SYLLABUS


 

Course:        MATH 344  Linear Algebra               Term:   Winter 2010-11              Meets:   MWF 9:20-10:30

 

Instructor:   Craig Kalicki       Office:   H-284      E-mail:  craig.kalicki@briarcliff.edu       Phone:   279-5541

 

Text:            Kolman and Hill,  Introductory Linear Algebra: An Applied First Course , Eighth Edition,

                        Pearson Prentice Hall, c.2005  ISBN 0-13-143740-2

 

Prerequisites: 

 

Students in this course should have passed MATH 218 Calculus II or an equivalent course.

 

Goals of course:

 

This course is a survey of topics in linear algebra intended for students majoring in mathematics, physical
sciences, and pre-engineering.  Students in this course should expect to

   1)  become familiar with the basic concepts, theorems, and computational procedures of linear algebra.

   2)  gain an appreciation of linear algebra as a tool fundamental to many applications in mathematics and
           the sciences.

   3)  develop skills in the investigation and discovery of mathematical truths and in the construction of valid
           mathematical arguments.

   4)  achieve a degree of mathematical maturity necessary for success in other advanced mathematics
           courses.

 

Grading:       

Two exams @ 25%

50%

 

A   = 100 - 90

C+ =  73 - 70

Final exam

30%

 

A-  =  89 - 87

C   =  69 - 64

Assignments

20%

 

B+ =  86 - 83

C-  =  63 - 61

 

 

 

B   =  82 - 77

D+ =  60 - 57

Total

100%

 

B-  =  76 - 74

D   =  56 - 50 

 

Grading rubric:

 

The grading rubric below will be used to assess written work, including text assignments and exam
questions.

 

       Level

                Characteristics

 4     Superior

Solution is correct and clearly presented.
All essential steps are shown, are readable, and are in logical order.
Solution is free of irrelevant or redundant statements.

 3     Good

Method of solution is substantially correct and clearly presented.
Most essential steps are shown.
Minor computational or logical errors occur. 

 2     Adequate

Method of solution is flawed but mostly correct.
Some essential steps are not clearly stated or are omitted.
Mathematical tools are appropriate but incorrectly applied.

 1     Minimal

Solution is attempted but significant errors occur.
Mathematical tools are inappropriate or incorrectly applied.
Some essential steps are omitted.

 0     Unacceptable

Solution is omitted or an answer is given with no supporting evidence.

 

 

Expectations of students:

 

Exams and assignments will require that students demonstrate the ability to

   state precisely important definitions and theorems;

   supply illustrative examples of the concepts discussed;

   perform basic computational procedures;
   use the procedures to solve applied problems;

   use technology as a problem solving tool;

   verify elementary results involving the concepts discussed.

 

Clarity of expression is essential in presenting mathematics well.  Students are expected to observe the
standard rules of grammar and punctuation in all work that is handed in.

 

Some suggestions:

 

1)  Attendance at all class meetings is expected.  You will need to take some notes in class, but the basic
       lecture notes will be posted on BCU Online as the term progresses.  You may want to bring hard
       copy of the notes to class.

2)  Come to class prepared.  Read the text, paying particular attention to definitions of terms and
       examples.  Be prepared to discuss and present solutions of assigned problems.  Not all material that
       you are responsible for will be covered in class.

3)  Make reasonable attempts to solve most of the assigned problems.  Credit will be given for
       assignments handed in and selected problems will be graded.  Solutions of more difficult problems
       can be posted online if requested.  Assignments are to be handed in at the beginning of class on the
       date due.  No late work will be accepted except in cases of serious illness or family emergency.

4)  Make use of your instructor’s office hours.  Time constraints do not permit solution of all problems in

       class, so seeking help outside of class is encouraged.

5)  Use computing resources whenever appropriate as problem solving tools.  Have a graphing calculator

       available for use in class and on exams.  Many of the assigned problems may be done with the aid of

       graphing calculators or computer software. 

 

Learning outcomes:

 

Expected learning outcomes for this course are listed below.  Assessment of the degrees to which these

outcomes have been achieved will be done via written exams and graded homework assignments.

 

Students who have completed MATH 344 will be able to

   1)    perform standard operations involving matrices.

   2)    solve linear systems using matrix methods and technology.

   3)    solve applied problems involving linear systems.

   4)    compute and apply determinants.

   5)    perform and apply vector operations in n-space.

   6)    understand and apply linear transformations on n-space.

   7)    describe the effects of matrix operators on the plane.

   8)    compute and apply cross products in 3-space.

   9)    solve problems involving lines and planes in 3-space.

   10)  demonstrate understanding of the concepts of real vector space and subspace.

   11)  solve problems involving span, linear independence, basis, and dimension.
   12)  use matrices to do least-squares estimation.

   13)  compute eigenvalues and eigenvectors of a square matrix.

   14)  verify basic results involving eigenvalues and eigenvectors.

   15)  identify and analyze linear transformations on real vector spaces.

   16)  use matrices to analyze and apply linear transformations.

  

Course material:

 

Ch 1   Linear Equations and Matrices   [6 classes]

   Linear systems /  matrices /  Gaussian and Gauss-Jordan elimination /  matrix operations / properties of

   matrix operations /  inverse of a matrix.

 

Ch 2   Applications of Linear Equations and Matrices   [2 classes]

   Selected topics.

 

Ch 3   Determinants   [2 classes]

   Determinants / cofactor expansions / applications / adjoint of a matrix.


Ch 4   Vectors in Rn   [3 classes]

   Vectors in the plane /  vectors in n-space / length and angle /  dot products /  linear transformations.

 

Ch 5   Applications of Vectors in R2 and R3   [2 classes]

   Cross products /  lines and planes.

 

Ch 6   Real Vector Spaces   [6 classes]

   Real vector spaces /  subspaces /  linear independence /  basis and dimension /  rank of a matrix  /

   coordinates and change of basis /  orthonormal bases.

 

Ch 8   Eigenvalues, Eigenvectors, and Diagonalization    [2 classes]

   Eigenvalues of a square matrix /  eigenvectors /  diagonalization /  orthogonal matrices.

 

Ch 9   Applications of Eigenvalues and Eigenvectors   [2 classes]

   Selected topics.

 

Ch 10  Linear Transformations and Matrices   [3 classes]

   Linear transformations /  kernel and range /  matrix of a linear transformation /  affine transformations /

   fractals.

                                         



c.2010  by  Craig Kalicki PhD  Briar Cliff University  Sioux City IA  51104