Course

Unit 1: 

Euclidean vector space- 2 space, 3 space, n space, dot product, Norm, orthogonality, Solution of system of linear equations- Row reduction method, Four fundamental spaces of a matrix, independent vectors, Gram Schmidt Process.

Unit 2 

Eigenvalues, Eigenvectors, Cayley Hamilton theorem, Orthogonal matrices, Singular value Decomposition- Singular values, singular vectors, Relationship between singular value decomposition and eigen value decomposition, Principal component analysis, Interpretation of PCA results.

Unit 3 

Sampling theory: Population and sample, random sample, population parameters, Sample statistics, sampling distribution of means, sampling distribution of proportion, sample variance. Estimation: unbiased, maximum likelihood, Bayesian. Test of hypothesis and significance: Type I and type II error, Power of test, P-values, Analysis of variance.

Course outcomes: 

Students who complete this course will be able to

CO1: Apply the concept of a matrix to solve biological systems like sequence alignment or gene expression

CO2: Implement Calculus to calculate the rate of change of substrate or to find the area under the curve in enzyme kinetics.

CO3: Apply distance calculation to predict protein structure

• Linear Algebra and Its Applications by Gilbert Strang, 5th ed., Wellesley-Cambridge Press, 2016.

• Introduction to Linear Algebra by Gilbert Strang, 5th ed., Wellesley-Cambridge Press, 2016.

• Fundamentals of Mathematical Statistics– S. C. Gupta & V. K. Kapoor.

• Mathematical Statistics with Applications by Irwin Miller, Marylees Miller, and Karl E. Mosier, 8th ed., Pearson, 2022.