E071 Applied Discrete Mathematics, catalog number MATH 2850, is the three-CU E-series course covering logic, Boolean algebra, sets, functions, relations, graphs, combinatorics and modular arithmetic applied to technology. It is the single-course alternative to the older C959 and the D420 to D422 module sequence. Applied is the operative word: the material arrives attached to technology problems rather than as abstract structure.
What the applied framing changes
The topic list overlaps heavily with the other discrete courses in the catalog, so the difference is emphasis rather than subject. In an applied treatment, a question is less likely to ask you to prove a set identity and more likely to describe a network, a permission system or a scheduling problem and ask you to model it.
That shifts the skill being scored from proof craft toward modeling craft. You still need the definitions to be exact, because the modeling depends on them. What changes is the direction of travel: instead of being handed a structure and asked to reason about it, you are handed a situation and asked which structure describes it.
The reliable habit is to keep a short mental catalog of what each structure is good for. Graphs model things connected to other things: networks, dependencies, routes, social links. Trees model hierarchies and decisions. Relations model associations between two collections, which is what permissions and lookups are. Combinatorics answers how many, which is what test coverage, key spaces and configuration counting need. Modular arithmetic handles anything cyclic, from clock time to hashing to checksums. Reading a scenario and reaching for the right one is most of what this course develops.
E071 against the other discrete entries
The catalog carries more than one route through this material. C959 Discrete Mathematics I under MATH 2800 is the four-CU course, and it is also delivered as three one-CU modules: D420 Discrete Math: Logic, D421 Discrete Math: Functions and Relations and D422 Discrete Math: Algorithms and Cryptography. E071 is the three-CU single-course alternative in the E series.
They are separate catalog entries with separate competency lists, so requirements follow the code on your Degree Plan rather than the topic overlap. What the overlap does give you is a much wider pool of usable study material, since a resource written for any of these will be mathematically relevant. Read your own Course of Study for what is actually assessed.
Combinatorics is where applied questions concentrate
Counting problems appear more heavily in an applied course than in a proof-focused one, because how many is the question technology work asks constantly. How many passwords of this form exist, how many distinct configurations does this system have, how many test cases would cover every combination of three settings.
Every counting problem reduces to two questions asked in order. Does order matter, and is repetition allowed. Those two produce four cases and four corresponding methods, and the overwhelming majority of wrong answers in this material come from answering them carelessly rather than from arithmetic.
Two further habits help. The addition principle applies when choices are alternatives, and the multiplication principle applies when choices are made in sequence, so read the problem for and against or. And when a direct count is awkward, count the complement instead: the number of arrangements with at least one repeat is usually far easier to reach by subtracting the arrangements with no repeats from the total.
A plan for three competency units
Open your Course of Study before planning, since 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 and a score of 2 in each passes the task, with no averaging. Where the instrument is a proctored objective assessment, the preassessment result tells you where the hours belong.
A worked plan with numbers. Six blocks: logic and Boolean algebra, sets and functions, relations, graphs and trees, combinatorics, and modular arithmetic. Over six weeks at nine hours a week you have fifty-four hours, or nine per block. Inside each, use two hours for definitions, five for problems, and two for building your own applied scenario and modeling it. That last slice matters more here than in a proof-focused course, because inventing a scenario forces you to understand which structure fits, which is exactly the skill an applied assessment tests.
Where a written task exists, budget six scored aspects across a 1,600-word submission at roughly 250 words each after an opening and a close. Modeling aspects want more, since they need the structure named, justified and then applied.
How to write up an applied discrete problem
Where task directions set a format, follow them. Otherwise this order makes an applied answer complete.
| Stage | What you write | Where answers fall short |
|---|---|---|
| Scenario in your words | The system or situation, and the question being asked about it | Restating the prompt without identifying the question type |
| Structure chosen | Graph, tree, relation, set, or a counting model, named | Starting to compute before committing to a structure |
| Justification | One sentence connecting a feature of the scenario to the structure | Choosing correctly by instinct and never saying why |
| Mapping | What the vertices, edges, elements or positions represent | A model whose parts are never tied back to the situation |
| Working | The computation or the reasoning, shown | Answers produced with no traceable path |
| Result in context | The answer as a sentence about the original system | A bare number that answers nothing on its own |
| Assumptions | Anything the scenario left unstated that you decided | Silent assumptions that change the answer |
The mapping row is the one to insist on. A graph with unlabelled vertices proves nothing about the network it was supposed to model. Saying that each vertex is a server and each edge is a permitted connection takes one line and makes the entire answer verifiable.
Working habits for an applied course
- Draw the structure before computing anything. Graphs, trees and relations are all visual, and the picture usually answers half the question.
- For counting, write the two questions explicitly on the page: does order matter, is repetition allowed. Then choose the method.
- Sanity check counts against a smaller version of the problem you can enumerate by hand. If the formula disagrees with the enumeration on four items, it is wrong.
- Do modular arithmetic reductions by hand so the properties become familiar. Cyclic behaviour is easier to trust once you have produced it.
- Check graph claims by counting degrees. Many results follow immediately from the degree sum, which is faster than any argument.
- Keep every scenario you model in one file, with the structure chosen noted beside it. That file is your revision resource and it is more useful than any formula list.
What Competent looks like in E071
Results arrive as Competent or Not Competent. No letter grade is issued, no ordinary grade point average is kept, performance assessment work can be revised and resubmitted with no penalty attached to the earlier version, and objective assessments are proctored and sat by you alone.
Applied discrete work that passes cleanly tends to show:
- A structure named and justified before any computation.
- Every element of the model tied to something in the scenario.
- Counting answers preceded by explicit statements about order and repetition.
- Working shown so a reader can follow the path to the answer.
- Results written as sentences about the original system, with assumptions stated.
Proctored assessments do not move. We prepare with modeling drills, counting practice, graph exercises and modular arithmetic sets, plus timed practice and an honest readiness read. We do not sit or assist during any assessment and we never ask for portal credentials.
Six mistakes that cost time in E071
- Computing before choosing a structure. The modeling decision is the assessed skill, and skipping it leaves the reasoning aspect empty.
- Answering a counting problem without settling order and repetition. The four cases give four formulas, and the wrong one always looks plausible.
- Leaving a graph unlabelled. A drawing with no mapping back to the scenario cannot support any claim about it.
- Confusing the addition and multiplication principles. Alternatives add, sequences multiply, and the words and and or in the problem usually tell you which.
- Treating modular arithmetic as remainder syntax. The useful part is the properties that survive reduction, which is what makes cyclic reasoning work.
- Assuming the topic overlap makes another course's rubric relevant. Competency lists and assessments belong to the code on your plan.
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 built for the applied framing: scenario-to-structure drills, counting problems that force the order and repetition questions, graph and relation exercises with labelled mappings, modular arithmetic practice, and where a written task exists, a model submission with the structure named, justified and mapped.
Terms at WGU run six months at a flat rate, so what lowers your effective cost per course is how many you close inside a term. Three CUs of applied discrete mathematics moves quickly for students who build the modeling habit early, and slowly for students who try to memorise formulas, which is the largest single difference in how long this course takes.
Questions students ask about E071
Is E071 the same as MATH 2850?
Is E071 a replacement for C959 or the D420 modules?
How much proof writing does an applied course require?
Scenarios to model and no structure in mind?
Send your competency list. You get scenario-to-structure drills, counting practice that forces the right questions, and graph exercises with labelled mappings.
Where E071 sits in WGU's programs
The July 2026 catalog places this code in 1 current WGU program. 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.