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My undergraduate studies were in the area of applied mathematics and statistics and I am interested in doing postgraduate studies in the area of mathematical biology. But when I looked into different courses offered by universities, there are so many other areas that look similar to mathematical biology. It would be a great help if someone can clarify the difference between mathematical biology, systems biology, bioinformatics, and synthetic biology.

  • Which are more extensively related to biology?
  • Which are more suited for a background in applied mathematics and statistics?
  • Does systems biology require engineering knowledge and could it be pursued with applied-mathematics knowledge.
  • What are the differences between systems biology and synthetic biology?
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As a point of note often times several of those terms are used as synonyms, or interchangeably.

Mathematical biology is a kind of non-specific overarching domain, it could contain anything from population level dynamics to single protein dynamics.

Systems biology is field specific, but it refers to studying a whole systems as opposed to say a single gene in a a disease.

Bioinformatics is typically used in reference to the analysis of genetics data (proteomics, transcriptomics...)

Synthetic biology (at least in my understanding) is creating a new molecule (protein, DNA sequence...) out of "building blocks" - similar to building a widget out of stand alone electronic modules.

To answer your question about pursuing these fields, in my opinion bioinformatics lends itself best to a statistics background, it's highly dimensional, huge data sets... and can benefit a lot from a statistics background.

I'd hesitate to answer your question about systems biology because it can vary from large coupled ODE's to no math at all depending on what "sub-field" you're looking at.

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I don't have any experience in any of these fields, so take my answer with a grain of salt. I do, however, come from a mathematics background like yourself.

From a cursory reading of each topic's Wikipedia page:

  • Mathematical biology is also known as theoretical biology, dependent upon where you choose to focus your coursework. It stresses the modeling of anything from small- to intermediate-scale biological systems and interactions. It also employs a vast array of mathematical disciplines in its applications.
  • Systems biology is very similar to mathematical biology, in that it focuses on interactions within biological systems. It emphasizes the modeling aspects of large-scale and complex systems. Emphasis is placed on computational mathematics.
  • Synthetic biology is heavily reliant upon knowledge of engineering and biology, not so much mathematics. It employs various engineering disciplines in the fabrication of biological components. Synthetic biology draws upon knowledge from systems biology, but is much more pragmatic than systems biology. I would say synthetic biology is just another phrase for "biotechnology", with various biological disciplines contributing to it.
  • Bioinformatics seems like something you'd be most interested in. Much like how data science is the application of mathematical tools and software to study data, bioinformatics is data science with strictly biological data. It deals with finding meaningful ways to interpret biological data.

To reiterate, I am not an expert in these fields and have drawn all of my knowledge on these subjects from Wikipedia. Regardless, hope this helps.

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