HSST MATHEMATICS/KERALA PSC HSST NOTIFICATION 2021-2022

Kerala PSC has already announced the notification for HSST (Higher Secondary School Teachers) Exam 2022. Higher Secondary School Teacher is one of the finest professions that any eligible candidate could ever imagine. Kerala PSC HSST exam is one of the greatest opportunities for people who have been in the same field. Freshers with all the requisite qualifications (mentioned by Kerala PSC in the official notification) can also utilize this opportunity.

QUALIFICATIONS

• Master’s Degree in the concerned subject with minimum 50% marks.
• B.Ed. in the concerned subject (M.Ed. qualified candidates are exempted from B.Ed. qualification).
• Must be SET qualified.
• Degrees (non-qualifying degrees) like Ph.D./MPhil/Post-Doctoral Fellowship) will be given weightage, as they are additional qualifications.

SYLLABUS

History of Development of Mathematics, 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 number theory, Continued fractions, Sets and binary operations, groups, Sylow 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, Cayley-Hamilton theorem, Hyperspaces and linear functionals, Normed spaces, Banach spaces and related theorems, Linear Maps, inner product spaces, Hilbert spaces and related theorems, Polynomial Equations, Trigonometry, Analytical geometry of two dimension and three dimensions, vectors, matrices. Calculus, applications of differentiation and integration, elementary functions. Fundamental theorem of calculus, mean value theorems, maxima and minima-functions. Real numbers, rational, irrational numbers, 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. Lebesgue measure, Lebesgue integral, Complex numbers, De Moivre'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, Power series, Taylor series, Laurent series, Metric spaces, topological spaces, Neighborhood. Connectedness and compactness, locally connected, path connected, locally compact spaces, First order ordinary differential equations-formation, properties and various methods of solving, Picard’s method of approximation, Second order ordinary differential equations – formation, properties and various methods of solving. Equidimensional equations, Existence and uniqueness of solutions, Systems of first order equations, Series solutions of first order and second order ordinary differential equation at ordinary addition regular singular points. Hypergeometric functions and equations, Legendre equations and polynomials. Chebyshev's Equations and polynomials. Bessel’s equations and Functions, LaPlace transform, Fourier series, beta and Gamma functions, Partial differential equation in two independent variables. Functional dependence, analytic functions. Second order partial differential Equation, Wave equation, Laplace equation, Numerical solutions of algebraic equations, finite differences, interpolation, Fundamentals of Theory of Wavelets, Fuzzy set theory, Fractal geometry, Modular functions Jordan forms, elliptic functions, Riemann Zeta Function, Automate and formal languages, Block Designs, Topology Solutions at infinity of Differential Equations, Integral Equations, calculus of Variations, differential geometry, Fundamentals of Mechanics and Fundamentals of Fluid Dynamics.

HSST Mathematics: Study Materials

1. Edward Gaughan -"Sequences and Convergence"
2. Donu Arapura – “Notes on Algebra”
3. Bjorn Poonen – “Complex numbers”
4. Gregory Hartman – “Fundamentals of Matrix Algebra”

***Download our Leraning App***