ESSENTIAL MATHEMATICS AND STATISTICS
| 1. | Introduction, and role of Mathematics and Statistics in Biology |
| 2. |
Vectors and Matrices |
| 3. | Basic Calculus: Differentiation and Integration |
| 4. | Numerical Description of Data: Mean, Median, Mode, Quantiles, Standard Deviation, Variance, Coefficient of Variation |
| 5. | Essential Graphs: Visualization of Biological Data |
| 6. | Probability Theory: Sample Space and Events, Axioms of Probability, Conditional Probability, Independent Events, Bayes’ Formula |
| 7. | Random Variables: Discrete and Continuous, Expected Value, Variance |
| 8. | Discrete and Continuous Distributions, Chi-Square, Student’s t, Snedecor’s F and Z Distributions |
| 9. | Estimation Theory: Unbiased Estimator; Confidence Interval: Population Mean, Population Variance |
| 10. | Limit Theorems: Central Limit Theorem, Strong Law of Large Number, Weak Law of Large Number |
| 11. | Optimization Algorithms |
| 12. | Maximum Likelihood Estimation: Discrete and Continuous Distributions, Likelihood Function; Log-Likelihood Functions |
| 13. | Tests of Hypothesis: Formulation of Hypothesis - Simple and Composite, Type I and Type II Errors, Power of a Test, Significance of Test, p-value; Applications of t, χ2, F and Z Distributions |
Recommended Books
| 1. | Evens, W.J. and Grant, G.R., Statistical Methods in Bioinformatics: An Introduction 2005. |
| 2. |
Mathhew H. and Sergey Petoukhov, Mathematics of Bioinformatics: Theory, Practice, and Applications, 2011. |
| 3. |
Peter Clote and Rolf Backofen, Computational Molecular Biology: An Introduction, John Wiley & Sons, 2000. |