Preface
Part I Geometry
1 Preliminaries
1.1 Linear algebra
1.1.1 Vectors and matrices
1.1.2 Symmetric bilinear forms
1.1.3 Vector subspaces
1.1.4 Linear maps from Rn to Rn
1.1.5 A convention
1.2 Vector calculus
1.2.1 Vector-valued functions and differentials
1.2.2 Taylor expansion and extrema
1.2.3 Extrema and Lagrange multiplier theorem

2 Euclidean Geometry

Preface
Part I Geometry
1 Preliminaries
1.1 Linear algebra
1.1.1 Vectors and matrices
1.1.2 Symmetric bilinear forms
1.1.3 Vector subspaces
1.1.4 Linear maps from Rn to Rn
1.1.5 A convention
1.2 Vector calculus
1.2.1 Vector-valued functions and differentials
1.2.2 Taylor expansion and extrema
1.2.3 Extrema and Lagrange multiplier theorem

2 Euclidean Geometry
2.1 Orthogonal transformations
2.2 Rigid motions
2.3 Translation of vector subspaces
2.4 Conformal transformations
2.5 Orthonormal basis
2.6 Orthogonal projections
2.7 Areas and volumes

3 Geometry of Graphs
3.1 Graphs in Euclidean spaces
3.2 Normal sections
3.3 Cross sections in high dimension
3.4 First fundamental forms

4 Curvatures
4.1 Normal curvatures
4.1.1 Definition
4.1.2 Principal curvatures and principal directions
4.2 Sectional curvatures

5 Transformations and Invariance
5.1 Change of coordinates
5.2 Non-linear conformal transformations
5.3 Invariant curvatures Part II Statistics

6 Discrete Random Variables and Related Concepts
6.1 Preliminaries
6.2 Discrete random variables
6.2.1 Discrete random variables and probability function
6.2.2 Relative frequency histogram
6.2.3 Cumulative distribution function
6.3 Population parameters and sample statistics
6.3.1 Population mean and expected value
6.3.2 Sample statistic
6.3.3 Sample mean
6.3.4 Sample and population variances
6.4 Mathematical expectations
6.5 Maximum likelihood estimation
6.6Maximum likelihood estimation of the probability of a Bernoulliexperiment

7 Continuous Random Variables and Related Concepts
7.1 Continuous random variables
7.2 Mathematical expectation for continuous random variables
7.3 Mean and variance and their sample estimates
7.4 Basic properties of expectations
7.5 Normal distribution
7.6 Maximum likelihood estimation for continuous variables
7.7 Maximum likelihood estimation for the parameters of normaldistribution
7.8 Sampling distribution
8 Bivariate and Multivariate Distribution
9 Simple Linear Regression
10 Topics on Linear Regression Analysis
11 Basic Concepts
12 Measuring Local Influence
13 Relations Among Various Measures
14 Conformal Modifications
Appendix A Rank of Hat Matrix
Appendix B Ricci Curvature
Appendix C Cook-s Distance-Deleting Two Data Points
Bibliography
Index