PUCAT

Candidates can check the space below to know about the syllabus of PUCAT mathematics Real Analysis section:
Sequences and series of real numbers. Convergent and divergent sequences, bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences, absolute and conditional convergence; Tests of convergence for series of positive termscomparison test, ratio test, root test, Leibnitz test for convergence of alternating series. Functions of one variable: limit, continuity, differentiation, Rolle's Theorem, Cauchy’s Taylor's theorem. Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor's and Maclaurin's, domainof convergence,  term-wise differentiation and integration of power series. Functions of two real variable: limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler's theorem.

Candidates can check the space below to know about the syllabus of PUCAT mathematics algebra section:
Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups; Normal subgroups, Lagrange's Theorem for finite groups, group homomorphism and quotient groups, Rings, Subrings, Ideal, Prime ideal; Maximal ideals; Fields, quotient field. Vector spaces, Linear dependence and Independence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, Range space and null space, rank-nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues and eigenvectors. Cayley-Hamilton theorem. Symmetric, Skew symmetric, Hermitian, Skew-Hermitian, Orthogonal and Unitary matrices.

Candidates can get an idea of PUCAT Geology syllabus below:

Origin of Earth; Radiometric dating methods of rocks, Geological time scale; Internal structure and chemical composition of the Earth, Weathering, Landforms related to wind, rivers and glaciers. Basic concepts of plate tectonics and sea-floor spreading; Basic concept of stress and strain. Measurement of dip, strike and thickness of beds; Forms of igneous bodies; Fold and faults. Basic
idea about crystal, crystal growth and crystallization; Crystal systems. Twinning and common twin laws; Physical properties, chemical composition, occurrences and uses of minerals belonging to the Silica, Feldspar, Feldspathoid, Amphibole, Pyroxene, Olivine, Mica and Garnet families. Principles of stratigraphy. Physical and structural subdivisions of the Indian subcontinent and their characters. Brief idea of Archaean and Proterozoic successions of Peninsular India. Marine and non-marine Palaeozoic, Mesozoic and Cenozoic successions of the Himalayan and Peninsular India; Gondwana super group; Deccan traps and Siwalik Group. Process of fossilization; Preliminary idea of origin of life and Precambrian fossil records; Morphology and geological history of Bivalvia, Gastropoda,  Brachiopoda, Cephalopoda and Trilobita. Igneous, Sedimentary and Metamorphic rocks; Bowen’s
Reaction series; Magmatic differentiation and assimilation; Texture of igneous rocks; IUGS classification of igneous rocks, Phase rule; mineralogical characteristics of acidic, basic, alkaline and ultramafic igneous rocks. Origin and classification of sedimentary rocks; Diagenesis; Texture of sedimentary rocks; Sediment characteristics; Sedimentary structures. Definition, agents and
types of metamorphism; Metamorphic rocks: texture, structure and classification; Process of formation of ores, Occurrence, origin and distribution of important mineral deposits of India. Conventional and non-conventional Energy resource; Concept of surface and subsurface mining. Remote sensing concepts and its applications in Geology; Groundwater and its vertical distribution
types; Types of aquifers. Geological hazards namely Earthquakes, Landslides, Floods and Tsunami.