# Differences between subfields of biology related to mathematics?

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?

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.

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.