C960 Discrete Mathematics II, catalog number MATH 2810, is the four-CU continuation covering searching and sorting algorithms, big-O estimates, number theory and cryptography, recursion and induction, counting, discrete probability and models of computation. It is the course where discrete mathematics stops being background and starts explaining why the software you write behaves the way it does.
The course that makes computing make sense
Students often arrive at C960 having survived the first discrete course and expecting more of the same. The content is heavier but the payoff is much more immediate. Every topic here answers a question a working developer actually asks.
Why does one search feel instant on a million records and another crawl? Big-O. Why does a recursive function that looks elegant fall over on real input? Recursion depth and the recurrence relation that describes its cost. How does a message stay private across an open network? Number theory, specifically modular arithmetic and the difficulty of factoring. How many test cases would exhaust this input space? Counting. What is the chance this hash collides? Discrete probability. What can a machine of this shape compute at all? Models of computation.
Framing each block with its question is not a study trick. It is the difference between memorising complexity classes and being able to derive one for code you have never seen.
Big-O is about growth, not speed
The concept that causes the most trouble is the simplest to state and the easiest to misuse. Big-O describes how the cost of an algorithm grows as the input grows. It says nothing about how fast the code runs on your machine, and an algorithm with worse growth can easily be faster on small inputs.
Three habits make it reliable. Count operations as a function of input size before naming a class, rather than pattern matching on the shape of the loops. Drop constants and lower-order terms only at the end, so you can see what you dropped. And be explicit about which case you are describing, since best, average and worst can differ enormously for the same algorithm, and sorting is the standard example where that difference matters.
Recurrence relations are the second half of this. A recursive algorithm's cost is defined in terms of itself, and the analysis is the process of turning that self-reference into a closed form. Practise by writing the recurrence for a familiar recursive procedure and then unrolling it by hand three levels deep. The pattern that appears is usually the answer, and induction is what turns the pattern into a proof.
A study plan for four heavy competency units
Read your Course of Study first, 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 compensation between aspects. Where the instrument is a proctored objective assessment, your preassessment result is the allocation tool.
A worked plan with numbers. Seven blocks: searching and sorting, complexity and big-O, recursion and recurrences, induction, number theory and modular arithmetic, cryptography, and counting with discrete probability, plus a short eighth on models of computation. Over nine weeks at twelve hours a week that is one hundred and eight hours, or roughly thirteen per block. Give each block four hours of concept, seven of problems and two of implementing or tracing an algorithm by hand on paper. That last slice is what makes complexity analysis intuitive rather than memorised.
Where a written task exists, budget by aspect: seven scored aspects across a 2,000-word submission leaves about 250 words each after an opening and a close, and analysis aspects deserve more than description aspects, since a complexity claim needs its derivation shown rather than asserted.
How to present an algorithm analysis
Follow your task directions where they set a format. Otherwise this order is what a reader checking an analysis needs.
| Element | What to write | Frequent omission |
|---|---|---|
| Problem statement | What the algorithm takes in and what it must produce | Analysing an algorithm without pinning down its input |
| Algorithm description | Pseudocode or a numbered procedure, unambiguous | Prose that hides a loop boundary or an off-by-one |
| Correctness argument | Why it produces the right output, often by induction on the loop | Assuming correctness because the code ran once |
| Operation count | The counting, shown, as a function of input size | Jumping straight to a complexity class |
| Complexity class | The class, with the case named | Not saying whether it is best, average or worst case |
| Space analysis | Additional storage as a function of input size | Ignored entirely, which recursive algorithms punish |
| Comparison | How it stands against an alternative, and when each wins | Declaring one better with no crossover discussion |
The comparison row is where good answers separate themselves. Saying that one sort is better than another is weak. Saying that one has better growth but higher constants, so the other wins below a certain input size, is the kind of statement that shows you understand what the notation does and does not claim.
Working habits for the number theory and counting blocks
- Do modular arithmetic by hand until the reductions feel natural. Working modulo a small number is a skill that transfers directly into every cryptography question.
- Practise the greatest common divisor algorithm on paper. It underpins the key generation ideas, and running it manually makes the reasoning behind those ideas visible.
- For counting problems, decide first whether order matters and whether repetition is allowed. Those two questions determine the formula, and almost every wrong answer comes from answering them carelessly.
- Draw the sample space for small probability questions. Discrete probability is countable by definition, and enumeration catches errors that formulas hide.
- Trace algorithms on tiny inputs, four or five elements, writing every intermediate state. This is slow, and it is the fastest route to understanding.
- Keep a page listing each algorithm with its best, average and worst case side by side. Building it yourself is the revision.
For the cryptography material specifically, keep the mathematics and the security claim separate in your writing. The mathematics shows what an operation does. The security claim depends on what is computationally hard, and stating that distinction clearly is what a well-written answer does.
What Competent looks like in C960
WGU records outcomes as Competent or Not Competent, without letter grades or an ordinary grade point average. Performance assessment work can be revised and resubmitted with no penalty for the earlier version, and proctored objective assessments are yours alone to sit.
Work that passes cleanly in this course tends to show:
- Operation counts shown before any complexity class is named.
- The case named, so a claim about worst case is not read as a claim about all cases.
- Induction used where a claim covers all inputs, with the hypothesis actually used in the step.
- Counting answers accompanied by a sentence saying whether order and repetition mattered.
- Cryptographic reasoning that separates what the mathematics does from what makes it secure.
Proctored assessments do not move. We prepare only, with diagnostics, algorithm-tracing drills, worked complexity derivations and timed practice, plus 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 C960
- Naming a complexity class by looking at loop nesting. Two nested loops are not automatically quadratic if the inner bound depends on something that shrinks.
- Ignoring the case. A sorting algorithm can be linear in the best case and quadratic in the worst, and an answer that gives one number without saying which is incomplete.
- Forgetting space complexity. Recursive solutions consume stack, and an analysis that only counts time misses half the comparison.
- Applying a counting formula without checking order and repetition. The four combinations produce four different formulas and the wrong one looks perfectly plausible.
- Treating modular arithmetic as a calculator operation. The properties matter more than the computation, and they are what the cryptography block rests on.
- Leaving models of computation to the last night. It is short, it is abstract, and it does not reward rushing.
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 targeted at the analysis skills: complexity derivations shown step by step, recurrence unrolling practice, counting drills that force the order and repetition question, modular arithmetic sets, and where a written task exists, a model analysis laid out the way an evaluator reads one.
WGU terms run six months at a flat rate, so closing more courses inside a term is what lowers your effective cost per course. C960 is one of the heavier four-CU courses on a computing plan and it benefits from being taken close behind the first discrete course, while the logic and proof material is still fresh enough to use without relearning.
Questions students ask about C960
Is C960 the same as MATH 2810?
Do I need C959 first?
How much programming is in this course?
Complexity, recursion and cryptography in one term?
Send your competency list and preassessment result. You get complexity derivations shown step by step, recurrence practice and counting drills that force the right questions.
Where C960 sits in WGU's programs
The July 2026 catalog places this code in 3 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.