United States $900-$1200 daily driver for college STEM

United States
$900-$1200
Are you open to refurbs/used options?

Yes
Screen size

14”-16”
Weight limit

Up to 4lbs is okay, this is not a hard restriction just a guideline.
Purpose

Schoolwork, entertainment, daily driver, future personal projects/business use
Form factor

Standard
Intended usage

I'm a soon to be undergrad student in college, who is mainly going to be focusing on CS and Math heavy workloads, and would like to be able to do general other engineering tasks on this laptop too. I've been looking for a laptop to be my daily driver (no desktop at all in college other than university resources), and was looking at some gaming laptops, but figured from information online that a dedicated gpu was not really necessary for my use case and only made the battery life of the laptop worse.  
Desired battery life

10-12+ hours of light usage (browsing, watching video, light programming/simulations), maybe 6 hours of heavy usage (just guidelines)
Please list, in order of most important to least important, the priority between Size, Weight, Performance, Battery life

Battery Life, Performance ,Size, Weight
(Battery life and performance could be swapped if battery still meets specifications)
Info/Requirements

32GB of ram would be nice, touchscreen if possible, backlit keyboard if possible, 1TB of solid state storage minimum