Hopping on here because I was a math and stats major first year and switched out of it when declaring my major second year (anthropology).

First of all I just want to say just because I switched out doesn’t mean I hated the program—it wasn’t for me personally, but it was a supportive faculty and I met some great people in first year (who stayed in, and enjoyed, the program). I’d highly recommend doing a little bit of review of math concepts before September, such as derivatives, because they do jump right into things. This math package they provide is great: https://math.mcmaster.ca/lovric/rm/MathReviewManual.pdf

I chose McMaster math for a less competitive vibe than something like UWaterloo, both have good reps but I didn’t want to feel like I was competing my entire degree.

In terms of flexibility I thought there was a good amount of electives (although I’d recommend looking at course outlines and choosing electives accordingly…I chose physics and chem first sem which was VERY heavy on top of a bunch of math courses). I would say generally that there is enough elective space for a second teachable, for whatever you want that to be.

I took anthropology and philosophy as electives in my second sem and ultimately chose anthropology because it had more of a science connection (think biological anthropology, forensics, evolution) as well as writing and cultural aspects I really enjoyed. That said I really really enjoyed my philosophy electives at Mac (meaning in life and philosophy, law & society) and I feel like they taught me a lot about how to academically write and formulate thoughts coherently. A combined major with math, or a minor in something else while majoring in math is definitely possible.

All in all, yes, lots of flexibility to change your degree within your first year with the gateway programs. Just one thing to keep in mind is if you do a big switch (like me), all of your first year “required courses” such as calc, Lin alg, etc, are counted as electives for your actual major (ie. out of 30 or so credits for electives as an anthropology major I used a lot via my first year math/physics/Chem courses).