University Of North Dakota Discrete Math

Discrete Math at University Of North Dakota – What Actually Happens When You Sit Through It

I took a bunch of discrete courses back when I was grinding through undergrad, and honestly the material itself is rough whether you are somewhere fancy or not. What distinguishes the University Of North Dakota Discrete Math sequence from every other school doing the same thing comes down to pacing, which proofs they force you to write, and how much they make you rely on textbook exercises versus something that looks like real work. UND usually strings discrete math across MAT 151 or similar intro courses, then pushes into MAT 350 or MAT 450 level classes where the work gets serious. You will cover propositional logic, predicate logic, sets, functions, relations, induction, combinatorics, graph theory, and sometimes basic number theory or Boolean algebra depending on which professor runs the section. That lineup is standard for any ABET-ish program, but UND tends to lean heavier on formal proof writing than some schools that skim the surface. I remember pulling an all-nighter in sophomore year trying to prove something about transitive closure on a directed graph using only induction. The textbook example used a matrix multiplication approach, which felt like cheating because it sidestepped the actual recursive structure they wanted. I ended up rewriting the proof three times, starting from the base case on a single edge and building up by adding one vertex at a time. That was the workaround. It took about forty-five minutes longer than it should have, but the professor marked it correct on the first read, which is rare for this kind of thing.

What the Work Feels Like Day to Day

You start with logic and truth tables. Easy enough. Then they hit you with quantifiers and you realize you do not actually know how to negate a statement with nested quantifiers without second-guessing yourself. I keep running into people who flip the quantifier but forget to negate the inner predicate. That mistake shows up on midterm one every single semester. You learn it eventually, but the first pass is annoying. Induction is where most students stall. The base case is trivial. The inductive step is where you earn your keep. If you treat the inductive hypothesis like magic advice instead of something you are allowed to assume, you will waste hours on problems that take five minutes once you stop overcomplicating them. I once spent an entire Saturday trying to prove a summation formula by expanding both sides instead of just applying the hypothesis directly. The shortcut is obvious in hindsight. It is not obvious when you are stuck.

Combinatorics and Graph Theory

Combinatorics at UND likes to hide simple counting arguments behind word problems that sound harder than they are. Pigeonhole principle shows up constantly. If you can recognize when a problem is really asking for pigeonhole instead of brute force enumeration, you save a massive amount of time. I have seen students write out thirty-line case analyses for problems that resolve in two sentences once you identify the right category. Graph theory is the part that actually feels useful. Trees, spanning trees, Dijkstra, bipartite matching. These concepts show up later in algorithms classes, so the discrete math section is your first chance to sit with them without the pressure of implementation. The proof-based angle can feel disconnected from the applications, but that disconnection is temporary. Once you take the algorithms class, everything clicks.

How to Actually Pass Without Burning Out

Do the homework early. Not the day before. The day it is assigned. Proof classes accumulate fast, and if you fall behind even one week, the next week becomes incomprehensible. I watched three people drop MAT 350 last spring because they skipped a couple of homework sets on relations and never recovered. The material does not get harder. You just miss the foundation. Use the proof templates. When you are doing direct proofs, write the conclusion first, then work backward to see what you need, then flip it around for the forward direction. When you are doing contradiction, assume the opposite and look for an explicit logical impossibility, not just a weird intermediate result. Most students stop too early in contradiction proofs and present something that looks surprising instead of actually impossible.

Where This Approach Falls Short

The biggest limitation is that discrete math at UND, like most places, assumes you already know how to read and write formal arguments. If your high school math experience was mostly computational, the transition is jarring. You can be a solid calculus student and completely freeze on a basic set theory proof on day one. There is no remedy except practice. The TA hours help, but they are often swamped during midterms, so showing up early in the semester matters more than showing up when you are drowning. Another downside is that some professors treat graph theory like an afterthought. You might get three weeks of it and then move on. If you are aiming for computer science, you will need to supplement with an algorithms class or online material to get real depth. The discrete course gives you vocabulary and basic proofs. It does not make you competent in network flow orNP-completeness.

Resources I Actually Used

The required textbook was something by Epp or Rosen, depending on the term. Both are fine. I also grabbed the proof-writing chapter from How to Prove It by Velleman, which is not assigned but makes induction and quantifier negation click faster than any lecture. For practice problems, the Schaum's outline for discrete math is ugly but effective. It gives you hundreds of solved problems without the fluff. If you are looking for the actual course catalog, go to the UND math department page and search for MAT courses with discrete in the title. The code changes occasionally, so do not trust a cached link. The current sequence usually lists discrete structures as a prerequisite for upper-division math and computer science courses, which is why they push you through it early.

One Thing Nobody Tells You

Graph theory proofs feel intuitive until you have to write them formally. Drawing a picture makes the answer obvious. Translating that picture into rigorous notation is where points get lost. I learned to keep a sketch next to every proof, then reference the sketch while writing the formal version. It sounds elementary, but it cuts your revision time roughly in half. Your grader will not care about the sketch, but you will thank yourself when you catch a missing case before submission. That is basically how the course goes. It is not hard if you put in the hours. It is hard if you treat it like a memorization class. The material rewards patience and punishes procrastination pretty consistently. Good luck.