CS103: Mathematical Foundations of Computing at Stanford is a core course exploring the limits of what computers can solve, how they do it, and why some problems are harder than others. It trades calculus for discrete mathematics, logic, and theoretical models.
The course is divided into four main areas:

1. Mathematical Logic & Proofs: Covers sets, formal proof techniques (contradiction, induction), first-order logic, functions, and graph theory to build mathematical rigor.
   
2. Automata Theory: Explores simple mathematical models of computation, including Finite Automata (DFAs/NFAs), Regular Expressions, and Context-Free Grammars.
   
3. Computability Theory: Introduces Turing Machines to define the absolute limits of computing, culminating in proofs of unsolvable problems like the Halting Problem.
   
4. Complexity Theory: Examines efficiency, focusing on the famous P vs. NP question and how to classify problems that are computationally difficult (NP-Completeness).