Analytical solutions in circuit analysis are impossible for the vast majority of nontrivial circuit designs and few subfields of electrical engineering require computer simulations so you wont see much mathematical rigor in practice. Electrical engineering is all about rules of thumb, experience, and intuition unless you're designing something like a high efficiency power circuit, a complex high speed digital or mixed mode design, or an antenna. Most of the time, my circuit designs are based off of reference designs provided by the part manufacturer, who also provide routing and design guidelines. As long as I'm not pushing the limits with fabrication (bigger board, more layers to route, few overlapping power domains, large vias and no microvias, etc) the first prototype usually just works, with a few minor mistakes and oversights, without having to do any math or simulations.
By the time intuition and documentation fails an experienced electrical engineer, they're probably designing something that costs tens of thousands of dollars to prototype and hundreds of thousands worth of testing equipment. It'll be a long while before you get to that point so I wouldn't worry about the math, although I still recommend studying it because it might help develop that intuition.