MH1300: pass the exams, not just read the notes
Your complete guide to Nanyang Technological University's foundations of mathematics course. See where the marks are, work real practice questions, and study with an AI tutor that knows MH1300.
Sia generates MH1300 practice questions, walks through elementary logic and truth tables step by step, and quizzes you on the material the exam weights most heavily.
Sharpen your argument
You must prove: for all integers n, if n squared is even then n is even. A direct proof stalls. What technique works, and why?
See why the direct route stalls. Assuming n squared is even gives n squared = 2k, and extracting information about n from that requires the very fact you are trying to prove. The hypothesis is hard to use directly.
Run the computation. If n is odd then n = 2m + 1, so n squared = 4m squared + 4m + 1 = 2(2m squared + 2m) + 1, which is odd. Done, and every step was forward computation from a usable hypothesis.
Note what the course is actually assessing. ILO8 asks you to distinguish between proof techniques and judge when each is more suitable. The mathematics here is trivial; recognising that contraposition converts an unusable hypothesis into a usable one is the assessed skill.
The weaker choice: Option C is the one that feels like mathematics to a student arriving from a computational background: examples confirm, so surely enough examples prove. They do not — a universal statement over an infinite set is never established by instances, though a single counterexample refutes it, which is ILO9. Option B misapplies induction, which needs a base case and a step over a well-ordered index and does not fit a statement of this shape. Option D is simply false about the logic: contraposition applies to conditionals precisely. watch this!
One exam decides 50% of your grade. Summative. This whole page is built around that.
Overview
What MH1300 is, and where it sits
MH1300 is the course that converts a computational mathematics student into one who can prove things. the course aims state it develops the skills necessary for a mathematically related job, that you should demonstrate a basic understanding of fundamental mathematical concepts and processes such as formal mathematical proofs, and that you should learn the rigorous way to approach mathematical problems and become familiar with the process of abstracting from examples.
NTU adds a sentence that explains the course's position in the degree: these skills are essential for all future mathematics courses. MH1300 is not one topic among many; it is the prerequisite habit of mind for everything after it.
The published thirteen-week schedule is unusually front-loaded on a single skill. Weeks 1 to 3 cover elementary logic. Weeks 4 to 9 — six consecutive weeks, nearly half the course — are mathematical proof. Weeks 10 and 11 cover sets, relations and functions; weeks 12 and 13 cover systems of numbers.
Always treat your own course outline and the exam timetable as authoritative.
Difficulty & time commitment
Is MH1300 hard, and how much time does it take?
MH1300 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 write proofs out in full sentences rather than as chains of symbols.
- You can state precisely what a quantified statement claims before trying to prove it.
- You attend consistently; 15% of the grade is in-class activities with no make-up.
- You treat the six proof weeks as the course's centre rather than as one topic among many.
You may struggle if
- You expect computation. This course asks for justification, and the shift catches most first-year students.
- You confirm statements with examples instead of proving them.
- You memorise proof techniques without judging which fits — ILO8 assesses exactly that judgement.
- You miss assessments; there are no make-up opportunities for any CA component.
- For every technique — direct, contraposition, contradiction, cases, induction — keep one statement it proves elegantly and one it proves clumsily. ILO8 is asking for that comparison.
- Write the negation of every statement before attempting a proof by contradiction; most failed attempts start from a wrong negation.
- Practise proving set statements both algebraically and by the element method; ILO15 names both.
- Rehearse under two-hour conditions before the final, which is assessed against all twenty-six ILOs.
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 · Elementary logic and mathematical statements
Content; Weeks 1-3, ILO1-3What makes a statement mathematical, and the rules of elementary logic.
T2 · Truth tables and logical equivalence
ILO3Deciding logical equivalence and the validity of an argument mechanically.
T3 · Quantified statements
Content; ILO4-6Universal and existential quantifiers, and how to prove or disprove each kind.
T4 · Direct and indirect proof
ILO7-8; Weeks 4-9Direct proof, proof by cases, contraposition and contradiction — and choosing between them.
T5 · Disproof and counterexamples
ILO9Showing a statement false, which is a different task from failing to prove it true.
T6 · Mathematical induction
ILO10-11Ordinary and strong induction, and recognising when strong induction is required.
T7 · The well-ordering principle
ILO12A third form of the same underlying idea, applied to problems induction handles awkwardly.
T8 · Sets and set operations
Content; ILO14-15; Weeks 10-11Set notation, operations, Cartesian products, and proving set statements by the algebraic and element methods.
T9 · Relations and equivalence classes
Content; ILO16-17Relations, equivalence relations, and the classes they partition a set into.
T10 · Functions: injective, surjective, bijective
Content; ILO18-20Functions rediscovered as relations, with composition and inverses.
T11 · Systems of numbers and complex arithmetic
Content; ILO21-23; Weeks 12-13Natural numbers through complex numbers, including complex roots.
