Computer Science 132 - Geometric Algorithms









2013-01-17lecture:
introduction &
motivation
  • course organization
  • lecture notes
  • high-level overview of course material
  • models, systems, and system states
  • review of algebra of real numbers
  • vectors and vector addition
  • related readings:
    • [Lay 2012]: 1.1; 1.3
2013-01-22lecture:
vectors
  • lecture notes
  • more about algebraic properties
  • more review of logical formulas
  • vector addition & scalar multiplication
  • vector norms and dot products in R2
  • linear dependence and independence
  • related readings:
    • [Lay 2012]: 6.1
    • [Bretscher 2009]: 1.3.6; 5.1; A.4
2013-01-24lecture:
vectors
  • lecture notes
  • properties of equality
  • more proof examples and strategies
  • orthogonality of vectors
  • projections of vectors onto vectors
  • related readings:
    • [Lay 2012]: 6.1; 6.2
    • [Bretscher 2009]: 2.2; 5.1; 5.5.2
2013-01-29lecture:
vectors
  • lecture notes
  • review of orthogonal projections
  • vector negation and subtraction
  • lines (as sets of vectors)
  • vector equations and y = mx + b
  • related readings:
    • [Lay 2012]: 6.1
    • [Bretscher 2009]: 2.2
2013-01-31lecture:
vectors
  • lecture notes
  • lines and planes (as sets of vectors)
  • linear combinations of vectors
  • more practice with vector properties
  • related readings:
    • [Lay 2012]: 6.1
    • [Bretscher 2009]: 2.2
2013-02-04
2013-02-05lecture:
matrices
  • lecture notes
  • linear combinations in applications
  • from linear combinations to matrices
  • interpretations of matrices
  • matrix operations and properties
  • related readings:
    • [Lay 2012]: 1.6; 1.10; 2.1
2013-02-07lecture:
matrices
  • lecture notes
  • review: maps and composition
  • matrix multiplication
    • derived dimension relationships
    • system states over time
  • some subsets of Rn×n and properties
    • identity matrix
    • scalar matrices
    • diaigonal matrices
  • related readings:
    • [Lay 2012]: 1.10; 2.1
    • [Bretscher 2009]: 2.1; 2.3
2013-02-12lecture:
matrices
  • lecture notes
  • invertible matrices
  • determinant & inverse of R2×2 matrix
  • related readings:
    • [Lay 2012]: 2.1; 2.2; 2.3
    • [Bretscher 2009]: 2.1; 2.3; 2.4
2013-02-14lecture:
matrices
  • lecture notes
  • more subsets of Rn×n and properties
    • upper triangular matrices
    • lower triangular matrices
  • Mv = w for M with various properties
    • M = LU
  • related readings:
    • [Lay 2012]: 1.2; 2.3; 2.5
    • [Bretscher 2009]: 1.2; 1.3; 2.4
2013-02-15
2013-02-19lecture:
matrices
  • lecture notes
  • elementary matrices & row operations
  • reduced row echelon forms of matrices
  • related readings:
    • [Lay 2012]: 1.2; 2.3; 2.5
    • [Bretscher 2009]: 1.2; 1.3; 2.4
2013-02-21lecture:
matrices
  • lecture notes
  • review of Python and homework
  • more on rref & row operations
  • more facts about invertible matrices
  • related readings:
    • [Lay 2012]: 1.2; 2.3; 2.5
    • [Bretscher 2009]: 1.2; 1.3; 2.4
2013-02-26lecture:
matrices
  • lecture notes
  • matrix PLU factorization
  • matrix transposition
  • orthogonal matrices
  • matrix rank
  • related readings:
    • [Lay 2012]: 1.2; 2.3; 2.5
    • [Bretscher 2009]: 1.2; 1.3; 2.4
2013-02-28lecture:
review
2013-03-01
2013-03-05
Tuesday
11-12:30 PM
midterm exam
    2013-03-07lecture:
    vector spaces
    • review of midterm problems
    • lecture notes
    • spans of vectors
    • equality of spans
    2013-03-12spring recess
      2013-03-14spring recess
        2013-03-19lecture:
        vector spaces
        • lecture notes
        • sets of vectors
        • span notation for sets of vectors
        • membership in spans
        • equality of spans
        • related readings:
          • [Lay 2012]: 4.1; 4.3
          • [Bretscher 2009]: 3.1.2; 3.2; 4.1
        2013-03-21lecture:
        vector spaces
        • lecture notes
        • equality of spans
        • abstract vector spaces
        • vector space of lines
        • related readings:
          • [Lay 2012]: 1.7
          • [Bretscher 2009]: 4.1
        2013-03-26lecture:
        vector spaces
        • lecture notes
        • sets of polynomials as vector spaces
        • fitting polynomials to points in R2
        • basis and dimension of a vector space
        • related readings:
          • [Lay 2012]: 4.3; 4.5
          • [Bretscher 2009]: 3.2; 3.3; 4.1
        2013-03-28lecture:
        vector spaces
        • lecture notes
        • basis and dimension of a vector space
        • orthonormal basis of a vector space
        • Gram-Schmidt process
        • related readings:
          • [Lay 2012]: 4.3; 4.5; 6.2; 6.4
          • [Bretscher 2009]: 3.2; 3.3; 5.1; 5.2
        2013-04-02lecture:
        vector spaces
        • lecture notes
        • projection onto a vector subspace
        • over- & underdetermined systems
        • homogenous & non-homogenous systems
        • related readings:
          • [Lay 2012]: 1.5; 6.2; 6.3
          • [Bretscher 2009]: 3.1.2; 3.2; 4.1
        2013-04-03
        2013-04-04lecture:
        vector spaces
        • lecture notes
        • least-squares curve fitting
        • related readings:
          • [Lay 2012]: 6.5; 6.6; 8.1
          • [Bretscher 2009]: 5.4
        2013-04-09lecture:
        linear
        transformations
        • lecture notes
        • distributed computation of least-squares
        • intersections & products of vector spaces
        • product spaces, relations, & maps
        2013-04-11lecture:
        linear
        transformations
        • lecture notes
        • domains, codomains, and images
        • linear transformations & examples
        • injections & surjections
        • related readings:
          • [Lay 2012]: 1.9
          • [Bretscher 2009]: 3.1; 3.2; 4.2
        2013-04-16lecture:
        linear
        transformations
        • lecture notes
        • projection as a linear transformation
        • injections & surjections
        • bijections and isomorphisms
        • matrices as linear transformations
        • related readings:
          • [Lay 2012]: 1.9; 2.9.1; 4.4.5
          • [Bretscher 2009]: 4.2; 5.4
        2013-04-18
        Monday sched.
        (section)
        practice
        quiz
        2013-04-23lecture:
        applications to
        linear systems
        • lecture notes
        • applications in communication
        • affine spaces
        • related readings:
          • [Lay 2012]: 8.1
        2013-04-24
        2013-04-25lecture:
        eigenvectors &
        eigenvalues
        • lecture notes
        • applications in optimization
        • fixed points and spaces
        • eigenvectors and eigenvalues
        • related readings:
          • [Lay 2012]: 5.1; 5.2; 5.4
          • [Bretscher 2009]: 7.1; 7.2; 7.3
        2013-04-29
        2013-04-30lecture:
        review
        2013-05-02lecture:
        review
        2013-05-08
        Wednesday
        12:30-2:30 PM
        KCB 106
        final exam