For an introduction to tensors, go to this series by eigenchris (this is part 1 of a 16 part series):
Video #4 in the series is enormously important, you will learn what "covectors" are and you will immediately see the relationship to level sets in the phase diagrams.
So let's say we have some small pieces of DNA called "transcription factors", and let's say they all control the same gene. We can write an equation for the amount of the gene that's being expressed, as a function of the transcription factors.
So g = f(t1) + g(t2) + h(t3) and so on for as many tf's as needed.
But since these are transcription factors we also have
t1 = a(t2) + b(t3) + ...
t2 = c(t1) + d(t3) + ...
...
which we can write in matrix form with 0's on the diagonal.
For this system of coupled equations we will often have complex roots, which means our solution will oscillate. There will be periods with more gene expression, and periods with less. This is how we get genes to express themselves during development and again in old age.
You don't need a course in complex analysis to understand the complex solutions, you'll learn everything you need to know from the quadratic formula in dynamics, and Euler's equation. What's important is that you understand
e^i€ = cos(€) + i sin(€)
Because e^i€ is a solution for most of your coupled equations. Most of the genetic equations are pretty simple, you don't need LaPlace transforms or Fourier transforms to solve them. However you need to be solid with the linear algebra, and you need to know about tensors because many of the genetic equations go up into 5 or 6 or 7 dimensions.
So for example, let's say we have a surface defined by the concentrations of tf1 and tf2, and we want to know how tf3 acts on that. Well, we can represent the influence as a "field", which is a vector at every point in the tf1-tf2 plane. Then if we add tf4 we can change coordinates to get a new influence map. If the underlying gene is a promoter for yet another gene, we can transform the tf3 field using a tensor, and thereby arrive at the influence of each transcription factor on the underlying gene. It sounds a lot more complicated than it is. It's really pretty easy. But you need the math background for the oddball cases, which sometimes can get a little hairy.
The oddball cases would include things like indels caused by histones that don't fully unwind the DNA for a polymerase. If you have tf's controlling the histone you want to know the odds of an indel in the underlying gene when a tf goes south.