MAT9004: pass the exams, not just read the notes
Your complete guide to Monash University's mathematical foundations for data science and ai unit. See where the marks are, work real practice questions, and study with an AI tutor that knows MAT9004.
Sia generates MAT9004 practice questions, walks through differentiation and vectors step by step, and quizzes you on the material the exam weights most heavily.
Worked example
Let f(x) = x^3 − 6x² + 9x + 2, a single-variable function of the kind drilled in the Week 3 optimisation material. At which value of × does f have a LOCAL MAXIMUM on the real line?
Find the stationary points by setting the first derivative to zero. f'(x) = 3x² − 12x + 9 = 3(x² − 4x + 3) = 3(x − 1)(x − 3), so f'(x) = 0 at × = 1 and × = 3.
At × = 1: f''(1) = 6(1) − 12 = -6, which is less than 0, so × = 1 is a LOCAL MAXIMUM.
At × = 3: f''(3) = 6(3) − 12 = +6, which is greater than 0, so × = 3 is a local minimum (not what was asked).
So the local maximum is at × = 1 (option index 1). For reference, f(1) = 1 − 6 + 9 + 2 = 6 is the local-maximum value.
The trap: Picking × = 3 confuses the two stationary points: f''(3) is positive, which marks a local minimum, not a maximum. The sign of the second derivative decides it (negative means local max, positive means local min), so you must test BOTH stationary points and read the sign, not just take the first or last one. Picking × = 0 or × = 2 forgets to solve f'(x) = 0 at all, since neither is a stationary point (f'(0) = 9 and f'(2) = -3 are both non-zero). classic slip!
One exam decides 60% of your grade. HURDLE: you must score at least 45 out of 100 on the exam to pass the unit; covers all six learning outcomes (the whole syllabus). This whole page is built around that.
Overview
What MAT9004 is, and where it sits
MAT9004 is Monash University's mathematical-foundations unit for the Master of Data Science and related Faculty of Information Technology degrees. It is deliberately not a data-science unit: it is the underlying mathematics toolkit that computing and statistics rest on, taught from the ground up. Across twelve teaching weeks it builds six largely independent areas in turn (single-variable calculus, linear algebra, multivariable calculus and optimisation, counting and combinatorics, probability and Bayes, and graph theory) and maps them onto six unit learning outcomes. The framing throughout is the mathematics a data scientist actually uses: fitting models by least squares, eigen-decomposition behind PageRank, Bayes for classification, and graphs for networks.
The teaching order is non-standard and worth knowing before you enrol. The unit opens with calculus (Weeks 1 to 4: sets and functions, univariate functions, differentiation and optimisation, integration), then linear algebra (Weeks 5 to 6: vectors, matrices, Gaussian elimination, determinants, eigenvalues), then multivariable calculus and optimisation (Weeks 7 to 8: partial derivatives, the gradient, the Hessian, stationary points), and only then the discrete-maths and probability block (Weeks 9 to 12: combinatorics, probability and Bayes, random variables and distributions, and graphs and networks). This is the reverse of a typical discrete-first foundations sequence, so the heaviest calculus and linear-algebra material arrives first while you are still settling in.
It is an exam-cram unit by design. Sixty per cent of the mark and a 45%-on-the-exam hurdle ride on a single 3-hour-10-minute final that is closed-book with no calculator (a formula sheet is provided inside the paper), so the whole semester is best treated as preparation for one paper. The exam answers are exact (integers or lowest-terms fractions, no decimals) and split between short-answer questions and a hand-written-and-uploaded response section. Because the six topic areas barely overlap, the unit rewards steady weekly drilling of every problem-sheet and past-paper question by hand, with no tools, rather than last-minute cramming.
Official outline: handbook.monash.edu · MAT9004 outline. Always treat the official outline and the exam timetable as authoritative.
Difficulty & time commitment
Is MAT9004 hard, and how much time does it take?
MAT9004 is manageable if you keep a weekly rhythm and treat the back half as the main event. Across student reviews 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 unit.
Is this unit for you
Who tends to do well, and who tends to struggle
You will likely do well if
- You are comfortable with secondary-school calculus and algebra: differentiating with the power, product and chain rules, solving quadratics by factorising or the formula, and rearranging linear equations by hand.
- You drill every technique by hand with no calculator (Gaussian elimination, eigenvalues from the characteristic polynomial, the Hessian-determinant test, Bayes by formula, counting by cases) until each is automatic, because the exam allows no tools.
- You do the weekly problem sheets and past papers by hand and self-mark against the posted solutions, keeping exact fractions rather than reaching for decimals.
- You keep pace with all six disjoint areas, including the discrete-maths and probability block taught last (Weeks 9 to 12), since it is fully examinable on the same closed-book final as the calculus and linear algebra taught first.
