Ahhh! I'm so glad someone recommended Lois McMaster Bujold. I meant to after reading your post, but procrastinated. </p>
The first book is Shards of Honor, which is often sold packaged as an omnibus edition with the second book, Barrayar. They're really one long book, so if you can't find the omnibus, do try and get both. Cordelia is a WONDERFUL female character - and a math nerd to boot.
So those books deal with the mother of Bujold's main protagonist, Miles Vorkosigan. Who is my favorite character in most of books. I love him so much I named my baby after him. True story!
If you like the Vorkosigan Saga, and I so hope you do, Bujold wrote a fantasy series that's also (mostly) tremendous. The first book is The Curse of Chalion, and it's wonderful. But the *second* book, Paladin of Souls, is one of my favorite books ever, in genre or out of it. So many things to love about that book. In fact I think I should reread it right now. The third book, The Hallowed Hunt, was probably the most meh thing I've read of hers. I should probably re-read it to see if I'm judging too harshly. But I recall it being distinctly disappointing.
One of the things about the Chalion series that was so wonderful is that it *makes sense.* It has consistent internal logic, and though there's magic, it doesn't just deus ex machina all over the place. It's so refreshing to not feel insulted by a fantasy writer.
She has another fantasy series called The Sharing Knife that I enjoyed a lot, but it's kind of quiet and poky. I'd only check it out if you read and love the Vorkosigan and Chalion books.
I am so jealous you're starting this trip - wish I could experience the Vorkosigan-verse for the first time.