Discrete Mathematics Tuition in Singapore

Discrete Mathematics

Discrete Mathematics forms the foundation of mathematical reasoning, enumeration, and algorithmic thinking.

Propositional and predicate logic, methods of proof, mathematical induction
Sets, relations, functions, equivalence relations, partial orderings, well-ordering principle
Combinatorics: permutations and combinations, binomial and multinomial formulae, pigeonhole principle, Principle of Inclusion and Exclusion, generating functions, recurrence relations
Graph Theory: connectivity, trees, planarity, matchings
Number Theory: divisibility, prime numbers, modular arithmetic, Chinese Remainder Theorem, number-theoretic functions, quadratic residues

Where discrete mathematics usually trips students up

Discrete mathematics looks approachable, and much of it is, but it is often a student's first real encounter with proof, and that is where the marks move.

Translating English into logic. Turning a sentence into a precise statement with the right quantifiers is harder than it looks, and a misread statement dooms the rest.
Choosing a proof method. Knowing when to argue directly, by contradiction, or by induction is a skill in itself, separate from carrying the argument out.
Setting up induction. A missing base case, a vague inductive step, or confusing weak with strong induction quietly loses marks on otherwise sound work.
Counting carefully. The classic trap is mixing up ordered with unordered, and with or without repetition, so seemingly similar problems need quite different formulae.
Recurrences and generating functions. These feel like sleight of hand until you have seen the technique unpacked slowly a few times.
Proving things about graphs. Graph results are intuitive to picture but demand careful definitions to prove, and a diagram is not a proof.

Before you start: a discrete mathematics prerequisites checklist

Discrete mathematics needs almost no calculus, which is part of why it suits computing students so well. What it does ask for is comfort with notation and a willingness to prove. Before week one, it is worth checking the following.

What to be comfortable with before week one
Be comfortable with	Why it matters for discrete mathematics
Basic algebra	Manipulating expressions and solving simple equations keeps the focus on the reasoning rather than the arithmetic.
Mathematical notation	Reading statements with sets, quantifiers and functions accurately is the daily work of the course.
A willingness to prove	No heavy prior proof experience is needed, but the readiness to argue rather than compute is essential.
Sets and functions	Unions, intersections, and what makes a function injective or surjective recur throughout.
Logical thinking	If you have written code or followed structured arguments, that same step-by-step instinct transfers directly.
Patience with definitions	Many proofs hinge on applying a definition exactly, so reading them slowly pays off.

A one-semester self-study plan for independent learners

Discrete mathematics is well suited to self-study, especially for computing students who meet it early in a degree. If you are working through it alone, here is a thirteen-week route map built around texts that pair theory with worked problems. Set your own pace, and reach out if logic, induction or counting is not yet clicking, since those foundations carry the rest.

Texts I often point self-study students to
Text	Author	Best for
Discrete Mathematics and Its Applications	Kenneth Rosen	The comprehensive, computing-oriented standard; the usual first choice
Discrete Mathematics with Applications	Susanna Epp	Especially strong on logic and learning to write proofs
Discrete and Combinatorial Mathematics	Ralph Grimaldi	A fuller treatment of the combinatorics and counting material
Introduction to Graph Theory	Douglas West	A clear reference for the graph-theory part of the plan
Elementary Number Theory	David Burton	A gentle, thorough companion for the number-theory weeks

A thirteen-week plan
Week	Focus	Suggested reading	Checkpoint
1	Propositional logic	Rosen or Epp, opening chapters	Build truth tables and recognise logical equivalences
2	Predicate logic and quantifiers	Epp	Translate statements to and from formal logic, and negate them correctly
3	Methods of proof	Epp or Rosen	Choose and carry out direct, contradiction and contrapositive proofs
4	Mathematical induction	Rosen or Epp	Write a complete induction, including strong induction
5	Sets and functions	Rosen	Reason about set operations and properties of functions
6	Relations, equivalence and orderings	Rosen or Epp	Work with equivalence relations and partial orders
7	Counting: permutations and combinations	Rosen or Grimaldi	Distinguish ordered from unordered counting reliably
8	Binomial theorem, inclusion-exclusion, pigeonhole	Grimaldi	Apply each counting principle to the right kind of problem
9	Recurrence relations	Rosen or Grimaldi	Solve linear recurrences with confidence
10	Generating functions	Grimaldi	Use a generating function to solve a counting problem
11	Graph theory: basics and trees	West or Rosen	Prove a simple result about connectivity or trees
12	Number theory: divisibility and modular arithmetic	Burton or Rosen	Use the Chinese Remainder Theorem and modular inverses
13	Applications and review	Rosen	Tie the ideas together, for example through public-key cryptography

Frequently Asked Questions (FAQ) - Discrete Mathematics Tuition

Which discrete mathematics topics and modules do you cover?

Logic and proof, sets, relations and functions, combinatorics and counting, recurrence relations and generating functions, graph theory, and elementary number theory. That covers the discrete-mathematics modules that computer science and maths students take at NUS, NTU, SUTD, SIT and the other local universities. Send me the outline and I will confirm whether it is a good match.

I am a computing student, not a maths major. Is this the right page?

Yes. Discrete mathematics is the maths module most computer science degrees require, and a good deal of my work here is with computing students. I can keep the examples close to the parts that matter for your degree, such as logic, counting, recurrences and graphs, while still building the proof skills the module assesses.

I find the proofs and logic harder than the rest. Can you help?

Absolutely, and that is where most students need the help. We work on reading a statement precisely, choosing a proof method on purpose rather than by guesswork, and setting out induction and counting arguments the way a marker expects. With practice and feedback, the proof side stops feeling like the hard part.

Do you cover graph theory and number theory as well?

Yes. Connectivity, trees, planarity and matchings in graph theory, and divisibility, modular arithmetic and the Chinese Remainder Theorem in number theory, are all part of the work I teach, and they sit on this same page rather than a separate one.

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