You may struggle if
- You rely on a calculator or software for arithmetic; the closed-book exam allows neither, and answers must be exact integers or lowest-terms fractions, so weak by-hand computation shows up immediately.
- You let the discrete-maths and probability block (combinatorics, probability and Bayes, graphs) slide because it is taught last, even though it carries as much exam weight as the calculus and linear algebra.
- You memorise formulas instead of being able to apply the method, such as eigen-decomposition or the Hessian-determinant test, under exam pressure with only the provided formula sheet.
- You leave practice to the final weeks; with six largely separate topic areas and a 45%-on-the-exam hurdle, there is no single thing to cram, so steady weekly drilling is what carries you over the hurdle.
- Build the by-hand technique for every area early (the derivative and integral rules, Gaussian elimination and the 2x2 inverse, eigenvalues from det(A − lambda I) = 0, the Hessian-determinant test, the four selection counts, Bayes, and the handshaking lemma) so the back half has a foundation.
- Re-derive rather than memorise: get the second-derivative test, the characteristic polynomial, the Hessian classification table, the inclusion-exclusion formula and Bayes' theorem from the idea, using the provided formula sheet only as a backstop.
- Work the past papers timed and by hand: they follow a stable template that drills each area with fresh numbers, so practise producing exact integer or lowest-terms-fraction answers under no-calculator conditions.
- Keep one running page per area summarising the method and signature worked example, and rehearse reproducing each computation (a Gaussian elimination, an eigen-decomposition, a stationary-point classification, a two-stage Bayes calculation) from scratch.
Syllabus
The 12 topics, week by week
The exam-weight marker on each topic shows where the marks concentrate. The amber topics carry the highest exam weight.
T1 · Introduction to sets and functions
Lectures 1 to 2; supports ULO5Sets, membership, subsets, unions, intersections and differences, intervals, sum and product (sigma and pi) notation, and functions as domain, codomain and rule, with graph and image.
T2 · Univariate functions for data analysis
Lectures 3 to 4; ULO5 calculusProperties of functions (zeroes, inverses, injective, surjective, bijective, convex and concave), linear and polynomial functions, exponentials, logarithms and power laws, and using log-log, log-lin and lin-log plots to identify a function type.
T3 · Differentiation and optimisation
Lectures 5 to 6; ULO5 calculusDerivative rules (power, exponential, logarithmic, product and chain), stationary points, the first- and second-derivative tests, convexity from the second derivative, and global extrema on a closed interval, with least-squares (RSS) as the application.
T4 · Integration
Lectures 7 to 8; ULO5 calculus; Quiz 1 (Week 4)Definite and indefinite integrals, antiderivatives and the constant of integration, standard antiderivatives, the Fundamental Theorem of Calculus, linearity and additivity, and rate-to-accumulated-quantity applications.
T5 · Vectors and matrices
Lectures 9 to 10; ULO4 linear algebraVectors in R^d, linear combinations, dependence and independence, the dot product, the Euclidean norm and orthogonality, matrix arithmetic and the non-commutative matrix product, linear systems Ax = b and Gaussian elimination.
T6 · Eigenvalues and eigenvectors
Lectures 11 to 12; ULO4 linear algebra; Quiz 2 (Week 6)The identity, inverse and determinant (with the 2x2 inverse and invertibility test), eigenvalues from the characteristic polynomial det(A − lambda I) = 0, eigenvectors, diagonalisation A = PDP^-1, matrix powers, and PageRank and Markov-style applications.
T7 · Multivariable functions
Lectures 13 to 14; ULO6 multivariable calculus; Assignment 1 dueRelations, circles, ellipses and inequalities, functions of two variables, level sets and contour maps, partial derivatives, the gradient vector and its steepest-increase and level-set-perpendicular properties, and first-order linear approximation.
T8 · Multivariable optimisation
Lectures 15 to 16; ULO6 multivariable calculus; Quiz 3 (Week 8)Stationary points where the gradient is zero, second partials and the Hessian, the Hessian-determinant test for local min, local max and saddle points, convexity in two variables, and global extrema with boundary reduction.
T9 · Counting principles and combinatorics
Lectures 17 to 18; ULO2 combinatoricsThe product, sum and complement rules, the four selection types (ordered or unordered, with or without repetition), factorials and binomial coefficients, Pascal's triangle and the binomial theorem, inclusion-exclusion and the pigeonhole principle.
T10 · Probability foundations
Lectures 19 to 20; ULO3 probability; Quiz 4 (Week 10)Probability spaces and events, uniform spaces with Pr(A) = |A|/|S|, the complement and union rules, mutual exclusivity and independence, conditional probability, the multiplication rule, the law of total probability and Bayes' theorem.
