Mathematical topics of interest to bioinformaticians and computational biologists

mathematics_topics.md

Mathematics Topics

List of running topics that may be of interest.

Statistics

• Maximum likelihood estimation (MLE)
• Experimental design
• Bayesian statistics with priors and posterior distributions
• Cross-correlations: correlations between entries of two random vectors X and Y, while the correlations of random vector X are considered to be the correlations between the entries of X itself, those forming the correlation matrix of X

Machine Learning

• Kernel method/trick

Probability Theory

• Probability distributions
  • Bernoulli distribution
  • Negative binomial distribution
  • Hypergeometric distribution

Discrete Mathematics

• TODO

Calculus

• TODO

Linear Algebra

• Determinant
• Eigenvectors and eigenvalues
• Spans
• Matrix decomposition
• Least squares approximation

Misc

• t-SNE (t-Distributed Stochastic Neighbor Embedding)
• UMAP (Uniform Manifold Approximation and Projection)
• Geoffrey Hinton's Capsule Networks (Deep Learning)
• Cross-correlation
• Autocorrelation

Resources and Books

• Abstract Math
• Mathematical Writing by Knuth, Larrabee, Roberts (PDF)
• Mathematics of Bioinformatics (Book) (PDF)
• Discrete Mathematics, 2nd Edition in Progress (Book 2017) (PDF)
• Various course notes in statistics from PennState Eberly College of Science - Excellent course notes e.g. Introduction to Applied Statistics
• PH525x Series - Biomedical Data Science