[修讀原因]

一個好的 Data Engineer, 與其說要去實作, 去做設計, 去做效能調校, 去做監控與維護好一個系統, 要完成這些都是須要一些數學基礎的, 有了這些數學才真的能夠把這部份做好. 只是這些數學有那些呢?

• Signal Analysis (Time Series)
• Distribution (Statics)
• Finite State Machine (Discrete Mathmatics)
• Network Analysis (Graph Theroy)
• Real Function Analysis (Statics)

這些都是用來讓你更了解系統的數學, 了解系統狀況才能夠做好效能調校, 做好調校才能做進一步的資料分析, 所以這也是很重要的基礎.

只是這些數學都是散見在各個數學範籌, 雖然都不會脫離之前講的, 只是對細節更深入一些, 這邊介紹幾個相關類型的書給大家.

[基本資訊]

• 課程題目:
• 大學學程:
• 困難度: ＊＊＊＊
• 必要度: ＊＊＊
• 所須時間: ＊＊＊
• 建議書籍: Analytical Network and System Administration: Managing Human-Computer Systems
• 建議書籍: Information Theory, Inference and Learning Algorithms
• 建議書籍: Discrete-Time Signal Processin

[基本介紹]

所有的電腦都是透過信號來處理, 這處理都是須要時間的, 所以 Time Series Signal 不只是要處理資料所使用, 更是在設計系統很必要的功能, 這包含下面所須要的數學:

13. Differential equations
14. Difference equations
15. Transform theory
16. Time-frequency analysis – for processing non-stationary signals[2]
17. Spectral estimation – for determining the spectral content (i.e., the distribution of power over frequency) of a time series[3]
18. Statistical signal processing – analyzing and extracting information from signals and noise based on their stochastic properties
19. Linear time-invariant system theory, and transform theory
20. System identification and classification
21. Calculus
22. Vector spaces and Linear algebra
23. Functional analysis
24. Probability and stochastic processes
25. Detection theory
26. Estimation theory
27. Optimization
28. Numerical methods
29. Time series
30. Data mining – for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns

這些幾乎是沒有之前沒講過的, 但這就是所謂的 Mathematical methods applied in signal processing 大家應該不意外吧...

而這些都更須要資訊原理去架構, 所須要的數學有:

• Data Compression
• Noisy-Channel Coding
• Probabilies and Inference
• Neural Network
• Sparse Graph Codes

這上面都是兩本書的基本架構, 而學習原因是 Analytical Network and System Administration 的架構, 把這三本書相關概念學完, 系統與網路管理的能力會更上一層, 當然也包含數學.

[修習方式]

開放課程:

• http://videolectures.net/course_information_theory_pattern_recognition/
• http://moodle.epfl.ch/course/view.php?id=13431

電子書:

• http://www.e-reading.me/bookreader.php/141504/Analytical_Network_and_System_Administration:_Managing_Human-Computer_Systems.pdf
• http://books.google.com.tw/books?id=0uvKF-LT_tMC&source=gbs_book_similarbooks
• http://books.google.com.tw/books?id=ngk2OvNW6SIC&source=gbs_book_similarbooks

關鍵字:

• Information Theory
• Normalized frequency
• Bernoulli process
• Discrete system
• Sampling (signal processing)