數學為科學之母一點都沒錯，不管未來想念哪一塊領域，數學能力將會扮演很重要的角色。基礎科學是相對枯燥的，然而大部分的我們都不是讀基礎科學的料子，就連很多under讀基礎科學的人，都不一定能掌握的很好，大家畢竟都是依照聯考成績去填志願，近十年最優秀的人才反而流向了那些能快速＂致富＂的科系：醫學、電機、化學材料、國企等等（以前幾志願學校來說）。在這裡所談的數學能力並非像做基礎研究需要的那種艱深的數理，而是應用面的能力。應用還是得建立在兼顧的基礎觀念上。

如果本學期我還健在，我將去聽鄭教授的多變量分析。

在進入研究所前其實對於數理能力增進有很多的規劃與想法，後來...不是你想要怎樣就怎樣，人一週就只有那麼多節課，能遇到沒衝堂，並需要take的選修課不容易。


在大學時期修完機率數統後，我想...好好對自己負責的時候到了！那些華麗的技術性層面，是需要慢慢體會，要藉由很多枯燥層面的東西去發酵才能領悟的，我始終相信：沒有基礎絕對沒有辦法做出好的application。存粹我個人想法，無關對錯。因此別與我爭論機率數統微分方程這些東西電腦都慧幫我們算，但是可曾想過，電腦會算是因為你寫了coding他才開始幫你跑！

感覺，不會的東西很多追也追不上，但有人能做到，我想我可以試試看！

下面這本書為多變量統計蠻有名的入門書，少了許多艱澀難懂的推導，比較多是從觀念著手來讓讀者了解。




Johnson and Wichern, Applied multivariate statistical analysis,5th edition.

以下書籍資料摘錄自: http://www.riskbook.com/link/johnson_and_wichern_(2002).htm

Applied Multivariate Statistical Analysis is a standard introduction to multivariate statistics. There are several books on the topic, which differ considerably in their choice of topics and exposition. I recommend this one because it offers the best mix of topics and level of exposition for quantitative professionals working in trading, financial engineering, or risk management.

Topics include: data issues, the joint-normal distribution, mean and covariance estimation, principal component analysis, factor analysis, regression and classification techniques. Readers should be familiar with probability and statistics, as covered by Casella and Berger (2001). The book includes an excellent review of relevant concepts from linear algebra, including positive definite matrices and the Cholesky factorization. However, readers should have some experience with linear algebra, as covered by Strang (1988).

For a sophisticated treatment of multivariate statistics, Applied Multivariate Statistical Analysis is the essential book.

context

GETTING STARTED

1. Aspects of Multivariate Analysis 
2. Matrix Algebra and Random Vectors 
3. Sample Geometry and Random Sampling 
4. The Multivariate Normal Distribution

INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR MODELS

5. Inferences About a Mean Vector 
6. Comparisons of Several Multivariate Means 
7. Multivariate Linear Regression Models

ANALYSIS OF A COVARIANCE STRUCTURE.

8. Principal Components 
9. Factor Analysis and Inference for Structured Covariance Matrices 
10. Canonical Correlation Analysis

CLASSIFICATION AND GROUPING TECHNIQUES.

11. Discrimination and Classification 
12. Clustering, Distance Methods and Ordination

 




see also:
Strang, Gilbert (1988). Linear Algebra and its Applications  is the standard practical introduction to linear algebra.

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