COMPSCI120: pass the exams, not just read the notes
Your complete guide to University of Auckland's mathematics for computer science course. See where the marks are, work real practice questions, and study with an AI tutor that knows COMPSCI120.
Sia generates COMPSCI120 practice questions, walks through integers and modular arithmetic step by step, and quizzes you on the material the exam weights most heavily.
Worked example
Prove or disprove: for every integer n, n squared plus n is even. Which argument is a correct proof?
Factor: n squared plus n equals n(n+1), the product of two consecutive integers.
Conclude: in both cases n(n+1) is even, so n squared plus n is even for every integer n. This is a direct proof by cases.
Reject the alternatives. Option B checks examples, which proves nothing for 'every integer'. Option C assumes the conclusion. Option D forgets that n odd makes n+1 even, so the sum n squared plus n is odd plus odd, which is even.
The trap: Treating a list of checked cases as a proof, or assuming the claim in order to prove it. The course marks the structure of the argument, and both errors score zero regardless of whether the claim is true. classic slip!
One exam decides 50% of your grade. Test + exam: at least 44.55 of 90 points required. This whole page is built around that.
Overview
What COMPSCI120 is, and where it sits
COMPSCI 120 is the University of Auckland's discrete mathematics course for the Computer Science major and the foundation for COMPSCI 220, COMPSCI 225 and the later algorithms, machine learning and theory courses. The catalogue frames it around one idea — mathematical proof — and warns that the course will feel different from most others because it cares as much about how an argument is formed as about the answer.
The published key topics are integers, primes, divisibility and modular arithmetic; sets and strings; the basics of combinatorics and probability; algorithms and their running time, functions and limit techniques; an introduction to graph theory; and the proof methods themselves — direct, by cases, by contradiction, by construction and by induction. The four learning outcomes run from reading and writing mathematical notation through modelling tasks as algorithms to proving the correctness of a simple algorithm.
Assessment is 100 points: 50 for the final exam, 40 for two tests, and 10 for tutorials, written assignments and a diagnostic quiz. Passing needs at least 49.5 points overall and at least 44.55 of the 90 points across tests and exam. Tutorials are unrecorded and attendance is required for credit. The course runs in Summer Semester, Semester One and Semester Two at the City campus.
Always treat your own course outline and the exam timetable as authoritative.
Difficulty & time commitment
Is COMPSCI120 hard, and how much time does it take?
COMPSCI120 is manageable if you keep a weekly rhythm and treat the back half as the main event. The pattern is consistent: it starts gently and steepens, and the heaviest assessment is the part that separates grades.
The difficulty curve and the assessment weighting point the same way: the back half is harder and worth more. Front-loading effort there is the highest-return decision in the course.
Is this course for you
Who tends to do well, and who tends to struggle
You will likely do well if
- You enjoy being asked why something is true, not just whether it is.
- You write proofs out in full sentences and check every step follows.
- You attend the weekly tutorial and do the problems there, where the proof habits form.
- You treat the two tests as the exam in miniature, because they carry 40 points.
You may struggle if
- You expect a programming course; this one is mathematics about programs.
- You verify claims with examples instead of arguments — the marks are for the argument.
- You skip induction because it feels mechanical; it is the technique the correctness outcome is built on.
- You lean on the 10 coursework points; the pass rule sits on the other 90.
- For every theorem in the course book, cover the proof and reconstruct it before reading it.
- Practise the five proof methods on the same statement where possible, so you can choose the right one under time.
- Write inductive proofs with the base case, the hypothesis and the step labelled every time.
- For graph and counting questions, draw the object first and name what you are counting before computing.
Syllabus
The 12 topics, topic by topic
The exam-weight marker on each topic shows where the marks concentrate. The amber topics carry the highest exam weight.
T1 · Integers, primes and divisibility
Key topicsDivisibility, primes and the division algorithm as the first objects to reason about.
T2 · Modular arithmetic
Key topicsCongruences and arithmetic mod n, the working example for many proofs.
T3 · Sets and strings
Key topics; learning outcome 1Set notation and operations; strings as the objects programs manipulate.
T4 · Direct proof and proof by cases
Key topics: methods of proofBuilding an argument from definitions; splitting into exhaustive cases.
T5 · Proof by contradiction and by construction
Key topics: methods of proofAssuming the negation; exhibiting an object that satisfies a claim.
T6 · Proof by induction
Key topics: methods of proof; learning outcome 4Base case, inductive step, and inductive proofs of algorithm correctness.
T7 · Formal logic
Learning outcome 4Statements, truth tables and validity, the tools for judging an argument.
T8 · Combinatorics
Key topics; learning outcome 3Counting arrangements and selections in easy real-life settings.
T9 · Probability
Key topics; learning outcome 3Basic probability and the expectation of a discrete random variable.
T10 · Functions and algorithms
Key topics; learning outcome 2Functions as mathematical objects; translating tasks into algorithms.
T11 · Running time and limit techniques
Key topicsComparing growth rates and reasoning about running time.
