Scientific Computing (科學計算)

Roger Jang (張智星)

Introduction to the course (課程簡介)

隨著電腦科技的發達，各種多媒體的展示已經屢見不鮮，各種基於科學計算的相關應用也是撲天蓋地而來。為了讓同學們能夠在學習微積分、線性代數、機率之餘，能夠快速瞭解到這些數學的相關應用，我們開授了「科學計算」這門課，這個課程注重 computational thinking，可以讓同學們瞭解如何經由簡單的程式碼來解決複雜的計算問題（例如個人財務計算、影像資料壓縮、自然語言處理、網頁排序、分類、分群、內差、逼近、最佳化等），並能夠讚賞數學之美，並體會電腦程式力量之強大。

Objective and Syllabus

The objective of this course is to provide the basic concepts, theory, and practice of scientific computing, which can be divided into 3 areas:
1. Programming (in MATLAB & Python):
   • Matrix computation
   • Programming paradigms
   • Visualization to present problems/solutions effectively
2. Methodologies:
   • Zero finding
   • Least-squares estimate
   • Approximation
     • Polynomial fitting
     • General linear equation fitting
   • interpolation
   • PDF modeling
     • 1D Gaussian (normal) density function
     • ND Gaussian (normal) density function
     • Gaussian mixture models (GMM)
   • Data clustering
     • Hierarchical clustering
     • K-means clustering
     • Vector quantization
   • Pattern recognition
     • K-nearest-neighbor classifier
     • Linear classifier
     • Naive Bayes classifier
     • Quadratic classifier
     • GMM-based classifier
   • Principal component analysis
   • Linear discriminant analysis
   • Dynamic programming
     • Longest common subsequence
     • Edit distance
     • Dynamic time warping
   • Numerical optimization
3. Applications:
   • Image data compression
   • Page/team ranking
   • Natural language processing
   • Color correction
   • Object detection
   • Pattern recognition
   • Dimensionality reduction