National Tsing Hua University
Institute of Information Systems & Applications

Course Title: ISA 530500: Computational Mathematics       Group Members    

Classes: 3:30-5:20 Monday, 10:10-12:00 Wednesday at Delta Bldg 102

Credits: 3 (Fall, 2018)

Instructor: Dr. Chaur-Chin Chen, http://www.cs.nthu.edu.tw/~cchen

Tel/E-mail: (03) 573-1078, cchen@cs.nthu.edu.tw

Prerequisites: Calculus (I,II), C/C++, Data Structure, [Linear Algebra, Matlab, Java, Python]

Contents:
1. Course Description     Background Review    
    Prepare a technical paper     2016 Image Sharing     2016 Steganography     2015 Data Visualization
     Matlab for Image I/O      6 Images by Matlab
     ORLface     NTHUface     300x300 fingerprint     Tiff Lenna     Color Koala     Microarry    
2. Solving Linear Systems of Equations     Exercise 1 and Solutions    
    gepp.c for solving Ax=b     Test input for gepp.c    
3. Determinants     Exercise 2 and Solutions    
4. Vector Space and Linear Transform    Exercise 3 and Solutions    
5. Orthogonality     dataQua.txt     Matlab Code Quadratic Curve Fit    Plot of Data dataQua     Exercise 4 and Solutions    
6. Eigenvalues and Eigenvectors    C Program for Computing Eigenvalues/Eigenvectors    Exercise 5 and Solutions    
7. Fundamentals     Basic Probabilities     Histogram of Lenna Image     Histograms of Color Images     Matlab Code    
    Exercise 6 and Solutions  
8. Discrete and Contiunous Distribution Functions       Matlab Code to plot p.d.f     Plot of p.d.f       Table of N(0,1)     Table of \chi^2(r)    
   Exercise 7     Key for Exercise 7     Exercise 8     Key for Exercise 8    
9. Multivariate Distributions     Sampling Distributions     Matlab Code for 2d-Gauss Distribution    A 2d-Gaussian Distribution
   Exercise 9    Key for Exercise 9   
10. Parameter Estimation      
11. Principal Component Analysis and Linear Discriminant Analysis       PCA and LDA (pdf)     ACEAT Paper    
      data8OX       dataIMOX       dataIRIS       Matlab Code for PCA     Matlab Function for PCA     Matlab Code for LDA    
12. Cluster Analysis        Data Mining and Machine Learning    Machine Learning    Pattern Recognition    Data Mining

Textbooks:
1. Lecture Notes
2. H. Anton and C. Rorres, Elementary Linear Algebra with Supplentary Applications, International Student Version, John Wiley and Sons (11e, 2015)
3. S. Leon, Linear Algebra with Applications, Global Edition (v9, 2015).
4. D. Hanselman and B. Littlefield, Mastering MatLab (2012)
5. S. Ghahramani, Fundamentals of Probability with Stochastic Processes, Prentice-Hall, (3rd ed., 2005)
6. S. Ross, Introduction to Probability and Statistics for Engineers and Scientists, Academic Press, (4th, 2009)

References:
1. C. M. Bishop, Pattern Recognition and Machine Learning (2006)
2. J.A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge Press (2006)
3. A.K. Jain and R.C. Dubes, Algorithms for Clustering Data, Prentice-Hall (1998+)
4. T. Hastie, R. Tibshirani, J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer (2001)
5. R.V. Hogg and E.A. Tanis, Probability and Statistical Inference, Pearson International Edition (8e, 2010)
6. S. Theodoridis and K. Koutroumbas, Pattern Recognition, 4th ed. Academic Press, 2010

Grading:
  • (40%) Assignments and Class Attendance
    Homework 1       Solution 1      
    Homework 2       Solution 2       Matrix T       Matrix B       Matrix A       Matrix C      
        shiftedQR Codes             C Program for Computing Eigenvalues/Eigenvectors
    Homework 3       Solution 3      
    Homework 4       Solution 4            

  • (30%) Tests
    Test 1     dataX.txt     dataY.txt    
        Matlab code for P1       Solutions for P1       Matlab code for P2       Solutions for P2      
        Matlab code for P3       Solutions for P3       Matlab code for P4       Solutions for P4      
    Test 2     Solutions for Test 2     Performance on Test 2      
    Matlab for Problem Solving    

  • (30%) Presentation and Report
    GroupNumber.ppt (no more than 10 slides) is submitted in an e-mail attachment     Oral Presentation during 15:30-18:20, Monday, December 24, 2018
    A Sample PPT Page

    Visualization of Projection and Clustering     8OX Data       dataIRIS       Wine Data       Due By 11:59 Wednesday, January 2, 2019
    Updated on June 3, 2018