, 23, 25
5.3 # 1, 2, 3, 4, 7, 8, 9, 10

WEEK 12 (beginning Mar.28, QUIZ # 3-covers  INSERT B, 3.1, 3.2)
                                                Lecture: Function Spaces
NOTE: Having covered the space Rn (all proofs here mimic the proofs in Rn)
            you have to read in chapter 6 the following parts only: sec.6.1 - the
            definition of the vector space and examples 5, 6 ; sec.6.2 - examples
            4, 5, 6, 7, 8, 9 ; sec.6.3 - examples 7, 9 and sec.6.4 - examples 1, 3.
6.2 # 1(b)(c)(f), 3, 6, 7(a)(b), 8, 9(b)
6.3 # 2(a)(e)(f), 3, 5(d), 6(c)(d), 11(a), 12(a)(b)(c)
6.4 # 2(b), 3(d), 6

WEEK 13 (beginning Apr.04) Lecture: Application to Differential Equations,
                                                                 Revision
NOTE: Just brief introduction, very simple cases considered.
6.6 # 1(d)  and  7.9 # 1(b)