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:
  • 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
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
  • 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
  • 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)
David Liao
  • 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)

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