Assistant professor Mathematics Detailed Syllabus
Kerala PSC announced
the exam for the post of Assistant professor Mathematics
in
the collegiate education Department. The main topics and detailed syllabus for the
Assistant professor Mathematics exam can be read and Syllabus pdf
can be downloaded in this page.
Exam
details
Category Number: 296/2019
Name of Post:
Date of Test: 01.01.2021
Duration: 2
Hours
Conducted by: Kerala
PSC
Mode of Exam: Descriptive Exam (offline) Written Test
(Question cum Answer Booklet)
Medium of Questions: English
Total Marks: 100
Main Topics
– Assistant professor Mathematics
In the Exam Calendar, the syllabus is given
as questions based on educational qualifications.
The main Topics of Assistant
professor Mathematics exam are:
Module I - Linear
Algebra
Module II
- Real Analysis
Module III
- Real Analysis(continued)
Module IV
- Abstract Algebra
Module V
- Abstract Algebra (continued)
Module VII
- Complex Analysis
Module VIII
- Functional Analysis
Module IX
- Ordinary Differential & Partial Equations
Module X
- Theory of Numbers
Detailed
Syllabus of Assistant Professor Geography
Hope you already got
to know the main topics of this exam. The detailed syllabus of Assistant
professor Mathematics is given below.
Comment below if you
need Books of Mathematics.
Books
for preparing Mathematics.
Syllabus for Mathematics
Assistant Professor Examination -Collegiate Education
Module I - Linear
Algebra:
Vector spaces, subspaces, linear dependence,
basis, dimension, algebra of linear transformations. Algebra of matrices, rank
and determinant of matrices, linear equations. Eigenvalues and eigenvectors,
Cayley-Hamilton theorem. Matrix representation of linear transformations.
Change of basis, canonical forms, diagonal forms, triangular forms-rational
forms, Jordan forms. Inner product spaces, orthonormal basis. Quadratic form.
Module II - Real
Analysis:
Sequences and series,
convergence, lim sup. lim inf. Bolzano Weierstrass theorem, Heine Borel
theorem. Continuity, uniform continuity, diferentiability, Rolle’s theorem,
Mean value theorem. Sequences and series of functionsuniform convergence.
Riemann sums and Riemann integral, Improper Integrals. Double and triple
integrals,
Module III - Real
Analysis(continued):
Lebesgue measure, Lebesgue integral. Functions
of several variables, directional derivative, partial derivative, inverse and
implicit function theorems. Special functions- Beta and Gamma functions,
Fourier series.
Module IV - Abstract
Algebra:
Groups, subgroups, normal subgroups, quotient
groups, homomorphisms, isomorphisms, cyclic groups, permutation groups,
Cayley’s theorem, Direct products, Fundamental theorem for abelian groups,
class equations, Sylow theorems.
Module V - Abstract
Algebra (continued):
Rings, ideals, prime
and maximal ideals, quotient rings, unique factorization domain, principal
ideal domain, Euclidean domain. Polynomial rings and irreducibility criteria.
Fields, fnite felds, feld extensions, Galois Theory.
Module VI - Topology:
Metric spaces, continuity, Topological spaces,
Base, subbase, countability properties, Separation axioms, Compact space, one
point compactifcation, locally compact space, connected spaces, pathwise
connectedness, Quotient spaces, Product topology.
Module VII - Complex
Analysis:
Complex numbers, polar form, properties of
complex numbers, Analytic functions, Cauchy Reimann equations, Conformal
Mappings, Mobius transformation, Power series, Zeros of analytic functions,
Liouvillis theorem, Complex integration, real integrals using complex
integration, Cauchy’s theorem and Cauchy’s integral formula, Morera’s theorem,
open mapping theorem, Singularities and its classifcation, residues, Laurent
series, Schewarz lemma, Maximum modulus principle, Argument principle.
Module VIII -
Functional Analysis:
Normed Linear spaces, Continuity of linear
maps, Banach spaces, Hahn Banach spaces, Open mapping theorem, closed graph
theorem, uniform boundedness principle, Inner product spaces, Hilbert spaces
Projections, Bounded operators, Normal, unitary and self adjoint operators.
Module IX - Ordinary
Diferential & Partial Equations :
Existence and
uniqueness of solutions of initial value problems for frst order ordinary
diferential equations, singular solutions of frst order ODEs, system of frst
order ODEs. General theory of homogenous and non-homogeneous linear ODEs.
Lagrange and Charpit methods for solving frst order PDEs, Cauchy problem for
frst order PDEs. Classifcation of second order PDEs, General solution of higher
order PDEs with constant coefcients, Method of separation of variables for
Laplace, Heat and Wave equations.
Module X - Theory of
Numbers:
Fundamental theorem
of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem,
Euler’s Ã˜-function, Fermat’s theorem, Wilson’s theorem, Euler’s theorem,
primitive roots.
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syllabus of Assistant professor Mathematics exam. You can get the
previous question papers of Assistant professor Mathematics HERE.
Syllabus of other PSC Exams Download pdf HERE
Previous yearQuestion papers of PSC Exams Download PDF HERE.
Comment below if you
need Books of Mathematics.
Books
for preparing Mathematics.
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