Math 227 - Introduction to Linear Algebra

[Top]     [Home]             Instructor: Alex Degtyarev     Office: SA 130     Phone: x2135     Mail: no spam
The (common) make-up will take place on May 24 at 3:30, meeting at my office (SA-130). Please, keep in mind that I will not grade your make-up paper unless I have a report!
You can see your final papers on May 25 at my office. Final grades will be submitted on May 25 after 17:30. Obviously, no changes afterwards!!!
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  • Tentative course schedule * (Spring 2006)
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  • Exam rules and terms
  • Current quiz results   [NEW]
    • * This schedule is tentative. Depending on the class and/or requests of other related departments, I reserve the right to skip/fast forward certain topics in order to pay more attention to certain others
    ** Exam dates can be changed provided the request is filled in advance and majority of the class supports it
    Exam contents listed below are tentative and are subject to change (depending on the actual pace of the class)
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    Midterm I    (25%)   March 10, 2006 @ 1:40 pm    
    See:   [    important remarks]   [samples]   [room assignment]   (updated 07/03/2006)

    Topics covered (tentative): (updated 5/18/2001)
  • Systems of linear equations. Solving by Gaussian elimination* (row echelon form)** and Gauss-Jordan reduction (reduced row echelon form)
  • Matrices and matrix operations. The matrix form of a linear system
  • Invertible matrices; finding A-1. Invertibility of a matrix and properties of the corresponding systems
  • Special matrices (diagonal, triangular, symmetric): just the notions and their usage as hints
  • Determinants: elementary properties and evaluation
  • The cofactor expansion of a determinant
  • Applications of determinants: Cramers's rule and the formula for A-1

    Chapters:   1, 2
    * I do not request a particular way of solving a problem. However, keep in mind that certain ways may be much easier than certain others :)
    ** Remember that this is your primary tool for most problems in linear algebra
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    Midterm II    (25%)   April 28, 2006 @ 1:40 pm    
    See:   [    important remarks]   [samples]   [room assignment]   (updated 12/07/2004)

    Topics covered (tentative)*:
  • Geometric vectors: definition, dot- and cross-product, length, angle, etc.
  • Lines and planes in the space: general equations in various forms; finding an equation from various data (line through 2 points, plane through 3 points, etc.)**
  • Various distance and angle related problems (distance from a point to a line or a plane, angle between lines, planes, etc.)**
  • Euclidean n-space: the concept, arithmetics, matrix notation, the Cauchy-Schwartz inequality and its applications, extending the geometric notions (norm, angle, Pythagorean theorem, etc.)
  • Linear transformations: definition (and understanding), properties, relation to matrices and linear systems, one-to-one and onto transformations, invertibility and the inverse transformation
  • Eigenvalues and eigenvectors
  • General vector spaces: definition, examples,*** basic properties
  • Subspaces: detecting a subspace, solution (null-) space, span (including the notion of linear combination); representing the solution space as a span

    Chapters:   3, 4, 5 (1-2), 7 (1)
    * The material covered in Midterm I is fully included
    ** As it is impossible to list all problems, actual understanding of the subject would be helpful
    *** Primary examples are Rn , Pn , and P. All other notation (including various function and matrix spaces) will be explained
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    Final    (40%)   May 23, @ 3:30 pm    
    See:   [    important remarks]   [samples]   (updated 05/18/2006)

    Topics covered (tentative)*:
  • Linear independence; relation to homogeneous linear systems
  • Basis and dimension
  • Row, column, and nullspace of a matrix; rank and nullity

    Chapters:   5 (3-6)
    * The material covered in Midterm I and Midterm II is fully included
    Quizzes and Homeworks     (10%)   Quizzes are to be held weekly on Tuesday in class (10-15 mins at the end) except midterm weeks. Hopefully, 8 to 9 quizzes will be given, with disregarding the two worst.

    All questions regarding the quizzes are to be directed to the assistant. The assistant is instructed to  give no credit  to identical papers. The same applies to the exams.
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    Remarks    

    Most exam problems will be taken from the textbook. Solve them in advance, and you will do well! Same concerns quizzes.
    During the exams please keep in mind the following:
  • Calculators are  not  allowed 
  • Identical solutions (especially identically wrong ones) will  not  get credit. I reserve the right to decide what "identical" means. You still have the right to complain 
  • Do not argue about the distribution of the credits among different parts of a problem. I only accept complaints concerning my misunderstanding/misreadung your solution 
  • Show all your work. Correct answers without sufficient explanation might  not  get full credit 
  • Indicate clearly and unambiguously your final result. In proofs, state explicitly each claim 
  • Do not misread the questions or skip parts thereof. If you did, do not complain 
  • If you believe that a problem is misstated, do not try to solve it; explain your point of view instead. However, do not take advantage of this option: usually problems are stated correctly! 
  • Each problem has a reasonably short solution. If your calculation gets completely out of hand, something must be wrong (e.g., you might have chosen a wrong basis) 

    Grading policy     *
    I will take off a few (2-3) points for arithmetical mistakes. However,  a lot  of points will be taken off for `obvious' mistakes, i.e., either those that you can easily avoid or those showing a deep misunderstanding of the subject. This includes, but is not limited to, the following:
  • Wrong dimension in a physical problem
  • Things that don't make sense (like operations on matrices of incompatible sizes, determinants of non-square matrices, etc.)
  • Inverse matrix with a row/column full of "0"s
  • An eigenvalue without eigenvectors
    Furthermore, solving a different problem (other than stated), even if perfect, will give you  no credit 
    * Of course, this only applies to problems that I am grading personally
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    Last update: January 31, 2006