Hello Sir/Ma'am. In computer science, it is essential to learn the basic structure of how the software performs its tasks. It is their task to make sense of the Mathematica formulas of the real world and convert it into a series of steps that the computer can follow. The areas that were considered to be major parts of computer science was initially set to:

Programming Languages and Methodology

Data Structures

Algorithms

Computer Architecture and Elements

And theories in computation

Computer Engineering, on the other hand, is deeply rooted in the field of electronics and deals with how the computer and its devices interact regardless of the software that is installed. It is up to them to design and create devices that can actually communicate with established hardware. Here are a few samples on topics that computer engineering deals with:

Digital Logic

Electronics

Microprocessor Programming

Algorithms

Digital Signal Processing

Embedded Systems

VLSI Design and Manufacture