Key takeaways
- Relations, logic, counting, groups and graph theory together cover most of the paper.
- Always state the property you are checking (reflexive, symmetric, transitive) before proving it.
- Each section has exam tips and formula boxes, and the last page lists the most asked practice questions.
- These are original Uncodemy revision notes, not official university notes; check your own syllabus.
About these Discrete Maths handwritten notes
This page offers Uncodemy's Discrete Mathematics notes as a free handwritten-style PDF. Discrete Mathematics is the maths of countable structures such as sets, logic, relations, graphs and groups, which underpin most computer science subjects. The notes are written in short points with neat tables, labelled diagrams, boxed formulas and exam tips, so you can revise a full unit in one sitting instead of reading a long textbook chapter.
Please note: these are original Uncodemy revision notes. They follow the common syllabus that most Indian universities share for this subject, but they are not official university notes. Check your own university syllabus and add anything it lists that is missing here.
What's inside the Discrete Maths notes
The PDF is arranged in 7 sections plus a final page of most asked practice questions. The sections follow the usual unit order of a Discrete Mathematics syllabus, so you can map them to your own units quickly. Here is what each section covers.
Sets and functions
Set operations and laws, Venn diagrams, and one-to-one, onto and bijective functions with composition and inverse.
Relations
Properties of relations, equivalence relations and classes, partial orders, Hasse diagrams and lattices.
Propositional logic
Connectives, truth tables, tautology and contradiction, logical equivalence, rules of inference, and predicate logic with quantifiers.
Combinatorics
Permutations, combinations, the pigeonhole principle, inclusion-exclusion and solving linear recurrence relations.
Group theory
Groups, subgroups, cyclic and abelian groups, cosets and Lagrange's theorem.
Graph theory
Types of graphs, degree, Euler and Hamiltonian graphs, planar graphs and Euler's formula, trees and graph colouring.
Probability (GATE part)
Basic probability, conditional probability, Bayes' theorem and common random variables used in GATE questions.
Most asked questions (practice)
Ten exam-style questions, from equivalence relations to chromatic numbers.
How to use handwritten notes to revise Discrete Maths
Discrete Mathematics is proof and problem based, so the notes work best when you solve a problem for every definition you revise.
- Draw the Hasse diagram for the divisors of a number and check if it is a lattice.
- Build truth tables for three formulas and decide which are tautologies.
- Translate five English statements into predicate logic with correct quantifiers.
- Solve two recurrence relations using the characteristic equation and check the first few terms.
A simple three-pass method works well with handwritten notes. In the first pass, read one section and underline only what you do not already know. In the second pass, close the notes and write the definitions, diagrams and steps for that section on a blank sheet, then compare and correct in a different colour. In the third pass, a day or two later, answer two or three exam-style Discrete Maths questions in timed conditions using only memory. Add your own examples and doubts in the margins so the PDF becomes your personal revision copy.
Formulas, diagrams and definitions to memorise
- Number of relations on a set of n elements: 2^(n^2); reflexive relations: 2^(n^2 - n).
- Rules of inference: modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism and resolution.
- Permutation nPr = n! / (n - r)! and combination nCr = n! / (r! (n - r)!).
- Handshaking lemma: sum of degrees = 2 x number of edges, and Euler's formula V - E + F = 2 for connected planar graphs.
- Lagrange's theorem: the order of a subgroup divides the order of the group.
Common mistakes that cost marks
- Mixing up the order of quantifiers when translating English to predicate logic.
- Showing only reflexive and symmetric properties when proving an equivalence relation and forgetting transitivity.
- Using permutations where order does not matter.
- Drawing Hasse diagrams with arrows or with edges implied by transitivity.
Exam focus: Discrete Maths topics that carry the most marks
These Discrete Mathematics topics carry the most marks in university papers and in GATE.
- Relations, equivalence classes, posets and lattices.
- Propositional and predicate logic and rules of inference.
- Counting, pigeonhole principle and recurrence relations.
- Group theory proofs and graph theory (Euler, Hamiltonian, planarity, colouring).
Typical long questions
- Prove that a relation is an equivalence relation and find its classes.
- Draw a Hasse diagram and check whether the poset is a lattice.
- Check whether a formula is a tautology using a truth table.
- Prove an argument valid using rules of inference.
- Solve a linear recurrence relation using the characteristic equation.
- Prove that every cyclic group is abelian and state Lagrange's theorem.
- Explain Euler and Hamiltonian graphs and verify Euler's formula.
Marks per question change between universities and years, so confirm the pattern on a recent official paper. In long answers, start with a definition, add a labelled diagram or table, explain the steps and finish with an example or comparison. Underline the key term in each answer and leave a line between steps, because examiners mark faster when the structure is easy to see.
A 7-day revision plan for Discrete Maths
- Day 1: Sets and functions, Relations.
- Day 2: Propositional logic, Combinatorics.
- Day 3: Group theory.
- Day 4: Graph theory.
- Day 5: Probability (GATE part).
- Day 6: redo the problems: one Hasse diagram, one inference proof, one recurrence, one counting problem and one graph colouring.
- Day 7: answer the most asked practice questions at the end of the notes from memory, then solve one official previous year paper in three hours and mark the units that cost you time.
Keep a single sheet of formulas, definitions and diagrams from the notes for the last hour before the exam, and do not start new topics on the final day.
Who these notes are for
- B.Tech CSE and IT students preparing for the semester Discrete Mathematics exam.
- BCA and MCA students with a discrete or mathematical foundations paper.
- GATE CS and GATE DA aspirants revising discrete maths.
- Students who want a stronger maths base for algorithms and theory of computation.
The notes are a revision aid, not a first textbook. If a Discrete Maths topic is new to you, learn it from your prescribed book or class lectures first, then come back to the notes to compress and revise it. For practice, pair them with the Discrete Mathematics Important Questions PDF page and your university's official previous year papers. If your syllabus has a topic that is not covered here, you can ask for it through the handwritten notes request page linked below.
Download Discrete Mathematics Handwritten Notes PDF
Discrete Mathematics Handwritten Notes PDF (Free)
The PDF carries the same content as this page in a clean, print-ready layout, so you can read it offline and keep it for revision.
6 pages · 266 KB · PDF · Updated 5 Nov 2026