T12 · Graph theory
Key topics; learning outcome 2Vertices, edges, paths and trees as models for real-life tasks.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Assignments | 4% | Written assignments. Across the semester. Individual coursework. |
| Diagnostic Quiz | 1% | Diagnostic quiz. Start of semester. Individual coursework. |
| Tutorials | 5% | Weekly tutorials; attendance required to receive credit. Weekly. Group and individual coursework. |
| Final Exam | 50% | Final examination, on campus. Examination period. Test + exam: at least 44.55 of 90 points required. |
| Tests | 40% | Two tests, on campus, 20 points each. Across the semester. Test + exam: at least 44.55 of 90 points required. |
- Two conditions: at least 49.5 of the 100 points overall, AND at least 44.55 of the 90 points available for the tests plus the final examination. Tutorial, assignment and quiz points cannot lift a test-plus-exam total under that line.
- Ninety of the hundred points are two on-campus tests (20 each) and a 50-point exam, all marked on the quality of the argument. The 10 coursework points reward attendance and practice rather than carrying the grade.
This is an exam-cram course. With the exams at 50% of the grade and the final exam alone at 50%, your result is overwhelmingly decided by how well you perform under time pressure. Test + exam: at least 44.55 of 90 points required.
Final exam timing: During the examination period. Confirm the exact date and venue on your exam timetable.
How to actually pass it
A weekly rhythm, two checklists, and the traps to avoid
The course rewards consistency over cramming, and practice over re-reading. Here is the loop that works, then what to have nailed before each exam.
The weekly loop
Before the mid-semester checklist
- Read and write basic notation for numbers, sets, functions and strings.
- Prove a divisibility or modular-arithmetic statement directly and by cases.
- Construct a proof by contradiction.
- Write a correct inductive proof.
Before the final heaviest topics
- Count arrangements and selections and compute a discrete expectation.
- Determine the validity of a logical statement by truth table.
- Model a task with functions, trees or graphs and reason about running time.
- Prove the correctness of a simple algorithm.
The mistakes that cost marks
Examples offered as proof. Checking a claim for n = 1, 2, 3 proves nothing. The course exists to break this habit.
Induction without a stated hypothesis. The inductive step must say what is assumed; markers look for it explicitly.
Assuming what is to be proved. Circular arguments are the most common way a proof scores zero.
Formula & concept sheet
The vocabulary and formulas you must own
- Divisibility
- a divides b when b is an integer multiple of a; the basic relation of number theory.
- Modular arithmetic
- Arithmetic on remainders after division by n.
- Set
- A collection of distinct objects, manipulated with union, intersection and complement.
- String
- A finite sequence of symbols over an alphabet.
- Direct proof
- An argument from definitions and known results straight to the conclusion.
- Proof by contradiction
- Assuming the negation of the claim and deriving an impossibility.
- Proof by induction
- Proving a base case and that each case implies the next.
- Truth table
- A tabulation of a compound statement's truth value for every assignment of its variables.
- Combination
- A selection of items where order does not matter.
- Expectation
- The probability-weighted average of a discrete random variable.
- Graph
- A set of vertices joined by edges; a tree is a connected graph with no cycles.
- Running time
- How the number of steps an algorithm takes grows with input size.
Set texts
The prescribed reading
The syllabus references map straight onto these.
COMPSCI 120 course book
.
Where it fits
Prerequisites, related courses & why it matters
Prerequisite: MATHS 102, or at least 13 credits in NCEA Level 3 Mathematics, or D in CIE A2 Mathematics, or C in CIE AS Mathematics, or 3 out of 7 in IB Mathematics. Restriction: COMPSCI 225, MATHS 254. COMPSCI 120 is 15 points at Stage 1, core to the Computer Science major, offered in Summer Semester, Semester One and Semester Two at the City campus.
Your COMPSCI120 study toolkit
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Each tool already knows COMPSCI120: your syllabus, your texts, and where the marks are. Grouped by how you study, from first contact to exam week.
FAQ
Frequently asked questions
Is COMPSCI 120 hard?
It rates moderately hard. Proof-based mathematics is a genuine step for most first-year students, 90% of the marks are tests and exam, and the pass rule requires 49.5% on that component as well as overall.
What is the assessment breakdown?
Assignments 4%, diagnostic quiz 1%, tutorials 5%, two tests totalling 40% and a final exam 50%, per the catalogue page. You need at least 49.5 points overall and at least 44.55 of the 90 test-plus-exam points.
What are the prerequisites?
MATHS 102, or at least 13 credits in NCEA Level 3 Mathematics, or D in CIE A2 Mathematics, or C in CIE AS Mathematics, or 3 out of 7 in IB Mathematics. It cannot be taken with or after COMPSCI 225 or MATHS 254.
Is programming involved?
The course is mathematics. It models tasks as algorithms and proves things about them, but the published outcomes are about notation, modelling, counting, probability, logic and proof, not writing code.
Are tutorials compulsory?
Attendance at tutorials is required to receive credit for that component (5%). Tutorials are not recorded.
What does it lead to?
COMPSCI 220 and COMPSCI 225, and the advanced courses on algorithms, machine learning and theoretical computer science that the catalogue names.
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