# 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 edit

The 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 edit

This 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
- Daily lesson 2.3:
- Daily lesson 2.4:
- Daily lesson 2.5:
- Daily lesson 2.6:
- Daily lesson 2.7:

### Week 3: edit

- Daily lesson 3.1:
- Daily lesson 3.2:
- Daily lesson 3.3:
- Daily lesson 3.4:
- Daily lesson 3.5:
- Daily lesson 3.6:
- Daily lesson 3.7:

### Week 4: edit

- Daily lesson 4.1:
- Daily lesson 4.2:
- Daily lesson 4.3:
- Daily lesson 4.4:
- Daily lesson 4.5:
- Daily lesson 4.6:
- Daily lesson 4.7:

### Week 5: edit

- Daily lesson 5.1:
- Daily lesson 5.2:
- Daily lesson 5.3:
- Daily lesson 5.4:
- Daily lesson 5.5:
- Daily lesson 5.6:
- Daily lesson 5.7:

### Week 6: edit

- Daily lesson 6.1:
- Daily lesson 6.2:
- Daily lesson 6.3:
- Daily lesson 6.4:
- Daily lesson 6.5:
- Daily lesson 6.6:
- Daily lesson 6.7:

### Week 7: edit

- Daily lesson 7.1:
- Daily lesson 7.2:
- Daily lesson 7.3:
- Daily lesson 7.4:
- Daily lesson 7.5:
- Daily lesson 7.6:
- Daily lesson 7.7:

### Week 8: edit

- Daily lesson 8.1:
- Daily lesson 8.2:
- Daily lesson 8.3:
- Daily lesson 8.4:
- Daily lesson 8.5:
- Daily lesson 8.6:
- Daily lesson 8.7:

### Week 9: edit

- Daily lesson 9.1:
- Daily lesson 9.2:
- Daily lesson 9.3:
- Daily lesson 9.4:
- Daily lesson 9.5:
- Daily lesson 9.6:
- Daily lesson 9.7:

### Week 10: edit

- Daily lesson 10.1:
- Daily lesson 10.2:
- Daily lesson 10.3:
- Daily lesson 10.4:
- Daily lesson 10.5:
- Daily lesson 10.6:
- Daily lesson 10.7: