C959 Discrete Mathematics I, catalog number MATH 2800, is the four-CU course covering logic and proofs, Boolean algebra and functions, set theory, sequences and series, relations, graphs and trees. It is the un-split predecessor of the one-CU modules D420, D421 and D422, so if your Degree Plan shows those three instead, the material is the same ground broken into pieces. Either way, the course is where computing students first meet mathematics that is written in sentences rather than computed.
Proof is the skill, and it is a writing skill
Discrete mathematics feels different from every mathematics course before it because the answer is usually an argument rather than a number. That catches people who were comfortable in algebra and calculus, where a wrong answer is visibly wrong. Here a wrong proof can look entirely reasonable, and a correct proof written badly gets marked as incomplete.
Treat proof as a genre with rules. State exactly what you are proving before you prove it. Say which technique you are using: direct, contrapositive, contradiction, or induction. Define your symbols. Move one step at a time, and make every step follow from something already established or from a definition. Finish by saying you have shown the thing you said you would show.
The technique choice is more mechanical than students expect. A statement of the form if this then that usually wants a direct proof, unless the negation is easier to work with, in which case take the contrapositive. A claim that something cannot exist almost always wants contradiction. Anything about all positive integers wants induction. Learning to read the shape of the claim and pick the tool is most of the battle, and it can be practised deliberately in a way that staring at proofs cannot.
C959, D420, D421 and D422 are the same material
WGU carries both arrangements in the catalog. C959 is the four-CU course, and the one-CU modules cover it in three parts: D420 Discrete Math: Logic takes logic, proofs and Boolean algebra, D421 Discrete Math: Functions and Relations takes set theory, finite sequences, series and relations, and D422 Discrete Math: Algorithms and Cryptography takes searching and sorting, big-O and number theory.
Two practical points. Study material moves freely between the arrangements, so a resource written for one of the modules is directly useful in C959 and the reverse. And the split changes the pacing rather than the content: three one-CU courses can each be closed on their own, which suits students who want visible progress inside a term, while the single four-CU course suits students who prefer to learn the connections in one continuous run. Check which arrangement your Degree Plan uses before planning your weeks.
A study plan for four competency units
Open your Course of Study before anything else. WGU keeps the competency list and assessment detail there rather than in the public catalog. Where a performance assessment exists, each scored aspect is judged on its own three-point scale, a score of 2 in each passes the task, and nothing averages. Where the instrument is a proctored objective assessment, the preassessment tells you where your hours belong.
A worked plan with numbers. Six blocks: propositional logic, predicate logic and proof, set theory, functions, relations, and graphs and trees. Over eight weeks at eleven hours a week that is eighty-eight hours, or about fourteen per block. Inside each block, take three hours for definitions, eight for problems, and three for writing out two complete proofs from that block in full prose. The prose hours are the ones students cut and the ones that decide whether the assessment goes well, because a proof you can follow is not the same as a proof you can write.
Where a written task exists, budget words by aspect. Six scored aspects across a 1,800-word submission gives roughly 280 words each after an opening and a close. Proof aspects deserve more, because a proof written to length rather than to completeness is the most common cause of a return in this subject.
A layout for writing a proof that scores
Where directions set a format, follow it. Otherwise this order is what a reader checking a proof expects to find.
| Part | What it contains | Where proofs fail |
|---|---|---|
| Claim | The statement being proved, written out in full | Proving a slightly different statement than the one asked |
| Technique | Direct, contrapositive, contradiction or induction, named | Starting to write without deciding, then switching mid-proof |
| Definitions | Every term used, in the form the course defines it | Using an intuitive meaning of divides, subset or relation |
| Assumption | What you are taking as given, stated explicitly | Assuming the thing being proved, which is the classic circularity |
| Chain of steps | Each step justified by a definition, a hypothesis or a previous step | Jumps that are obvious to the writer and invisible to the reader |
| Base and inductive step | For induction, both, with the hypothesis stated precisely | An inductive step that never uses the hypothesis |
| Conclusion | A sentence saying what has been shown | Stopping at the last algebraic line and leaving the reader to infer |
The definitions row carries more weight than it looks. In discrete mathematics almost every proof is unpacked directly from a definition, and students who write from intuition rather than from the formal statement of what a term means produce arguments that feel right and prove nothing.
