CS070/CS170, Spring 2013
Numerical and Computational Tools for Applied Science
About Syllabus

This page will be updated frequently with current and upcoming topics.

Schedule

DateTopicsReferencesOutDue
March 26Introduction, class objectives and policies
HW 0
March 28Hands-on Introduction to Matlab HW 0
April 2
HW 1
April 4
April 9
HW 2HW 1
April 11
April 16Orthogonality
HW 2
April 18SVD
April 23Eigenvalue problem continued; PCA HW 3
April 25
April 30
Project ProposalHW 3
May 2
May 7No class
Project Proposal
May 9No class
May 14
May 16
May 21Project presentations:
  • Haddadan Shahrzad, Panotopoulou Athina, Sarroff Andrew
  • Kang Yaozhong, Li Tian, Liu Zheyu, Xing Yue
  • Zhang Rongxiao, An Chao, Feng Wenyuan, Li Yanan
  • Li Xin, Tan Jie, Zhou Jianfu
May 23Project presentations:
  • Hou Ruixuan, Li Jing
  • Jenkins Ira, Pierson Timothy
  • Cheng Yuting, Su Chengwei, Wang Xin, Wang Zhenghui
  • Miao Yusheng, Wang Qiuhan
May 28Project presentations:
  • Hansen Anders, Lachance Katherine
  • Madsen Thomas, Zupan Nejc
  • Chen Fanglin, Wang Rui
  • Mao Weijia, Xu Ye
May 29Final Project due
Final Project

Syllabus

  • Matlab, part I:
    basic arithmetic; vectors and matrices; matrix arithmetic; control structures; input/output; scripts and functions.

  • Linear Algebra, solving Ax=b:
    row and column picture; Gaussian elimination; matrix inverse; Gauss-Jordan; LU factorization and its applications; vector spaces; geometric interpretations of nullspace, rowspace, columnspace and left nullspace of a matrix; algorithms to compute the nullspace, rowspace, columnspace and left nullspace of a matrix.

  • Matlab, part II:
    data structures; 1-D plotting; 2-D images; 3-D surfaces; GUI programming.

  • Least-squares estimation:
    applications: linear and nonlinear regression, data fitting; the calculus view: system of normal equations; the linear algebra view: geometric interpretation of least-squares fitting via projection onto the columnspace.

  • Singular Value Decomposition:
    orthogonal bases and matrices; geometric interpretation of SVD; applications: dimensionality reduction, rank computation; least squares-fitting via SVD: the pseudoinverse.

  • Eigenvectors and eigenvalues:
    discussion of special cases: projection matrix, permutation matrix, triangular matrix; characteristic equation; remarks on iterative methods for eigendecomposition; application: solving recursive matrix equations; application: Principal Component Analysis; PCA via SVD; eigenfaces for face recognition.

  • One dimensional optimization:
    golden section search; Newton's method.

  • Multidimensional unconstrained optimization:
    steepest descent, discussion of methods for line search; Newton's method; conjugate gradient (geometric interpretation, derivation for quadratic function, generalization to arbitrary function).

  • Constrained optimization:
    method of Lagrange multipliers.

  • Linear programming:
    simplex algorithm.