<p>I am interested in all engineering disciplines, but more in mechanical/electrical and may be planning to probably double major along with physics (may drop my math major). So, which engineering discipline utilizes the most advanced topics in math and physics (quantum mechanics, classical mechanics, abstract algebra, topology, etc.)? Is it true most engineers from all disciplines do not use any math more in-depth than ordinary and partial differential equations?</p>
<p>Most advanced math? I don’t know whether you count Computer Science as engineering, but probably that, if you do. Otherwise, there are highly mathematical areas of industrial engineering. For the most part, the rest of engineering is going to be applied analysis (complex, diffy-q’s, etc.) of the let’s-make-the-MATLAB-do-it variety.</p>
<p>Most advanced physics? I don’t know whether you count Engineering Physics as engineering, but the whole point of this is that you study more modern (hence more advanced) physics. Otherwise, my gut reaction would be to rank disciplines based on how long people have been doing them, with the assumption that disciplines which have been practiced longer rely on more fundamental physical notions. So… Chemical (uses quantum), Electrical (uses E&M), Aerospace/Mechanical (uses dynamics), Civil (uses statics). Computer Science and Industrial Engineering don’t really use any physics.</p>
<p>Certain branches of EE (signal processing) are very math heavy.
Certain branches of CS (algorithms) are heavy in discrete mathematics.
And industrial engineering is very mathematical…</p>
<p>Most people say EE. Haven’t taken Signals yet but I’ve heard it’s literally all math.</p>