Designing a mathematics course for 1st year chemistry students Background:
I am a mathematician with very little knowledge in chemistry (I do know some
physics). I will probably teach a course &quot;mathematics for (1st year) chemistry
students&quot; in the future (1st semester 3h + 1h exercises per week, 2nd semester
2+1h). This will be the only (mandatory) mathematics course in the chemistry Bachelor curriculum (and even the subsequent Master curriculum, as far as I know). The students should have high school mathematics background, such as onedimensional derivates and integration (at least of polynomials), but probably no complex numbers. I will have a lot of freedom in the selection and presentation of topics.
Questions:

Which topics are commonly covered in a &quot;mathematics for chemistry
students&quot; courses?
Closely related: Which textbook are most commonly used?


In more detail:

Can I safely assume that mathematical proofs and even rigorous definitions can/should mostly be skipped?

How black-boxy is Quantum physics used in the typical chemistry curriculum?
Even the most basic Quantum physics will need, as minimum, some linear algebra (Hermitian, normal and unitary operators, exponention of operators, etc.) as well as Fourier transformation and a little bit of differential equations. Should these topics be coverd, or is it enough to say &quot;one can show that in an H atom, orbitals look like this&quot;, and just talk a bit about complex valued functions in R^3?
Do you ever do calculations with spins? (Mostly spin 1/2, I would assume? That might be a motivation to show some calculations with complex 2x2 Matrices?)

Which computer mathematics software are most commonly used in a chemistry curriculum? (Mathematica? Maple?) I assume it would make sense to do some calculations and exercises using such software?


Update answering some comments:

I am in Austria (sorry, do not know how to add an according tag), but I would be interested in how these things are handled in other countries as well.
This course has been held before at our department (not by me), but I would like to get &quot;unbiased&quot; input from people from chemistry, and therefore did not list the traditional topics / lecture plan.
Of course I will speak to people in the Chemistry department, but I would be happy to get some ideas here first (I do not know the Chemistry department people, and it could be that a randomly selected person who happens to be willing to indulge me has some unorthodox views).
At least in the US, most undergraduate chemistry curricula do not go deep enough into the math of QM that you need to spend a great deal of time on it. Students that do take more advanced QM classes can learn the math at that time. I also am not sure it's safe to assume that all incoming students at that level have a good understanding of 1D calculus, though most will have had some exposure.
With that in mind, here are topics that I'd include (not in any specific order), structured around the relevant applications:

basic calculus review of integration and differentiation in 1D - main intro level application is chemical kinetics. Also applies to intro quantum.

setting up and solving systems of equations, especially including iterative solving methods - intro level application is solving systems of multiple equilibria by mass and charge balance

a module on statistics with a focus on dealing with experimental error and error propagation. Include methods of curve fitting and associated pitfalls. - applies to lab component of curriculum. Probably one of the more commonly overlooked aspects of math in chemistry

Fourier transform and other techniques involved in spectroscopy

Basics of symmetry operations and group theory