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

(525 ratings)

25,217 students

Created by David Liao

English

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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:

Undergraduate students
Graduate students
Postdoctoral scholars
Lab managers
Funding agency program staff
Principal investigators and grant writers
Citizen scientists
Patient advocates
Lifelong learners
Integrative Cancer Biology Program members
Physical Sciences Oncology Network members
National Centers for Systems Biology members

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

Uncertainty propagation a: Quadrature
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

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

David Liao

Physicist (PhD, Princeton 2010)

4.4 Instructor Rating
525 Reviews
25,217 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)

Advisor: Robert H. Austin

2006-2009 National Defense Science and Engineering Graduate Research Fellowship

2009-2010 National Science Foundation Graduate Research Fellowship

Harvey Mudd College BS, Physics, 2005

Advisor: Robert J. Cave

A mathematical way to think about biology

Requirements

Description

Who this course is for:

Course content

Welcome to mathematics for insightful biology1 lecture • 2min

Using deterministic models to study aspects of stochastic systems15 lectures • 2hr 24min

Probability and statistics14 lectures • 1hr 38min

Uncertainty propagation9 lectures • 59min

Computation of stochastic dynamics6 lectures • 47min

Linear algebra10 lectures • 1hr 28min

Differential equations13 lectures • 1hr 39min

Physical oncology4 lectures • 21min

Spatially-resolved systems1 lecture • 6min

Statistical physics11 lectures • 1hr 35min

Instructor