Discrete Mathematics
Discrete Mathematics was a ten-week course covering the branch of math that computing actually runs on. It works in distinct, countable things rather than continuous curves, which is exactly how machines represent state. Coming in as a sysadmin, I kept noticing that the abstract topics were describing tools I already use without naming them formally.
What the course covered
The first weeks were propositional logic: propositions that are true or false, the AND, OR, NOT, and IF-THEN operators that combine them, truth tables, and logical equivalence. From there we moved into number theory, including modular arithmetic and congruence, and then into sequences and the difference between linear and exponential growth modeled as geometric sequences.
The middle of the course dealt with sets and set operations, difference, complement, and nested sets, then combinatorics. That unit covered permutations versus combinations, which comes down to whether order matters, and led into probability with the binomial formula, independent events, and the complement rule for "at least one" cases. The last stretch was graph theory and trees: vertices and edges, weighted and directed graphs, Euler and Hamiltonian paths, shortest-path thinking, and the properties that make a structure a valid tree.
What connected to my work
The logic unit was the most direct hit. A truth table is the same reasoning I use writing a conditional in PowerShell, and getting the operators wrong on a service-state check is exactly the kind of bug that restarts a service mid-startup. Sets map onto filtering and group membership. Combinatorics put numbers to how quickly configuration options explode even in a small environment.
Graph theory was the surprise. Once you see infrastructure as vertices and edges, a lot of daily work reframes cleanly. A Terraform dependency graph is a directed acyclic graph. Network topology, failure propagation, and redundancy planning are all graph problems, and shortest-path algorithms are what GPS and routing quietly rely on.
Takeaway
The honest value of this course was giving formal names and rules to reasoning I was already doing by instinct. Logic underpins every conditional, and graphs underpin every network. Being able to reason about both on purpose, rather than by feel, is worth the ten weeks.