By Piyush Wairale (M.Tech, IIT Madras) · Former Instructor, IIT Madras BS Degree Programme · Mentor to 20,000+ GATE aspirants · Updated November 2026

GATE CSE 2027 Engineering Mathematics Syllabus (Official, IIT Madras)

As released by IIT Madras, the organising institute for GATE 2027, Section 1 of the CS paper reads:

For the full paper (all 10 sections, marking scheme and cutoffs) see the GATE CS 2027 syllabus and exam pattern guide.

Topic-wise Weightage and Priority

Approximate marks based on the pattern of recent GATE CS papers (the exact split varies every year):

Discrete Mathematics: What GATE Actually Tests

Propositional and first order logic. Expect tautology checks, logical equivalences (p → q ≡ ¬p ∨ q), and translating English into predicate logic with correct quantifier order. ∀x ∃y P(x,y) is not the same as ∃y ∀x P(x,y); the second implies the first, never the reverse.

Sets, relations and functions. On a set with n elements: total relations = 2^n², reflexive relations = 2^n²−n, symmetric relations = 2^n(n+1)/2, functions from A (m elements) to B (n elements) = n^m, one-one functions = n!/(n−m)! for m ≤ n. Equivalence relations on n elements equal the Bell number B_n.

Partial orders and lattices. Draw the Hasse diagram, then check whether every pair has a least upper bound and greatest lower bound. Know distributive and complemented lattices; in a distributive lattice every element has at most one complement.

Monoids and groups. Check closure, associativity, identity and inverse. Lagrange’s theorem: the order of a subgroup divides the order of the group. Every group of prime order is cyclic.

Graphs. Handshaking lemma (sum of degrees = 2|E|), Euler’s formula for connected planar graphs (v − e + f = 2), chromatic number of K_n = n, a bipartite graph has no odd cycle, maximum edges in a simple graph = n(n−1)/2, and a tree on n vertices has n−1 edges. Matching questions usually ask for a maximum or perfect matching in a small graph.

Combinatorics. Permutations, combinations, pigeonhole principle, inclusion-exclusion, derangements (D_n = n! Σ (−1)^k/k!), recurrence relations solved by characteristic equations, and generating functions to count solutions of x₁ + x₂ + … = n.

Linear Algebra Essentials

Sum of eigenvalues = trace, product of eigenvalues = determinant. A system Ax = b is consistent iff rank(A) = rank([A|b]); unique solution iff that rank equals the number of unknowns. Eigenvalues of a triangular matrix are its diagonal entries; eigenvalues of A^k are λ^k; A is singular iff 0 is an eigenvalue. LU decomposition writes A = LU with L lower triangular (unit diagonal in Doolittle form) and U upper triangular, so solving Ax = b becomes two triangular solves.

Calculus Essentials

Use L’Hospital’s rule for 0/0 and ∞/∞ forms. A function differentiable at a point is continuous there (not the converse: |x| at 0). For maxima and minima, solve f'(x) = 0 and check the sign of f”(x), and always compare endpoint values on a closed interval. Mean Value Theorem: if f is continuous on [a,b] and differentiable on (a,b), some c gives f'(c) = (f(b) − f(a))/(b − a).

Probability and Statistics Essentials

Bayes theorem: P(A|B) = P(B|A)P(A) / P(B). The exponential distribution is memoryless: P(X > s+t | X > s) = P(X > t).

Four GATE-Style Problems, Solved

Q1 (NAT). How many reflexive relations exist on a set of 3 elements?
Solution: The 3 diagonal pairs are forced in; each of the remaining 9 − 3 = 6 pairs is in or out. Answer: 2⁶ = 64.

Q2 (MCQ). The eigenvalues of A = [[2, 1], [1, 2]] are?
Solution: Trace = 4, determinant = 3, so λ satisfies λ² − 4λ + 3 = 0, giving 1 and 3.

Q3 (NAT). 1% of a population has a disease. A test detects it 99% of the time and gives a false positive 5% of the time. A person tests positive. What is the probability they have the disease?
Solution: P(+) = 0.01 × 0.99 + 0.99 × 0.05 = 0.0099 + 0.0495 = 0.0594. P(D|+) = 0.0099/0.0594 = 0.167 (about 1 in 6).

Q4 (NAT). How many binary strings of length 5 contain no two consecutive 1s?
Solution: a_n = a_n−1 + a_n−2 with a₁ = 2, a₂ = 3. So a₃ = 5, a₄ = 8, a₅ = 13.

Common Mistakes to Avoid

Mixing up relation counts: reflexive is 2^n²−n, symmetric is 2^n(n+1)/2; write the derivation, do not guess the exponent.

Quantifier order: swapping ∀ and ∃ changes the meaning entirely.

Ignoring endpoints in maxima/minima questions on closed intervals.

Assuming independence in probability questions when the events are conditional.

MSQ traps: there is no partial credit for MSQ in GATE, so verify every option, not just the first correct one you find.

60-Day Preparation Strategy

Days 1 to 25: Discrete Mathematics. Logic, sets and relations, then graph theory, then combinatorics. Solve the last 10 years of GATE CS questions on each topic as you finish it.

Days 26 to 40: Linear Algebra and Probability. These are high-return, formula-driven topics. Make a one-page formula sheet for each.

Days 41 to 48: Calculus. Limits, maxima/minima and definite integrals cover almost everything asked.

Days 49 to 60: Test and fix. Take the Engineering Mathematics subject-wise tests in the GATE CSE 2027 Test Series, review every wrong answer, and re-test weak topics. Also cover the 15 General Aptitude marks with the GATE Aptitude Test Series and the free GA topic guides.

FAQs: GATE CSE 2027 Engineering Mathematics

GATE CSE 2027: All Subject-wise Guides

1. Engineering Mathematics · 2. Digital Logic · 3. Computer Organization & Architecture · 4. Programming & Data Structures · 5. Algorithms · 6. Theory of Computation · 7. Compiler Design · 8. Operating System · 9. Databases (DBMS) · 10. Computer Networks

Full paper overview: GATE CS 2027 Syllabus, Exam Pattern & Cutoff. Practise all ten subjects in one place with the GATE CSE 2027 Test Series.