National Tsing Hua University
Institute of Information Systems & Applications

Course Title: ISA 530500: Computational Mathematics       Group Members    

Classes: 3:30-5:20 Monday, 10:10-11:00 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       Solving Ax=b    
    Exercise 1 and Solutions    
    C Program for A=LU     Matlab Code for A=LU    
    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   
   Matlab for Problem Solving   
7. Fundamentals     Basic Probabilities     Histogram of Lenna Image     Histograms of Color Images     Matlab Code    
   Exercise 6   Exercise 6 and Solutions  
8. Discrete and Contiunous Distribution Functions      Plots of p.d.f.    
    Matlab Code for 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    
    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     Clustering Big Data (Video from YouTube by Prof. A.K. Jain, MSU)
     Data Mining and Machine Learning     Machine Learning    

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       Data for Problem 1      
    Homework 2       Partial Solution 2       Matrix T       Matrix B       Matrix A       Matrix C      
        Drive program for shiftedQR       shiftedQR Codes       C Program for Computing Eigenvalues/Eigenvectors
    Homework 3       Solution 3      
    Homework 4       Solution 4            

  • (30%) Tests
    Test 1     Solution 1    
    Test 2    

  • (30%) Presentation and Report
    GroupNumber.ppt (no more than 12 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 9, 2019
        Texture Data       Gene Expression Data      
    Updated on December 12, 2018