Are there job positions that can have you do a little of both?
There is, sort of. That sort of thing isn't an entry level role though.
The job keyword you're looking for is "DevOps". If you're particular about being in the Security side of it, "DevSecOps" has been getting thrown around in some circles for a while now, but it's not something I'd expect to find a lot of hits for when job hunting.
Honestly, considering you're just starting out, this is probably a fine long-term goal, but realistically, if this interests you, then you should start with getting a job in IT or Operations, and then just learn programming as you go. You're going to naturally find repetitive tasks that you can automate, and programming is the way to do it. Over time, you'll gain experience and the scope of your responsibilities will grow/change, and you'll apply the lessons you've learned to those domains, and suddenly you'll find that you tick most of the requirement boxes people are looking for.
I suppose I should actually explain the field some:
This is a field that is in high demand (and therefore rather lucrative), particularly in the web/cloud/startup shops you'll find all over the country, but predominantly in tech hubs like Silicon Valley, Seattle, New York, etc. So, particularly when starting out, you might need to be prepared to move if you're good/lucky enough to land a job. Remote work is becoming increasingly common (I did it for 5 years, across three companies), but it's unlikely you'll land a remote gig without at least a few years of prior experience.
Speaking of experience, it's for all intents and purposes a "jack of all trades" role, which means any employer looking for this sort of thing is looking for someone with already demonstrated experience in the field. It really depends on how the company defines the role, but in general, you can be expected to at least touch every single part of the technology stack, and directly interact with every engineering team in the company.
I've had to work on/with (back- & front-end) software development, infrastructure architecture, networking, security (internal & external), database administration, uptime monitoring/alerting... I'm probably forgetting some things, but you get the idea. I'm nowhere near the foremost expert in any of these fields, but I'm comfortable in all of them. You have to be capable of digging in to a domain you may have little practical experience with and either figuring out a basic plan of action by yourself (when no other expert is available on the team), or plugging into an existing dedicated team, and helping them figure out how to quickly interface with other parts of the infrastructure/stack and if possible, automate the process.
And as for math: well, I don't generally need to use anything beyond Algebra concepts, but if I end up working with a team that's doing something math heavy (i.e. I'm interfacing with a Machine Learning/Big Data team now), then being able to at least understand the basic concepts of what they're working with could potentially be a key part of figuring out ways to help them set up the right infrastructure to solve those problems. It's really not common though, so I wouldn't stress about it if you go down this road.