
"Physical Biology of the Cell is a biophysics textbook that explores how the basic tools and insights of physics and mathematics can illuminate the study of molecular and cell biology. Drawing on key examples and seminal experiments from cell biology, the book teaches physical model building through a practical, case-study approach, demonstrating how quantitative models derived from basic physical principles can be used to build a more profound, intuitive understanding of cell biology."--Jacket.
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
I can recommend 3 really good books, SICP-level good:
1. Biological Sequence Analysis by Durbin et al.
How to model DNA, RNA and proteins as probabilistic languages / generative models. There is also a companion book with all exercises solved.
2. Physical Biology of the Cell by Phillips et al.
A massive amount of quantitative cell biology models that use simple undergrad physics.
Originated from a Caltech course. After reading this book, all other intro to biology books look like a bag of tricks.
3. An Introduction to Systems Biology: Design Principles of Biological Circuits by Alon.
Bacterial circuits from the perspective of an electrical engineer.
Sadly, NSF discontinued funding for a totally epic Cold Spring Harbor Summer school for postdocs that taught [2,3].
A shame, we need more quantitative biology and less bags of tricks.
Introduction to Modern Statistical Mechanics - David Chandler
Physical Biology of the Cell - Phillips, Kondev, Theriot, & Garcia
http://www.amazon.com/Physical-Biology-Cell-Rob-Phillips/dp/...