# Quantitative biology I

This is an introductory course in the mathematical and computational methods useful to students of the life sciences. The course is not intended to recapitulate a full degree program in physics, mathematics or computer science. Rather, the goal is to provide hands-on training, so that the student can *use* already available techniques and canned software, even if they are not ready to develop new tools. The course is intended to be useful to students in a wide variety of disciplines, e.g., biochemistry, genetics, cellular biology, microbiology, physiology, systems biology and metabolomics.

This course falls within the Department of Biochemistry within the School of Biology.

## Rough syllabus

editThe plan is to present the topics in the following order; the rationale is that each topic builds on those preceding it.

- Basic math
- Basic statistics
- Statistical correlations
- Curve fitting
- Noise and noise reduction
- Diffusion, estimates of hydrodynamic size and molecular weight
- Matrix methods, computational efficiency
- Kinetics, linear and nonlinear
- Equilibrium; thermodynamics and statistical mechanics
- Electronic structure, spectroscopy and covalent bonds
- Non-covalent molecular forces
- Nuclear isotopes and NMR
- Resolution in various guises
- Fourier transforms
- Normal modes, molecular dynamics, Monte Carlo methods
- Computational predictions in molecular biology

Alternatively, these topics can be sorted into four major groups

- Group 1: Statistical topics
- Basic statistics, statistical correlations, curve fitting
- Noise and noise reduction
- Diffusion and hydrodynamic methods

- Group 2: Matrix methods and kinetics
- Matrix methods, computational efficiency
- Kinetics, linear and nonlinear
- Equilibrium; thermodynamics and statistical mechanics

- Group 3: Chemical/physical topics
- Electronic structure, spectroscopy, and covalent bonds
- Non-covalent molecular forces
- Nuclear isotopes and NMR

- Group 4: Mathematical and computational methods
- Fourier transforms and linear differential equations
- The concept of resolution
- X-ray crystallography
- Molecular dynamics, Monte Carlo methods, normal modes

It is anticipated that the full curriculum would correspond to two semester-long courses.

## Detailed syllabus

editThis is an initial draft; the timings should not be taken seriously.

### Week 1: Basic mathematics

edit- Daily lesson 1.1: Units; basic measurements: gel-box volume
- Daily lesson 1.2: Solution math:serial dilutions, colony-forming units
- Daily lesson 1.3: Calibration of a pipette
- Daily lesson 1.4: pH, pI; maleic/fumaric acids
- Daily lesson 1.5: linear, semilog and log-log plots; polar plots
- Daily lesson 1.6: asymptotic behavior; perturbations
- Daily lesson 1.7: powers of 10; Fermi problems

### Week 2: Basic statistics

edit- Daily lesson 2.1: discrete vs. continuous stochastic variables
- Daily lesson 2.2: 1-dimensional statistical distributions; error bars vs. confidence limits
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### Week 10:

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