Chapter 3. Mathematics in a Nutshell

  1. Dr. E. Klipp,
  2. Dr. R. Herwig,
  3. Dr. A. Kowald,
  4. C. Wierling,
  5. Prof. Dr. H. Lehrach

Published Online: 11 MAY 2005

DOI: 10.1002/3527603603.ch3

Book Title

Systems Biology in Practice: Concepts, Implementation and Application

Systems Biology in Practice: Concepts, Implementation and Application

Additional Information

How to Cite

Klipp, E., Herwig, R., Kowald, A., Wierling, C. and Lehrach, H. (2005) Mathematics in a Nutshell, in Systems Biology in Practice: Concepts, Implementation and Application, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527603603.ch3

Author Information

  1. MPI für Molekulare Genetik, Ihnestraße 73, 14195 Berlin, Germany

Publication History

  1. Published Online: 11 MAY 2005
  2. Published Print: 17 FEB 2005

ISBN Information

Print ISBN: 9783527310784

Online ISBN: 9783527603602

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Keywords:

  • mathematics;
  • linear algebra;
  • matrices;
  • ordinary differential equations;
  • statistics;
  • graph and network theory;
  • stochastic processes

Summary

This chapter contains sections titled:

  • Linear Algebra

    • Linear Equations

      • The Gaussian Elimination Algorithm

      • Systematic Solution of Linear Systems

    • Matrices

      • Basic Notions

      • Linear Dependency

      • Basic Matrix Operations

      • Dimension and Rank

      • Eigenvalues and Eigenvectors of a Square Matrix

  • Ordinary Differential Equations

    • Notions

    • Linearization of Autonomous Systems

    • Solution of Linear ODE Systems

    • Stability of Steady States

      • Global Stability of Steady States

      • Limit Cycles

  • Difference Equations

  • Statistics

    • Basic Concepts of Probability Theory

      • Random Variables, Densities, and Distribution Functions

      • Transforming Probability Densities

      • Product Experiments and Independence

      • Limit Theorems

    • Descriptive Statistics

      • Statistics for Sample Location

      • Statistics for Sample Variability

      • Density Estimation

      • Correlation of Samples

    • Testing Statistical Hypotheses

      • Statistical Framework

      • Two-sample Location Tests

    • Linear Models

      • ANOVA

      • Multiple Linear Regression

  • Graph and Network Theory

    • Introduction

    • Regulatory Networks

      • Linear Networks

      • Boolean Networks

      • Bayesian Networks

  • Stochastic Processes

    • Gillespie's Direct Method

    • Other Algorithms

    • Stochastic and Macroscopic Rate Constants

      • First-order Reaction

      • Second-order Reaction

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