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is a foundational course typically required for computer science majors at many universities (most notably at the University of Illinois Urbana-Champaign). The course bridges the gap between calculus-level mathematics and the logical reasoning needed for advanced CS topics like algorithms, data structures, compilers, and theory of computation.

The course emphasizes and clear written arguments . Students learn not just how to compute, but how to prove that their solutions are correct. Success in CS 173 is often a strong predictor of success in upper-level CS theory courses.

: Early units often cover modular arithmetic, greatest common divisors, and prime numbers, providing a basis for later studies in cryptography. is a foundational course typically required for computer

We learned that some problems are undecidable. That the Turing Machine halts, Or it spins forever, And there is no algorithm to know which. I wrote a program to check if you loved me, But the compiler just returned: Error: Infinite Loop.

: The course introduces Big-O notation, teaching students how to quantify the efficiency of code, especially recursive functions. Course Structure and Philosophy Students learn not just how to compute, but

We studied the P versus NP problem— Easy to verify, hard to solve. I could check the warmth of your hand in a millisecond, But to compute the path that led there Would take longer than the heat death of the universe.

The course moves away from the continuous mathematics of calculus to focus on "discrete" objects—things that are distinct and countable. We learned that some problems are undecidable

CS 173 has evolved over the years, notably through the work of Professor Margaret Fleck, who authored the primary textbook, Building Blocks for Theoretical Computer Science . CS173: Discrete Structures Syllabus