# Kerala PSC Lecturer in Mathematics Exam Syllabus

Detailed Exam Syllabus of Kerala PSC Lecturer in Mathematics Examination with Category no. 589/2012 on August 2014 published by Kerala public service commission.

Post Name: Lecturer in Mathematics.
Category Number: 589/2012.
Department: Collegiate Education.
Examination Date: 08/08/2014 Friday 07.30 AM to 09.15 AM.

Mode of Examination:
An Objective Type Test (OMR Valuation) based on the qualification prescribed for the post.

#### Exam Syllabus

Module-I
Mensuration, length of arcs, area of sectors of circles, tangents to circles, circumcircle and incircle of polygons, area of polygons, solids-volume and surface area. Fundamentals of mumber theory. Continued fractions. Boolean Algebra, Fundamentals of graph theory.

Module-II
Sets and binary operations, groups, Sylon's Theorems, Rings and ideals, Fields, extension fields, rings of polynomials, finite fields, Galois Theory, constructible numbers. System of Linear Equations - Vector spaces, linear transformations, characteristic values, characteristic polynomial, Minimal polynomial, Cayley-Hamilton theorem, triangulation and diagonalization of matrics. Hyperspaces and linear functionals.

Module-III
Normed spaces, Banach spaces and related theorems, Linear Maps, inner product spaces, Hilbert spaces and related theorems, finite dimensional and infinite dimensional normed spaces, bounded operators, spectrum, duals and transposes. Adjoints, normal, unitary and self adjoint operators.

Polynomial Equations, Trigonometry, Analytical geometry of two dimension and three dimension, similarity of triangles, vectors, matrices. Calculus, applications of differentiation and integration, elemetary functions (logarithms, exponential, hyperbolic, trigonometric etc), Fundamental theorem of calculus, mean value theorems, maxima and minima-functions of more than one independent variables, derivatives, partial derivatives, saddle point, critical point.

Module–IV
Real numbers, rational, irrational numbers, algebraic and order properties of Real numbers, supremum property, countable and uncountable sets, completeness property, sequences and series of red numbers, relations and functions, limits and continuity of functions, uniform continuity, differentiability and integrability of functions, Riemann integral, Riemann-Stieltges integral, sequences and series of functions. Term by term differentiation and integration of series of functions. Lebesgue measure, lebesgue integral, convergence theorems and applications.

Module -V
Complex numbers, De Moirre's Theorem, Algebraic properties of complex numbers, regions in the complex plane. Complex functions, analytic functions, harmonic functions, conformal mapping, elementary functions, derivatives and integrals of complex functions and related theorems, sigularities, residue theorem and its applications, Power series, Taylor series, Laurent series. Metric spaces, topological spaces, basis, subbasis, closed set, closure, interior, boundary, neighbourhood. Connectedness and compactness, locally connected, path connected, locally compact spaces. Functions, continuous functions, homeomorphism, quotient space. Seperation axioms and related theorems.

Download Detailed Exam Syllabus of Kerala PSC Lecturer in Mathematics Examination in PDF file.

Maximum Marks: 100
Exam Duration: 1 hour 15 minutes.
Medium of Questions: English.

Candidates can download the Admission Tickets through their One Time Registration Profile in the Website www.keralapsc.gov.in from 18/07/2014.