A Practical Approach to Microarray Data Analysis is for all life scientists, statisticians, computer experts, technology developers, managers, and other professionals tasked with developing, deploying, and using microarray technology including the necessary computational infrastructure and analytical tools. The book addresses the requirement of scientists and researchers to gain a basic understanding of microarray analysis methodologies and tools. It is intended for students, teachers, researchers, and research managers who want to understand the state of the art and of the presented methodologies and the areas in which gaps in our knowledge demand further research and development. The book is designed to be used by the practicing professional tasked with the design and analysis of microarray experiments or as a text for a senior undergraduate- or graduate level course in analytical genetics, biology, bioinformatics, computational biology, statistics and data mining, or applied computer science. -Format of result from data analysis, analytical modeling/experimentation; -Validation of analytical results; -Data analysis/Modeling task; -Analysis/modeling tools; -Scientific questions, goals, and tasks; -Application; -Data analysis methods; -Criteria for assessing analysis methodologies, models, and tools.

CONTENTS

CHAPTER I

POLYNOMIALS AND THEIR MOST FUNDAMENTAL PROPERTIES

1. Polynomials in One Variable
2. Polynomials in more than One Variable
3. Geometric Interpretations
4.  Homogeneous Coordinates
5. The Continuity of Polynomials
6. The Fundamental Theorem of Algebra

CHAPTER II

A Few Properties of Determinants

7. Some Definitions
8. Laplace’s Development
9. The Multiplication Theorem
10. Bordered Determinats
11. Adjoint Determinats and their Minors

CHAPTER III

THE THEORY OF LINEAR DEPENDENCE

12. Definitions and Preliminary Theorems
13. The Condition for Linear Dependence of Sets of Constants
14. The Linear Dependence of Polynomials
15. Geometric Illustrations

CHAPTER IV

LINEAR EQUATIONS

16. Non-Homogeneous Linear Equations
17. Homogeneous Linear Equations
18. Fundamental Systems of Solutions of Homogeneous Linear Equations

CHAPTER V

SOME THEOREMS CONCERNING THE RANK OF A MATRIX

19. General Matrices
20. Symmetrical Matrices

CHAPTER VI

LINEAR TRANSFORMATIONS AND THE COMBINATION OF MATRICES

21. Matrices as Complex Quantities
22. The Multiplication of Matrices
23. Linear Transformation
24. Collineation
25. Further Development of the Algebra of Matrices
26. Sets, Systems and Groups
27. Isomorphism

CHAPTER VII

INVARIANTS. FIRST PRINCIPLES AND ILLLUSTRATIONS

28. Absolute Invariants; Geometric, Algebraic, and Arithmetical
29. Equivalence
30. The Rank of System of Points or System of Linear Forms as an Invariant
31. Relative Invariants and Covariants
32. Some Theorems Concerning Linear Forms
33. Cross-Ratio and Harmonic Division
34. Plant-Coordinates and Contragredient Variables
35. Line-Coordinates in Space.

CHAPTER VIII

BILINEAR FORMS

36. The Algebraic Theory
37. A Geometric Application