Kerala PSC or Kerala Public Service Commission has released the Assistant Professor in Mathematics admit card. The exam is scheduled on 23 May 2022(Monday) from 10:30 am to 1:30 pm. In this article, we are going to give you a brief note on the exam syllabus and pattern and how to download the admission ticket for the Kerala PSC Assistant Professor in Mathematics exam. Usually, Kerala PSC publishes the admit cards 15-20 days prior to the exam for all aspiring candidates who submitted the application for the same. Likewise, the commission has now generated the admit card for the Assistant Professor in Mathematics examination. Read the complete article to learn all about Kerala PSC Assistant Professor in Mathematics Admit Card 2022.
How to download Kerala PSC Assistant Professor Admit Card 2022?
As the Kerala PSC has officially released the admit card on 11 May 2022, the aspirants who were able to submit their applications successfully can download their admit cards by logging in to their registered accounts in Kerala PSC’s official website. Have look into some simple steps you may have to follow to download the Kerala PSC Assistant Professor in Mathematics admission tickets:
Step 1: log in to official website for downloading the admit cards which is Kerala PSC Thulasi Portal.
Step 2: log in to your personal profile by using your user ID and password which you had created during the registration process.
Step 3: From the admit card link of the Assistant Professor in Mathematics examination, download your admit card.
Step 4: Take the printout of the Kerala PSC Assistant Professor in Mathematics admit card and take it with you to the examination center.
Kerala PSC Assistant Professor Admit Card 2022: Download link
Click on the link below to download your Kerala PSC Assistant Professor in Mathematics Hall Tickets 2022.
Kerala PSC Assistant Professor Admit Card 2022: Exam Date
The Kerala PSC has also revealed the exam date for the Assistant Professor in Mathematics Exam 2022 along with the release of the admit cards. According to the notification the exam is scheduled on 23 May 2022, Monday from 10: 30 am to 1: 30 pm. All the aspiring candidates can download their hall tickets and can attempt their exams on the above said date and time.
Kerala PSC Assistant Professor Admit Card 2022: Syllabus
|I||Linear Algebra||(i) Vector spaces, linear dependence, subspaces, basis, dimension, algebra of linear transformations.
(ii) Algebra of matrices, rank and determinant of matrices, Eigenvalues and eigenvectors, linear equations, Cayley-Hamilton theorem. Matrix representation of linear transformations.
(iii) Change of basis, canonical forms,triangular forms-rational forms,diagonal forms, Jordan forms.
(iv) Inner product spaces, orthonormal basis.
(v) Quadratic form.
|II||Real Analysis||(i) Convergence, Sequences and series, lim sup. lim inf.
(ii) Continuity, uniform continuity, diferentiability, Bolzano Weierstrass theorem, Heine Borel theorem. Rolle’s theorem, Mean value theorem.
(iii) Sequences and series of functions uniform convergence.
(iv) Riemann sums and integral, Improper Integrals, Triple and double integrals.
|III||Real Analysis (Continued)||(i) Lebesgue integral, Lebesgue measure.
(ii) Functions of several variables,partial derivative, directional derivative, inverse and implicit function theorems.
(iii) Special functions- Fourier series, Beta and Gamma functions.
|IV||Abstract Algebra||(i) Groups, subgroups, homomorphisms, isomorphisms, normal subgroups, quotient groups, cyclic groups, permutation groups,
(ii) Cayley’s theorem
(iii) Direct products
(iv) Fundamental theorem for abelian groups.
(v) Class equations
(vi) Sylow theorems.
|V||Abstract Algebra (Continued)||(i) Rings, ideals, prime and maximal ideals, quotient rings,,Euclidean domain unique factorization domain, principal ideal domain.
(ii) Polynomial rings and irreducibility criteria.
(iii) Fields, finite fields, field extensions, Galois Theory.
|VI||Topology||(i) Metric spaces, countability properties, continuity, Topological spaces, Compact space, Base, subbase, Separation axioms, one point compactifcation, pathwise connectedness, Quotient spaces, locally compact space, connected spaces, Product topology.|
|VII||Complex Analysis||(i) Complex numbers, properties of complex numbers, polar form, Analytic functions, Cauchy Reimann equations, Mobius transformation, Power series, Conformal Mappings,Zeros of analytic functions, Liouvillis theorem, Complex integration, real integrals using complex integration.
(ii) Cauchy’s integral formula and Cauchy’s theorem
(iii) Morera’s theorem, open mapping theorem, Singularities and its classifcation, residues.
(iv) Laurent series, Argument principle, Schewarz lemma, Maximum modulus principle.
|VIII||Functional Analysis||(i) Normed Linear spaces, Hahn Banach spaces, Continuity of linear maps, Banach spaces, Open mapping theorem, closed graph theorem, uniform boundedness principle, Bounded operators, Normal, unitary and self adjoint operators, Inner product spaces, Hilbert spaces Projections.|
|IX||Ordinary Differential and Partial Equations||(i) Existence and uniqueness of solutions of initial value problems for I order ordinary diferential equations.
(ii) singular solutions of I order ODEs, system of I order ODEs. General theory of homogenous and non-homogeneous linear ODEs.
(iii) Lagrange and Charpit methods for solving I order PDEs, Cauchy problem for I order PDEs.
(iv) Classification of II order PDEs.
(v) General solution of higher order PDEs with Method of separation of variables for Laplace, constant coefficients, Heat and Wave equations.
|X||Theory of Numbers||(i) Fundamental theorem of arithmetic, Chinese Remainder Theorem, divisibility in Z, congruences, Euler’s Ø-function, Euler’s theorem, Fermat’s theorem, Wilson’s theorem, primitive roots.|
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