Technical Skills

SHORT-MODULES ON MATHEMATICAL BIOLOGY:

A. Basic Mathematical Population Biology (Videos)

  1. Discrete-time population models – V. Guttal
  2. Logistic map and linear stability analysis – V. Guttal
  3. Process of model building and introduction to continuous-time population models – V. Guttal
  4. Continuous-time population models, graphical stability analysis, Allee effect, introduction to evolutionary game theory – V. Guttal

B. Basic Mathematical Evolutionary Dynamics: (Videos) (Assumes knowledge of mathematical population biology above)

  1. Introduction to evolutionary game theory – (Vishwesha Guttal)
  2. Evolutionary game theory: cooperation – (Vishwesha Guttal)
  3. Evolutionary game theory: exercises – (Vishwesha Guttal)

C. Basic Nonlinear Dynamics, Critical Transitions and Early Warning Signals Theory in Ecology (Videos)

  1. Introduction to non-linear dynamics: catastrophe theory and tipping points – (Vishwesha Guttal)
  2. Critical transitions and early warning signals in ecology – (Vishwesha Guttal)

D. Stochasticity and Bistability in Ecological Systems (Vishwesha Guttal) — Talks delivered at ICTS QSB Winter School, Jan 2025.

  1. Stochasticity and Bistability in Ecological Systems – Part 1
  2. Stochasticity and Bistability in Ecological Systems – Part 2
  3. Stochasticity and Bistability in Ecological Systems – Part 3

E. Network Dynamics (Videos): L1 L2 L3 – S. Krishna

F. Interacting particle systems (Videos): L1 L2 L3 L4 L5 – A. Kundu

G. Statistical physics of active matter (Videos): L1 L2 L3 L4 L5 – S. Ramaswamy

RESEARCH TALKS BY VISHWESHA GUTTAL (Videos)

  1. Stochasticity and Bi-stability in Ecological Systems by V. Guttal (at ICTP):
    • Part 1: Mean-field approach of bi-stability and early warning signals (~1 hr)
    • Part 2: Spatial models of bi-stability and early warning signals (~1 hr)
    • Part 3: Collective behavior (~1 hr)
  2. Collective Animal Movement (A general intro, with our research; 1 hour; in 2020)
  3. Noise-induced schooling in fish (short talk, 12 mins, in 2020)
  4. Big Data Makes Sense Only in Light of Theory: Examples from Ecology! (webinar,~1 hr; in 2021)

OTHER RELEVANT RESEARCH TALKS (Videos)

  1. Living matter and matter brought to life – S. Ramaswamy
  2. Order and patterns in randomness – A. Dhar
  3. Data-driven discovery of governing physical laws – N. Kutz

FULL LENGTH COURSES:

  1. Theoretical and Mathematical Ecology – V. Guttal
  2. Stochastic and Spatial Dynamics in Biology – V Guttal
  3. Probability and statistics – J. Blitzstein
  4. Linear Algebra – G. Strang
  5. Nonlinear dynamics – S. Strogatz
  6. Non-equilibrium statistical physics – V. Balakrishnan
  7. Physical applications of stochastic processes – V. Balakrishnan

EEB Books:

Experiments in Animal Behavior: Cutting-Edge Research at Trifling Cost by Raghavendra Gadagkar.

SHORT VIDEOS:

  1. Essence of calculus – 3B1B’s visual treat on what calculus is at its core.
  2. Essence of linear algebra – 3B1B on what vectors, matrices and that eigen-stuff is all about.
  3. Differential equations – A partially complete series by 3B1B.
  4. But what is a Fourier transform? – 3B1B answers.

PROGRAMMING TUTORIALS:

  1. Beginner Python tutorials – An introduction to programming in Python.
  2. Intermediate Python tutorials – For Python beginners looking to improve their workflow.
  3. Matplotlib tutorials – Tutorials on creating line graphs, scatter plots, bar charts, pie charts, 3D graphs and more using Python.
  4. Python libraries for interactive plots
  5. A Tour of C++ – Also available in book form.
  6. Linux command line – Also available in a extended book form for free.
  7. The Missing Semester of Your CS Education
  8. Building Skills in Quantitative Biology — especially the chapters on Github, Markdown are likely useful.
  9. LaTeX OCR – Package to convert equation images to latex code.

NOTES AND ARTICLES:

  1. Paul’s Online Math Notes – Comprehensive notes on calculus and differential equations.
  2. Solving equations using Wolfram Alpha – Tips on using Wolfram Alpha to solve systems of linear and non-linear equations.
  3. Statistics Notes by Doug Altman – Notes on statistics.
  4. A Course on Calculus – by Prof. Herbert Gross, MIT.