Shminux, there are plenty of writers—mostly far more skilled than me!---who have attempted to connect our physical understanding of dynamics to our mathematical understanding of dynamical flows. So please don’t let my turgid expository style needlessly deter you from reading this literature!
In this regard, Michael Spivak’s works are widely acclaimed; in particular his early gem Calculus on Manifolds: a Modern Approach to Classical Theorems of Advanced Calculus (1965) and his recent tome Physics for Mathematicians: Mechanics I (2010) (and in a comment on Shtetl Optimized I have suggested some short articles by David Ruelle and Vladimir Arnold that address these same themes).
Lamentably, there are (at present) no texts that deploy this modern mathematical language in service of explaining the physical ideas of (say) Nielsen and Chuang’s Quantum Computation and Quantum Information (2000). Such a text would (as it seems to me) very considerably help to upgrade the overall quality of discussion of quantum questions.
On the other hand, surely it is no bad thing for students to read these various works—each of them terrifically enjoyable in their own way—while wondering: How do these ideas fit together?
Shminux, there are plenty of writers—mostly far more skilled than me!---who have attempted to connect our physical understanding of dynamics to our mathematical understanding of dynamical flows. So please don’t let my turgid expository style needlessly deter you from reading this literature!
In this regard, Michael Spivak’s works are widely acclaimed; in particular his early gem Calculus on Manifolds: a Modern Approach to Classical Theorems of Advanced Calculus (1965) and his recent tome Physics for Mathematicians: Mechanics I (2010) (and in a comment on Shtetl Optimized I have suggested some short articles by David Ruelle and Vladimir Arnold that address these same themes).
Lamentably, there are (at present) no texts that deploy this modern mathematical language in service of explaining the physical ideas of (say) Nielsen and Chuang’s Quantum Computation and Quantum Information (2000). Such a text would (as it seems to me) very considerably help to upgrade the overall quality of discussion of quantum questions.
On the other hand, surely it is no bad thing for students to read these various works—each of them terrifically enjoyable in their own way—while wondering: How do these ideas fit together?