
"At a time of unprecedented expansion in the life sciences, evolution is the one theory that transcends all of biology. Any observation of a living system must ultimately be interpreted in the context of its evolution. Evolutionary change is the consequence of mutation and natural selection, which are two concepts that can be described by mathematical equations. Evolutionary Dynamics is concerned with these equations of life. In this book, Martin A. Nowak draws on the languages of biology and mathematics to outline the mathematical principles according to which life evolves. His work introduces readers to the powerful yet simple laws that govern the evolution of living systems, no matter how complicated they might seem. Evolution has become a mathematical theory, Nowak suggests, and any idea of an evolutionary process or mechanism should be studied in the context of the mathematical equations of evolutionary dynamics. His book presents a range of analytical tools that can be used to this end: fitness landscapes, mutation matrices, genomic sequence space, random drift, quasispecies, replicators, the Prisoner's Dilemma, games in finite and infinite populations, evolutionary graph theory, games on grids, evolutionary kaleidoscopes, fractals, and spatial chaos.
Very true, these books are qualitative. There's a bit of basic math around delta-G for reactions and Chi-sq tests for genetic associations, but the conventional undergraduate introductory biology course is 99% descriptive.
There are reasonable arguments for taking that approach. These courses are foundations for subsequent study, with the intended outcome that students have a broad but shallow understanding of core basic ideas. Lots of biology makes intuitive, mechanistic, and visual sense, much like introductory computer science and introductory chemistry.
Obviously applied math plays a key role in biology but it tends to address specific needs like protein structure prediction, dynamic modeling of transcription/translation and metabolism, inferring phylogeny, high-throughput 'omics analysis, network simulation of epidemic outbreaks, and so on. These are great to study, but without the broader context the understanding would be relatively fragmented, lacking the big picture.
Rereading OP's question:
> good modern starting points to someone who would want to learn more about how living beings work (from bottom up)?
I interpret that as wanting a general understanding, starting with chemistry and working upwards towards evolution and populations. That's all in the standard two-semester introductory course, hence my book recommendation.
If that's wrong and OP wants a math-centric approach, here are a few gems:
Physical Biology of the Cell, Phillips, et. al
An Introduction to Systems Biology, Alon
Evolutionary Dynamics, Nowack
https://www.amazon.com/Evolutionary-Dynamics-Exploring-Equat...
The long and the short of it is that software can't evolve because too much of its genome space is lethal, and the non-lethal parts are non-contiguous, so the quasispecies decoheres -- if it survives at all -- instead of climbing to the top of the fitness landscape.
The link I provided is of particular interest in the area of moral theory. There is a good book called Evolutionary Dynamics that summarizes this group's work and contains, among other things, a rather beautiful equation predicting the optimal rate of forgiveness in cooperating populations.
Short reply -- Get Martin Nowak's book Evolutionary Dynamics
Long reply -- Even Nowak's work is just the beginning (disclaimer: my current Ph.D. thesis work is building off of Nowak's start). Let's start with this notion that TE's are vital for evolution. Real answer: sort of. You see, there's an awful lot of species that don't have an overabundance of "junk" DNA, yet are still able to adapt and evolve. The reason that TE's at least seem to be more important in higher order plants and animals is because of how such organisms organize their genomes.
Ok, before I get carried away on a long rant, here's the heart of the matter for the hacker audience:
Proteins fold into domains. These are compact structures with a rough upper limit to their size that typically can carry out one biochemical function. In E. coli, most genes code for proteins with only one domain. So, E. coli can evolve by grabbing new genes, turning genes on or off, or in some circumstances, evolve new functionality from existing domains through random mutation. (In reality, random mutation takes a long time to produce anything useful, and the creation of novel domains appears to no occur. There's a theory growing in prominence that all of the protein domain folds that exist today were present when life began, and may even represent independent life originating events...but I'm getting off track.)
In humans, most of our proteins are multi-domain. Not all of these domains, however, are catalytic. That is, in a human protein with 5 domains, maybe only one actually has biochemical activity. The function of the rest is to modulate that activity or localize the protein to one part of the cell or another. Also, the mechanisms controlling when genes get turned on and off in humans is much more complex than in bacteria. Therefore, evolution in higher order plants and animals is much more likely to occur through a "shuffling" of domains and regulatory elements. Because TE's are good at "shuffling" DNA, it's not surprising that having a healthy dose of this sort of "junk" DNA is advantageous. Of course, that's not all...there's also neutral evolution and pseudo-genes and epigenetic inheritance, etc. Biology is really on the cusp of exploding (oh, and I'm writing a book about that too ;-).
tl;dr -- The genetics of higher order plants and animals is not unlike a program which relies heavily on many libraries. If you swap out one XML parser for a better XML parser, you'll get better performance (and more customers!). Transposable elements function (sort of) like biology's equivalent of a linker, and can help organisms swap in and out libraries/protein domains.