T11 · Random variables and probability distributions
Lectures 21 to 22; ULO3 probability; Assignment 2 dueRandom variables and distributions, expectation and its linearity, variance and standard deviation, the discrete distributions (uniform, Bernoulli, geometric, binomial) and the continuous distributions (uniform, exponential, normal with the z-score).
T12 · Graphs and networks
Lectures 23 to 24; ULO1 trees and graphs; Quiz 5 (Week 12)Graphs, walks, paths, cycles and connectivity, degrees and the handshaking lemma, trees and spanning trees (n vertices and n − 1 edges), the adjacency matrix and walk-counting by matrix powers, and Euler and Hamilton circuits.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Assignment 1 | 10% | Individual project submitted via Moodle; no generative AI permitted. Due 11:55pm Wednesday of Week 7 (dates subject to change). Late penalty 10% per day up to 7 days, then zero; run through similarity detection. |
| Assignment 2 | 10% | Individual project with a strict page limit, submitted via Moodle; no generative AI permitted. Due 11:55pm Wednesday of Week 11 (dates subject to change). Late penalty 10% per day up to 7 days, then zero; run through similarity detection. |
| Quizzes (5) | 20% | Five in-class applied quizzes, 4% each, 30 minutes each; no generative AI permitted. Held in the applied class in Weeks 4, 6, 8, 10 and 12 (dates subject to change). All five count, 4% each; individual work. |
| Final exam | 60% | Closed-book e-exam, 3 hours 10 minutes, no calculator and no notes (a formula sheet is provided on page 2 of the paper); short-answer questions whose answer is an integer or lowest-terms fraction, plus a hand-written response section scanned and uploaded within 30 minutes of the exam ending. Formal exam period (date to be advised on the official timetable). HURDLE: you must score at least 45 out of 100 on the exam to pass the unit; covers all six learning outcomes (the whole syllabus). |
- Pass on a weighted average of at least 50%, AND score at least 45% on the final exam itself. The 45%-on-the-exam hurdle is confirmed in the unit materials: missing it fails the unit regardless of the weighted average.
- The final has two question types: short-answer questions whose answer is a rational number (an integer or a lowest-terms fraction a/b with no spaces and no decimals), and a hand-written response section that you scan and upload via phone within 30 minutes of the exam ending. Past papers follow a stable template that drills each of the six areas with fresh numbers, so working past papers by hand is the single most valuable preparation.
- Calculator policy: No calculator is permitted in the final exam, and no notes, books, dictionaries or online sources. A formula sheet is provided inside the exam paper (page 2). Unlimited blank A4 paper is allowed as working sheets. Every method must therefore be hand-computable.
This is an exam-cram unit. With the exams at 60% of the grade and the final exam alone at 60%, your result is overwhelmingly decided by how well you perform under time pressure. HURDLE: you must score at least 45 out of 100 on the exam to pass the unit; covers all six learning outcomes (the whole syllabus).
Final exam timing: approx Nov 2026 (S2 offering, confirm against the official exam timetable). Confirm the exact date and venue on the official exam timetable.
How to actually pass it
A weekly rhythm, two checklists, and the traps to avoid
The unit 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
- Lock in the calculus and linear-algebra core taught first (derivative and integral rules, stationary points and the second-derivative test, vectors and matrices, Gaussian elimination, the 2x2 inverse and eigenvalues), since the early quizzes and Assignment 1 land here.
- Drill the optimisation workflow by hand: find f', solve f' = 0, classify with f'' or the sign test, and compare values at stationary, singular and boundary points on a closed interval.
- Practise Gaussian elimination and eigen-decomposition (characteristic polynomial, then eigenvectors via (A − lambda I)x = 0) until you can do a clean 2x2 or 3x3 example with no calculator.
- Sit Quizzes 1 to 3 (Weeks 4, 6 and 8) seriously and self-mark, treating them as low-stakes rehearsals for the no-calculator final.
Before the final heaviest topics
- Cover all six areas, because the final examines the whole syllabus on one paper: single- and multi-variable calculus, linear algebra, combinatorics, probability and Bayes, and graph theory.
- Work the past papers timed and by hand: they follow a stable template, so practise each slot (sums and products, convexity, stationary points, Gaussian elimination, eigen-decomposition, counting, Bayes, handshaking) with fresh numbers.
- Drill the exact-answer discipline: produce integers or lowest-terms fractions with no decimals and no spaces, since that is how the short-answer section is marked.
- Rehearse the signature long-answer set-pieces: global extrema on a closed interval, the full gradient-Hessian-classify multivariable problem, a 2x2 eigen-decomposition A = PDP^-1, a parametrised linear system with a free variable, and a two-stage Bayes (total probability then reverse conditional).
- Practise the hand-written-upload workflow once before the exam so the scan-and-upload step within the 30-minute window is not a surprise on the day.
