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20F Course Information, Summer Session I, 2oo8

  • Lecture: Monday, Tuesday, Wednesday, and Thursday 9:30-10:50am in Center Hall 113. The class runs from 3o June to 31 July; the last day to drop without a W is 11 July; the last day to drop with a W is 29 July.
  • Instructor: Amanda Beeson
  • Textbook: we will be using the third addition of Linear Algebra by D. Lay
  • Section: Tuesday 11:00-12:50pm in Center 105.
  • MATLAB: Thursday 11:00-12:50pm in the CLICS open lab in Galbraith Hall (on the Revelle campus). You will have 5 labs, each of which is worth 3% of your grade.
  • Teaching Assistant: Kristin Jehring
  • Homework problems will not be handed in, however, there will be weekly homework quizzes during the MATLAB section, worth 4% of your grade each (see calendar for details). Reading the sections of the textbook covered in class is considered part of the homework assignment. As a word of advice, reading in advance of the lecture can help clarify subject matter.
  • There will be a single midterm in lecture on Thursday, 17 July, worth 25% of your grade.
  • The final exam will be worth 40% of your grade; it will be held on Friday, 1 August from 7:00 to 10:00pm in TBA.
  • Overall your grade will be calculated according to the following rubric:
    homework quizzes 20%
    matlabs 15%
    midterm 25%
    final 40%
  • Academic dishonesty is considered a serious offense at UCSD. Students caught cheating will face an administrative sanction that may include suspension or expulsion from the university

    20F Syllabus
    1. Introducing Vectors and Matrices: In this section we will study the common problem of solving simultaneous linear equations. We will devise an algorithm to solve this problem and, in the process, reformulate the problem and begin our study of linear transformations.

      1. Solving systems of linear equations
      2. Matrices, row reduction, echelon form
      3. Vector equations
      4. The matrix equation $ A\vec{x} = \vec{b}$
      5. Solution sets of linear systems
      6. Linear independence
      7. Introduction to linear transformations

    2. Matrix Operations: In this section we learn to work with matrices. We also observe several equivalent conditions for deciding if a system of simultaneous linear equations has a solution.
      1. Matrix operations
      2. Inverse of a matrix
      3. Characterization of invertible matrices

    3. Determinants: In this section we learn what a determinant is, how to compute it, and a physical interpretation.
      1. Introduction to determinants
      2. Properties of determinants
      3. Cramer's rule for computing the determinant
      4. Volume of a parallelepiped

    4. Vector spaces and subspaces: In this section we abstract the ideas we developed in chapter two and arrive at the culmination of a broad study of matrices and linear transformations: The Invertible Matrix Theorem.
      1. Definitions
      2. Spaces associated to a linear transformation: null space, column space
      3. Linearly independent sets, bases
      4. Dimension of a vector space, rank of a matrix
      5. Subspaces of $ \mathbb{R}^{n}$
      6. Change of basis

    5. Eigenvectors and Eigenvalues: In this section we make a more detailed analysis of the action of a linear transformation.
      1. Introduction to eigenvectors and eigenvalues
      2. The characteristic equation
      3. Diagonalization

    6. Orthogonality and Least Squares: Up until now we have been focusing on how to tell if a matrix equation has a solution, and we have been able to say quite a bit about invertible matrices/linear transformations. Now we switch our focus a little to try to extend our results to matrix equations that do not have a solution. In fact, we will develop a method for finding a vector that is very close to being a solution.
      1. Inner product, length, orthogonality
      2. Orthogonal sets
      3. Orthogonal projections
      4. Gram-Schmidt process
      5. Least squares