Working habits for graphs, relations and sets
- Draw everything. Sets as regions, relations as arrows, graphs as vertices and edges. Discrete objects are small enough to picture and pictures prevent most reasoning errors.
- Test with small cases before proving. If a claim about all graphs fails for the graph with three vertices, you have saved an hour and found a counterexample.
- Check relation properties one at a time. Reflexive, symmetric, antisymmetric and transitive are separate questions and answering them as a group is how students miss one.
- Write set expressions with explicit element conditions rather than in words. The membership statement is what a proof manipulates.
- For graphs, count degrees before reasoning. Many results fall straight out of the sum of degrees, and counting is faster than arguing.
- Keep a definitions page in your own words next to the formal version. Understanding lives in the first and proofs are built from the second.
One habit separates students who find this course satisfying from those who find it maddening: after finishing a proof, write one sentence saying which definition did the actual work. It is almost always one, and identifying it makes the next proof of that type far faster.
What Competent looks like in C959
WGU records outcomes as Competent or Not Competent, with no letter grades and no ordinary grade point average. Performance assessment work can be revised and resubmitted with no penalty for the earlier version, and objective assessments are proctored and yours alone to sit.
Discrete mathematics work that passes cleanly tends to show:
- The claim restated before the argument begins.
- A named technique, used consistently to the end.
- Formal definitions used rather than paraphrased ones.
- Every step justified, with no leap the reader has to reconstruct.
- An explicit conclusion rather than an argument that simply stops.
Proctored assessments are yours to sit and that does not change. We prepare with diagnostics, proof-writing drills, worked examples and timed practice, and we give an honest readiness read. We do not sit or assist during an assessment, and we never ask for portal credentials.
Six mistakes that cost time in C959
- Reading proofs instead of writing them. Following an argument is a different skill from producing one, and only the second is assessed.
- Confusing the converse with the contrapositive. One is equivalent to the original statement and one is not, and mixing them invalidates the whole proof.
- Writing an inductive step that never uses the inductive hypothesis. If the hypothesis is not used, whatever you proved, it was not by induction.
- Treating examples as proof. Verifying a claim for five cases shows it is plausible. Only a general argument shows it is true.
- Skipping quantifiers. For all and there exists change a statement entirely, and dropping them makes a claim ambiguous enough to be unprovable.
- Postponing graphs and trees to the end. They are the most visual and most enjoyable part of the course, and leaving them until the week before the assessment wastes the momentum they provide.
How support works on this course
Send your competency list, any preassessment result and task directions from your Course of Study. What comes back is proof-focused: a technique-selection guide keyed to the shape of a claim, worked proofs written the way an evaluator wants to read them, drills that build from small cases to general arguments, and where a written task exists, a model submission with each aspect answered under its own heading.
Terms at WGU run six months at a flat rate, so how many courses you close inside a term is what lowers your effective cost per course. Discrete mathematics rewards continuity more than most courses, because the later blocks lean on the earlier ones. A concentrated run through it usually finishes faster than the same hours spread across a whole term.
Questions students ask about C959
Is C959 the same as MATH 2800?
My plan shows D420, D421 and D422 instead. What is the difference?
Do I need calculus before discrete mathematics?
Proofs that feel right and still come back?
Send your competency list or task directions. You get a technique-selection guide, worked proofs written the way evaluators read them, and drills that build to general arguments.
Where C959 sits in WGU's programs
The July 2026 catalog places this code in 2 current WGU programs. Open a program page for the complete standard path and term positions. The live Degree Plan remains authoritative after transfer credit, substitutions, and mentor planning.
The assessments, one by one
The public catalog does not publish this course's PA/OA identity or task count. WGU Tutors publishes at most one PA manual per course and only from a WGU-controlled public rubric. Until that source exists, PA help begins from the student's real Course of Study and OA support remains preparation only.