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Mathematics — Model Syllabus Roadmap

22 Official 2024 Lecturer Disciplines — Syllabus Directory · Subjects 12–22

Useful for: SSB Lecturer (Degree Colleges)

Overview

Postgraduate mathematics covers analysis, algebra, linear algebra, calculus, differential equations, complex analysis, numerical methods and statistics.

Key points

Real analysis: sequences, series, continuity, differentiability.
Abstract algebra: groups, rings, fields; Lagrange’s theorem.
Linear algebra: vector spaces, matrices, eigenvalues.
Differential equations: ordinary and partial.
Complex analysis: analytic functions, Cauchy–Riemann equations.
Numerical methods and statistics.

Explanation

Lagrange’s theorem: the order of a subgroup divides the order of the group.
Eigenvalues solve Av = λv.
Cauchy–Riemann equations test analyticity.
Proof writing is essential.

Step by step

Place the question in its unit of the syllabus.
Recall the theory, thinker, law or work involved.
Eliminate options from other schools, periods or units.

Examples

Subgroup order divides group order → Lagrange’s theorem.
Condition for complex differentiability → Cauchy–Riemann equations.
Av = λv → eigenvalue problem.

Traps and advanced points

Trap: Mixing theorems.
Trap: Weak proofs.
Trap: Ignoring numerical methods.

Quick revision

Analysis, algebra, linear algebra.
Lagrange; Cauchy–Riemann.
Differential equations.

Practice MCQs

The derivative of sin x is
1. −cos x
2. cos x
3. −sin x
4. tan x
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Answer: (b) cos x. d/dx (cos x) = −sin x.
The sum of the interior angles of a triangle is
1. 90°
2. 180°
3. 360°
4. 270°
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Answer: (b) 180°. In Euclidean geometry.
For a convex polyhedron, Euler's formula is
1. V + E − F = 1
2. V + E + F = 2
3. V − E − F = 0
4. V − E + F = 2
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Answer: (d) V − E + F = 2. A cube has 8 − 12 + 6 = 2.
The value of ∫₀¹ x dx is
1. 2
2. 1
3. 0
4. 1/2
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Answer: (d) 1/2. [x²/2] from 0 to 1.
Which of these is an irrational number?
1. √2
2. 0.25
3. 3/7
4. 4
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Answer: (a) √2. It cannot be written as p/q.