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I am really passionate about theoretical and quantitative biology and I would like to build my future career around this topic.

I've just got my bachelor's degree in biology (ecology) but scince I've had only one math class through the years, my math skills are very poor, so I have problems in understanding even simpe models. My main interests are population dynamics, adaptive dynamics and game theoretical models of social conflicts.

I would like to improve my skills, but I have just no idea where/how to start. Could you give me some advice about textbooks or online resources?

I have almost no knowledge in the field of math, I am interested in resources for complete beginners. And I would also appreciate any suggestions about skills/topics I should master if I am interested in these biological phenomena.

Thank you!

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There is one book that will perfectly suits your needs:

A biologist's guide to Mathematical Modeling in Ecology and Evolution, by Sally Otto

It is a very good book that is very easy to understand and in the meantime goes pretty far (It ends with the use of diffusion equation in Evolutionary Biology). I highly recommend it.

It covers:

  • How to create a model
  • Function approximation
  • Find general solution with $n$ variables for discrete and continuous model
  • Stability analysis
  • Find equilibrium
  • Analyzing cyclic behavior
  • Gives very good introduction in linear algebra and probability theory
  • Class structured population
  • Stochastic modeling (birth-death processes and diffusion approximations)
  • Transformations
  • All examples are from the field of ecology and evolution and the author derives many of the most important equations in ecology and evolution.

Online ressources

Also I think that Khan Academy is a very good and easy source of information for improving your math skills but it takes quite a bit of time to go through all these lectures.

For a good and complete introduction to probability theory, I'd recommend this MIT Opencourseware but again, it takes time to go through all these videos.

For further recommendations in population genetics, you should have a look to this post.

If you are interested in theoretical biology, you may also want to learn about programming (if you don't already know much about it). $R$ is used for data analysis purposes, $Mathematica$ or $Matlab$ for deal with mathematical modeling and $Python$, $Java$ or $C++$ for individual-based simulations.

Note: A bit less than 2 years ago, I had the same interests than you and had to face the same issues than you.

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  • $\begingroup$ Thank you so much for your answer. It is most helpful. May I ask, if these resources were enough for you to get on well in this field? $\endgroup$ – Sielu Jul 17 '14 at 15:40
  • $\begingroup$ @Alana Well..At the moment I just finished my Master degree and am starting my PhD (in theoretical population genetics at UBC, Vancouver) in early September. It is a bit hard to compare myself with specialist in this field but anyway these references allowed me to learn a lot and helped me to be creative and develop my own research projects. I feel I should still learn more about mathematics. I learned to program with online tutorials. $\endgroup$ – Remi.b Jul 17 '14 at 17:03
  • $\begingroup$ I edited my other answer here to add a new important reference. Wish you all the best in your readings and self education! Don't hesitate to ask further questions. $\endgroup$ – Remi.b Jul 17 '14 at 17:04
  • $\begingroup$ Thank you so much! Your answer really helped me a lot. I'll have only one more question: what programming language do you use? I've read aboutthe ones you recommended, but I've only used R so far. $\endgroup$ – Sielu Jul 17 '14 at 17:56
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    $\begingroup$ I mostly use R (data analysis and some very simple simulation), Mathematica (for mathematical modeling) and Python (for Individual-based simulation (Object-oriented programming) ). $\endgroup$ – Remi.b Jul 17 '14 at 18:04

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