
We can't explain the universe, just describe it; and we don't know whether our theories are true, we just know they're not wrong. >Harald Lesch
If you can hold on a little longer--maybe until black friday--with your purchase you can likely get 2 more cores for (almost) free. The 8th Gen Core-i is a response to AMD finally catching up (at least for multithreaded), so they offer more value for the money.
Then again, you mentioned planning to do calculations with the CPU. It's not something I'd recommend because all heavy computational load should be done by GPU by now. GPUs are so much faster it's not even funny. Like 20-100 times faster. At that point it doesn't matter which CPU you get. So do invest some time finding out if that stuff can't be done in parallel with the interfaces you mentioned. If not, why go for an i7 instead of i5? It's not faster for single threaded.
Unless the calculations can be done in parallel, but nobody bothered yet to write a GPU interface for the software... But then you should go the AMD route. Even more cores - they are dedicated for this stuff.
--it really comes down to the exact scenario what offers the best bang for the buck.
Although you are right, if you just wanna blindly buy a CPU that's decent all around i7 is the way to go. But Gen.8 please.

I just changed the CPU to the non-k variant because that's what I'd recommend. Is your gf really going to dabble into overclocking territory? She's not even gaming, so for what? Speed up 'dem Fouriers right and proper, right?
Onward. I like the cooler.

Pauper already mentioned the mobo mishap. Also, as a general rule, try to avoid µATX, especially if you have no need for the smallness and want the thing to last and be able to comfortably upgrade.
Memory is alright. I just found one that's a little cheaper with better timings. No need to go for "quality RAM" or "good brands" (if you're not overclocking!) because if they work, they work - they also don't age like other stuff.
Also just one thing to consider: While 16GB is recommended, you can still get by with 8GB at least for a year or two. I'm pointing this out because RAM prices are ridiculous right now, and are bound to go down eventually.
Storage is great. I guess I don't need to elaborate on storage space and SSD/HDD combo.
Again I agree with Pauper, the GPU is smallish. It will be more than enough for D3 since it's not a demanding game by any means. But times change and in 3 years you might have another game you're playing. If you go for just 1 tier higher, you place yourself in the midrange gaming. And cards there are notorious to last a long time for medium to light gaming. The upgrade is just $40 but will probably save you from having to buy a new card for another 2-3 years if your goal remains gaming at medium settings and 1080p. If that's likely going to change at some point, the econonomic choice is 1050 (no Ti) and upgrade when it happens.
Case: Ugh. I know it's an emotional choice and it looks cool, performs well but there's
cheaper choices for that look. Theoretically your gf doesn't need good airflow or cable management. Or even a window (right?), so you could just pick the cheapest off the shelf that you like and be done with it. But I know your inner geek wants something classy.

So why not really go for it with the one I included? (also available in black)
Also while mine doesn't have it, I'd recommend an USB-C slot for future proofing. I just couldn't find a good one quickly.
Nice PSU. But overpowered. Light gaming, right? Might probably do with 400W. Get 500-550W to have some headroom and account for aging.
Here's a review for the one I picked, for all you Corsair doubters.

All there things considered, here's my build based off of yours: (But remember to wait for Coffee-Lake!)
Sorry your initial build wasn't ridiculous, so I couldn't scrape off much of it. But here's an alternative that cuts the corners I mentioned.
Not quite under $750, but because starting with 8GB RAM doesn't make sense at all (would save $75!) if you only have 2 memory banks. You'd cap yourself to 16GB or have to throw the 8GB out at some point. If you get a 4-bank mobo this would be an option.
Overall it should perform about the same as the Intel build, but isn't as well rounded. The devil is in the details:
- CPU is bad for single threading and even a bit worse than the i7-7700 on multithreading; hopeless against an i7-8700.
- no backup GPU in the CPU
- RAM will be single channel initially, dual channel at best when upgraded later (due to only 2 banks on the mobo)
- SSD allows only 1-2 games on it for fast loading times
- Case: No idea, actually. Just went for something cheap that didn't immediately strike me as horrible.

- PSU isn't modular -> excess cables lying in the case.