T12 · Division and Euclidean algorithms
Content; ILO24-25Greatest common divisor, linear combinations, and modulo arithmetic.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Final examination | 50% | Two-hour summative examination, assessed against all twenty-six ILOs. Examination period. Summative. |
| Mid-semester Quiz | 25% | Mid-semester quiz, individual, covering ILOs 1 to 10. Mid-semester. No make-up opportunity. |
| In-class activities | 15% | Graded class participation through in-class activities, individual, covering ILOs 1 to 10. Throughout. No make-up opportunity. |
| Assignment | 10% | Assignments, individual, assessed against all twenty-six ILOs. Throughout. Must be submitted to your tutor by the end of the tutorial session. |
- The four components sum to 100. NTU states there are no make-up opportunities for continuous assessment components, and that absence from the midterm without a valid reason will affect your overall grade. Valid reasons are a medical certificate or an excuse letter for NTU-approved activities.
- The two-hour final examination carries 50% and is assessed against every one of the twenty-six ILOs, so it is genuinely comprehensive. With the 25% quiz alongside it, three quarters of the grade sits in timed assessment. The 15% of in-class activities is unusual for a mathematics course and rewards attendance with preparation, but it too has no make-up opportunity.
This is an exam-cram course. With the exams at 75% of the grade and the final examination alone at 50%, your result is overwhelmingly decided by how well you perform under time pressure. Summative.
Final exam timing: Two-hour final examination 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
- Distinguish kinds of mathematical statement and apply elementary logic.
- Use truth tables to decide logical equivalence and argument validity.
- Work with quantified statements and decide their truth.
- Apply direct proof, proof by cases, contraposition and contradiction, and judge which suits.
Before the final heaviest topics
- Disprove a statement and use mathematical induction, including strong induction.
- Apply the well-ordering principle.
- Prove statements about sets by the algebraic and element methods, and work with relations and equivalence classes.
- Handle functions as relations, and apply the division and Euclidean algorithms including modulo arithmetic.
The mistakes that cost marks
Examples treated as proof. A universal statement over an infinite set cannot be established by instances, however many. One counterexample does refute it.
Wrong negation. Proof by contradiction starts from the negation of the statement. Negating a quantified statement incorrectly invalidates everything after it.
Technique chosen by habit. ILO8 assesses judgement between techniques. Contraposition exists because some hypotheses are unusable directly.
Missing a CA component. NTU states there are no make-up opportunities for continuous assessment. In-class activities alone are 15%.
Teaching team
Who teaches MH1300
The bios below are factual. We do not rate lecturers; any star ratings are submitted by students who have taken MH1300.
Teaching team as listed in public course information. AskSia does not rate lecturers; star ratings are submitted by students who have taken MH1300.
Formula & concept sheet
The vocabulary and formulas you must own
- Mathematical statement
- A claim that is definitely true or definitely false, the object every proof concerns.
- Truth table
- A tabulation of a compound statement's truth value, used to decide logical equivalence and validity.
- Quantified statement
- A claim asserted for all members of a set, or for the existence of at least one.
- Contraposition
- The equivalence between 'if P then Q' and 'if not Q then not P'; often converts an unusable hypothesis into a usable one.
- Proof by contradiction
- Assuming the negation of a statement and deriving an impossibility.
- Counterexample
- A single instance refuting a universal statement; the standard method of disproof.
- Mathematical induction
- Proving a statement for all natural numbers via a base case and an inductive step.
- Strong induction
- A variant assuming the statement for all smaller values, needed when the step depends on more than the immediate predecessor.
- Well-ordering principle
- The fact that every non-empty set of positive integers has a least element; equivalent in strength to induction.
- Equivalence relation
- A relation that is reflexive, symmetric and transitive, partitioning a set into equivalence classes.
- Injective, surjective, bijective
- One-to-one, onto, and both; the classification determining whether an inverse function exists.
- Euclidean algorithm
- A procedure computing the greatest common divisor, and expressing it as a linear combination.
Common acronyms: AU · GCD · ILO · PLO.
Where it fits
Prerequisites, related courses & why it matters
Prerequisite published by NTU: none, beyond A-level mathematics or equivalent. The course carries 4 Academic Units and 51 contact hours, and is offered in Year 1 Semester 1. The main textbook is Susanna Epp, Discrete Mathematics with Applications, 4th edition, with Johnsonbaugh and Rosen listed as references.
Your MH1300 study toolkit
Study the course with Sia, not just read about it
Each tool already knows MH1300: 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 MH1300 hard?
It rates moderately hard. There is no prerequisite beyond A-level mathematics, but it demands a different kind of thinking from school mathematics: constructing arguments rather than computing answers. Three quarters of the grade sits in timed assessment.
What is the assessment breakdown?
Final examination 50% (two hours), mid-semester quiz 25%, in-class activities 15%, assignments 10%.
What happens if I miss the midterm?
NTU states that absence without a valid reason will affect your overall course grade, and that there are no make-up opportunities for continuous assessment components. Valid reasons are a medical certificate or an excuse letter for NTU-approved activities.
Why are six weeks spent on proof?
Because it is the point of the course. The published schedule gives weeks 4 to 9 to mathematical proof, and the course aims state these skills are essential for all future mathematics courses.
Who wrote the course?
The course author published in the OBTL document is Assoc Prof Ng Keng Meng, Division of Mathematical Sciences.
Can I collaborate on homework?
NTU explicitly encourages it, with a condition: you must write up solutions yourself, understand what you hand in, and name your collaborators on the solution sheet — or write 'No collaborators'. Failing to do so is treated as plagiarism.
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