Idealizations are concepts like point charges, infinitely thin wires, massless rods, infinitely sharp barriers, etc. — physics is full of them. They are enormously useful, but physicists need to understand how to deal with the real world, which is messier. To do this, physicists often exploit approximations. Thus, you will need to learn when and how to approximate and when and how to idealize. We'll use electrostatics as an example of how to use approximations.

Symmetry is an enormously powerful concept in physics. The simple observation that a small stone dropped in a pond produces circular ripples leads to the powerful conclusion that the water is isotropic (responds the same in all directions). Noether's theorems that translational and rotational invariance lead to conservation of energy and angular momentum are fundamental statements about our universe. And group theory places limitations on the nature of atomic orbitals and the properties of fundamental particles based entirely on symmetry arguments. We'll use the concept of symmetry to calculate electric fields of charges and magnetic fields of currents.

Geometric reasoning is the art of using geometry, not merely algebra, to solve problems. Science is about the relationships between physical quantities, not merely about functions. Geometric reasoning can be as simple as drawing a picture, but it also includes such techniques as using coordinates adapted to the problem at hand — and understanding the geometry of the tools of vector calculus, such as gradient, divergence, and curl.