# A mathematical way to think about biology

Why "is" biology log-normal? Why do some circuits oscillate? See biology from a physical sciences perspective.
Free tutorial
Rating: 4.1 out of 5 (509 ratings)
24,196 students
A mathematical way to think about biology
Free tutorial
Rating: 4.1 out of 5 (509 ratings)
24,196 students
Apply physical sciences perspectives to biological research
Be able to teach yourself quantitative biology
Be able to communicate with mathematical and physical scientists

### Requirements

• Algebra
• Exposure to calculus (there is an appendix for students interested in review)
Description

A mathematical way to think about biology comes to life in this lavishly illustrated video book. After completing these videos, students will be better prepared to collaborate in physical sciences-biology research. These lessons demonstrate a physical sciences perspective: training intuition by deriving equations from graphical illustrations.

"Excellent site for both basic and advanced lessons on applying mathematics to biology."
-Tweeted by the U.S. National Cancer Institute's Office of Physical Sciences Oncology

Who this course is for:
• Postdoctoral scholars
• Lab managers
• Funding agency program staff
• Principal investigators and grant writers
• Citizen scientists
• Lifelong learners
• Integrative Cancer Biology Program members
• Physical Sciences Oncology Network members
• National Centers for Systems Biology members
Course content
14 sections • 134 lectures • 15h 24m total length
• Welcome to mathematics for insightful biology
01:48
• Stochasticity a: Incommensurate periods
05:15
• Stochasticity b: Practically unpredictable deterministic dynamics
04:29
• Stochasticity c: Fundamentally indeterministic processes
05:03
• Stochasticity d: Memory-free (Markov) processes and their visual representations
04:46
• Canonical protein dynamics a: Translation and degradation events occur over time
08:57
• Canonical protein dynamics b: Differential equation and flowchart
09:50
• Canonical protein dynamics c: Qualitative graphical solution
04:12
• Canonical protein dynamics d: Analytic solution and rise time
11:02
• Mass action 1a: Law of mass action
13:02
• Mass action 1b: Cooperativity and Hill functions
11:58
• Mass action 1c: Bistability
06:32
• Evolutionary game theory Ia: Population dynamics
15:35
• Evolutionary game theory 1b: Preview comparison with tabular game theory
12:32
• Evolutionary game theory IIa: Cells repeatedly playing games
19:20
• Evolutionary game theory IIb: Relationship between time and sophisticated comput
10:58
• Statistics a: Probability distributions and averages
05:54
• Statistics b: Identities involving averages
03:43
• Statistics c: Dispersion and variance
05:33
• Statistics d: Statistical independence
06:26
• Statistics e: Identities following from statistical independence
07:20
• Probability a: Bernoulli trial
03:49
• Probability b: Binomial distribution
07:18
• Probability c: Poisson distribution
08:13
• Preparation for central limit theorem: Stirling's approximation
11:22
• Central limit theorem a: Statement of theorem
06:37
• Central limit theorem b: Optional derivation (special case)
09:01
• Central limit theorem c: Properties of Gaussian distributions
03:50
• Prevalence of Gaussians a: Noise in physics labs is allegedly often Gaussian
08:25
• Prevalence of Gaussians b: Noise in biology is allegedly often log-normal
10:35
07:45
• Uncertainty propagation b: Sample estimates
09:38
• Uncertainty propagation c: Square-root of sample size (sqrt(n)) factor
05:57
• Uncertainty propagation d: Comparing error bars visually
03:18
• Uncertainty propagation e: Illusory sample size
06:55
• Sample variance curve fitting a: Chi-squared
08:18
• Sample variance curve fitting b: Minimizing chi-squared
13:37
• Sample variance curve fitting c: Checklist for undergraduate curve fitting
03:44
• Sample variance curve fitting exercise for MatLab
5 pages
• Master equation
07:49
• Stochastic simulation algorithm a: Specifying reaction types and stoichiometries
03:13
• Stochastic simulation algorithm b: Time until next event
10:45
• Stochastic simulation algorithm c: Determining type of next event
03:18
• Poissonian copy numbers a: Stochastic transcription and deterministic degradation
08:11
• Poissonian copy numbers b: Stochastic transcription and stochastic degradation
14:11
• Linear algebra Ia: Teaser
05:19
• Linear algebra Ib: Vectors
09:56
• Linear algebra Ic: Operators
13:44
• Linear algebra Id: Solution of teaser (part 1)
09:35
• Linear algebra Id: Solution of teaser (continued)
17:50
• Intro quasispecies a: Population dynamics from single-cell mechanisms
06:37
• Intro quasispecies b: Eigenvalue-eigenvector analysis
06:42
• Euler II: Complex exponentials
04:29
• Linear algebra II: Rotation a: Rotation matrix
04:51
• Linear algebra II: Rotation b: Complex eigenvalues
08:43
• Numerical integration of differential equations
11:03
• Linear stability analysis a: Transcription-translation model
03:52
• Linear stability analysis b: Nullclines and critical point
07:17
• Linear stability analysis c: Eigenvalue-eigenvector analysis
16:30
• Linear stability analysis d: Cribsheet
11:49
• Almost linear stability analysis a: Incoherent feed-forward loop
07:49
• Almost linear stability analysis b: Adaptation
06:13
• Almost linear stability analysis c: Eigenvalue-eigenvector analysis
11:06
• Almost linear stability analysis d: Cribsheet
05:48
• Oscillations a: Romeo and Juliet
07:46
• Oscillations b: Twisting nullclines
03:42
• Oscillations c: Time delays
02:31
• Oscillations d: Stochastic excitation
03:48
• Introduction to physical oncology
01:54
• Dynamic heterogeneity a: Stochastic biochemistry
06:23
• Dynamic heterogeneity b: Phenotypic interconversion
04:54
• Dynamic heterogeneity c: Metronomogram
08:10
• Cellular automata a: Deterministic cellular automata
05:46
• Statistical physics 101a: Fundamental postulate of statistical mechanics
06:47
• Statistical physics 101b: Cartesian product
02:42
• Statistical physics 101c: Distribution of energy between a small system and a large bath
12:05
• Statistical physics 101d: Expressions for calculating average properties of systems connected to baths
05:15
• Ideal chain a: Introduction to model
04:09
• Ideal chain b: Hamiltonian and partition function
08:46
• Ideal chain c: Expectation of energy and elongation
17:00
• Macroscopic irreversibility a: Microstates of universe are explored over time
10:17
• Macroscopic irreversibility b: Microscopic reversibility
05:06
• Macroscopic irreversibility c: Ratio of volumes in phase space
11:08
• Macroscopic irreversibility d: Kinetically accessible volumes of phase space
11:44

Instructor
Physicist (PhD, Princeton 2010)
• 4.1 Instructor Rating
• 509 Reviews
• 24,196 Students
• 1 Course

David's illustrations have been published in Science, Physical Review Letters, Molecular Pharmaceutics, Biosensors and Bioelectronics, and the Proceedings of the National Academy of Sciences.

University of California, San Francisco

Associate Professional Researcher 2015-Current

Analyst, 2012-2014

Postdoc, 2010-2012 Tlsty Lab

Princeton University (PhD, Physics, 2010 MA, Physics, 2007)