If you are preparing for KVS PGT Mathematics or any other Post Graduate Teacher exam, the first step is to understand the syllabus of PGT Maths in detail. The PGT Mathematics syllabus is designed to test subject expertise along with teaching aptitude and general awareness.
In this article, we provide the detailed PGT Math syllabus, including KVS PGT syllabus Maths, broken down into units with key topics and weightage.
📌 Exam Structure – PGT Mathematics (KVS)
The KVS PGT syllabus Maths consists of multiple sections:
- General English & General Hindi – 20 Marks
- General Knowledge & Current Affairs – 10 Marks
- Reasoning Ability – 10 Marks
- Computer Literacy – 10 Marks
- Pedagogy (Teaching Methodology & Educational Concepts) – 20 Marks
- Subject Concerned (Mathematics) – 80 Marks
👉 The subject paper (Mathematics) carries the highest weightage and determines the final selection.
📝 Detailed PGT Mathematics Syllabus (Subject Concerned)
The PGT Math syllabus covers advanced mathematics topics from graduation and post-graduation levels.
🔹 Algebra
- Groups, subgroups, normal subgroups, quotient groups
- Homomorphism, isomorphism, cyclic groups
- Permutation groups, Lagrange’s theorem, Cauchy’s theorem
- Rings, integral domains, fields, ideals
- Polynomial rings, maximal and prime ideals
🔹 Analysis
- Sequences and series of real numbers
- Convergence tests (comparison, ratio, root test)
- Functions of one real variable – continuity, differentiability, Rolle’s theorem, Mean Value Theorem
- Riemann integration, improper integrals, uniform convergence
- Functions of two or more variables, partial derivatives, maxima and minima
🔹 Linear Algebra
- Vector spaces, linear independence, basis and dimension
- Linear transformations, rank and nullity theorem
- Eigenvalues, eigenvectors, Cayley-Hamilton theorem
- Inner product spaces, orthogonal matrices, Gram-Schmidt process
🔹 Complex Analysis
- Analytic functions, Cauchy-Riemann equations
- Cauchy integral theorem, Cauchy integral formula
- Taylor and Laurent series, residues and poles
- Applications of residue theorem to definite integrals
🔹 Differential Equations
- First-order ODEs (separable, exact, linear)
- Second-order linear ODEs with constant coefficients
- Method of variation of parameters
- Laplace transforms and applications
- Partial differential equations: classification, solutions of wave, heat, Laplace equations
🔹 Topology & Metric Spaces
- Open and closed sets, limit points
- Compactness, connectedness
- Continuous functions, homeomorphisms
- Metric spaces, convergence, completeness
🔹 Probability & Statistics
- Probability axioms, conditional probability, Bayes theorem
- Random variables, distributions (Binomial, Poisson, Normal, Exponential)
- Mean, variance, standard deviation
- Correlation, regression, hypothesis testing
🔹 Numerical Analysis
- Errors and approximations
- Interpolation (Newton, Lagrange)
- Numerical integration (Trapezoidal, Simpson’s rule)
- Solution of linear and non-linear equations (Newton-Raphson, Gauss-Seidel)
🔹 Mechanics & Vector Calculus
- Statics and dynamics of particles
- Newton’s laws of motion, work, power, energy
- Moment of inertia, center of mass
- Gradient, divergence, curl
- Line, surface, and volume integrals
- Green’s, Gauss’s and Stokes’ theorems
🔹 Discrete Mathematics
- Propositional and predicate logic
- Relations, functions, equivalence relations
- Graph theory: trees, Eulerian and Hamiltonian graphs, connectivity
- Combinatorics: permutations, combinations, recurrence relations
🔹 Mathematical Reasoning & Pedagogy (for PGT)
- History of mathematics and contributions of mathematicians
- Teaching methods in mathematics
- Lesson planning, assessment, evaluation techniques
- ICT in mathematics teaching
📊 PGT Mathematics Syllabus – Unit-Wise Weightage
| Unit | Key Topics | Weightage (Approx.) |
|---|---|---|
| Algebra | Groups, rings, fields, homomorphism | 8–10 Marks |
| Analysis | Sequences, series, real functions, integration | 10–12 Marks |
| Linear Algebra | Vector spaces, transformations, eigenvalues | 8–10 Marks |
| Complex Analysis | Analytic functions, residues, Cauchy theorem | 6–8 Marks |
| Differential Equations | ODE, PDE, Laplace transforms | 8–10 Marks |
| Topology & Metric Spaces | Compactness, continuity, convergence | 6–7 Marks |
| Probability & Statistics | Distributions, expectation, regression | 8–10 Marks |
| Numerical Analysis | Errors, interpolation, integration, solutions | 6–8 Marks |
| Mechanics & Vector Calculus | Motion, energy, vector theorems | 8–9 Marks |
| Discrete Mathematics | Graphs, logic, combinatorics | 6–8 Marks |
| Pedagogy & Reasoning | Teaching methods, lesson planning | 8–10 Marks |
✅ Final Thoughts
The KVS PGT Math syllabus is comprehensive and requires strong subject knowledge along with teaching methodology. To prepare effectively:
- Focus on core subjects like Algebra, Analysis, Differential Equations, and Probability.
- Revise teaching pedagogy concepts as they carry significant weight.
- Practice previous year question papers for both subject and general sections.
By covering the PGT Mathematics syllabus thoroughly, you will not only clear the exam but also build a strong foundation for your teaching career.