The mistakes that cost marks
Confusing the local max and local min in the second-derivative test. At a stationary point, f'' negative means a local maximum and f'' positive means a local minimum. Reading the sign the wrong way, or testing only one of the stationary points, is the most common single-variable optimisation error and it cascades into a wrong global extremum on a closed interval.
Reaching for a calculator or decimals. The final is closed-book with no calculator and answers must be exact integers or lowest-terms fractions. Building a habit of decimal approximations in practice leaves you stranded in the exam; keep everything as exact fractions and do the arithmetic by hand from the start.
Neglecting the discrete-maths and probability block. Combinatorics, probability and Bayes, and graphs are taught last (Weeks 9 to 12) but carry as much exam weight as the calculus and linear algebra taught first. Treating them as an afterthought leaves a large, examinable chunk of the paper under-practised.
Underestimating the 45%-on-the-exam hurdle. A strong weighted average does not save you if you score below 45% on the final itself, because the exam is a hurdle. With 60% of the grade and the hurdle both on one no-calculator paper, steady by-hand practice across all six areas, not last-minute cramming, is what carries you over.
Teaching team
Who teaches MAT9004
The bios below are factual. The star ratings are not ours: they are impressions from students who have taken the unit, so you can hear from people who sat in the lectures.
Dr Greg Markowsky
Chief Examiner and lecturer for MAT9004; the contact for extensions and the assessment regime, with office hours immediately following lecture or by appointment.
Meng Shi
Unit Coordinator for MAT9004 (Clayton Campus); the contact for problem sheets, assignments, general assessment questions and unit structure.
Foong Wei WONG
Unit Coordinator for the Malaysia Campus offering of MAT9004, available by email to set up an appointment or Zoom e-consultation.
Teaching team as listed in the unit materials reviewed. AskSia does not rate lecturers; star ratings are submitted by students who have taken MAT9004.
Where it fits
Prerequisites, related units & why it matters
MAT9004 is a postgraduate mathematics-foundation unit and assumes secondary-school-level calculus and algebra rather than a prior university maths unit. Confirm the exact enrolment prerequisites and any prohibited combinations against the current Monash handbook, as these are set by the faculty and can change.
Your MAT9004 study toolkit
Study the unit with Sia, not just read about it
Each tool already knows MAT9004: 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 MAT9004 hard?
It is hard for a foundation unit, mainly because of how it is assessed. The content itself is taught from the ground up, but 60% of the grade plus a 45%-on-the-exam hurdle sit in one 3-hour-10-minute final that is closed-book with no calculator, and the unit crams six largely separate mathematical areas into that single paper. It is very manageable with steady weekly practice of every problem sheet and past paper by hand, but it punishes leaving the by-hand technique to the last minute.
How is MAT9004 assessed?
Two assignments worth 10% each, five in-class quizzes worth 20% combined (4% each, in Weeks 4, 6, 8, 10 and 12), and a 60% final exam. Continuous assessment is therefore 40% and the exam is 60%. You pass on a weighted average of at least 50%, and there is an additional hurdle: you must score at least 45% on the final exam itself to pass the unit, regardless of your overall average.
What is the final exam format?
A closed-book e-exam of 3 hours 10 minutes with no calculator and no notes; a formula sheet is provided on page 2 of the paper, and unlimited blank A4 paper is allowed for working. There are two question types: short-answer questions whose answer is an integer or a lowest-terms fraction (no spaces, no decimals), and a hand-written response section that you scan and upload via phone within 30 minutes of the exam ending. It covers all six learning outcomes, so the whole syllabus is examinable.
Can I use a calculator in the exam?
No. The final exam is closed-book with no calculator, no notes, no books, no dictionaries and no online sources. A formula sheet is provided inside the paper, so every method must be hand-computable: Gaussian elimination, eigenvalues by the characteristic polynomial, derivative and integral rules, Bayes by formula, and counting by cases. Practising every technique by hand, with no tools, is the core of preparing for this unit.
Why is the topic order calculus first and discrete maths last?
MAT9004 teaches in a non-standard order: single-variable calculus (Weeks 1 to 4), then linear algebra (Weeks 5 to 6), then multivariable calculus and optimisation (Weeks 7 to 8), then counting and combinatorics (Week 9), probability and Bayes (Weeks 10 to 11), and graphs and networks (Week 12). This is the reverse of a typical discrete-first foundations sequence, so the heavier calculus and linear-algebra material arrives first while you are still settling in, and the discrete and probability block, though taught last, is fully examinable.
Do I need a textbook?
No textbook is prescribed. The unit provides everything you need: annotated lecture slides and recordings, weekly problem sheets with full typed solutions, the assignment sheets with solutions and walk-through videos, and official lecture notes. A free supplement (Gilbert Strang's Calculus on MIT OpenCourseWare) and the Maths Learning Centre videos are recommended for extra practice, but nothing needs to be bought.
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