RTMNU M.Sc. Sem 2 New Syllabus 2020 | RTMNU M.Sc. Revised Sem 2 Syllabus 2020 | Nagpur University M.Sc. Syllabus Part 1 | RTMNU First Year M.Sc. Syllabus
\nRTM Nagpur University M.Sc Semester New Revised Syllabus is given below for Downloading. The students can Download the respective Syllabus from following given details. Just go through the given links & read the given syllabus carefully. Nagpur University First Year New Semester Online Detail syllabus given below.<\/p>\n
Unit 1:<\/strong> Unit 2:<\/strong> Unit 3:<\/strong> Unit 4:<\/strong> Text Book :<\/strong> Reference Books :<\/strong> ____________________________________________________________________________<\/p>\n Unit 1:<\/strong> Unit 2:<\/strong> Unit 3:<\/strong> Unit 4:<\/strong> Text Book :<\/strong> Reference Books :<\/strong> ____________________________________________________________________________<\/p>\n Unit 1:<\/strong> Unit 2:<\/strong> Unit 3:<\/strong> Unit 4:<\/strong> Text books:<\/strong> Reference books:<\/strong> _____________________________________________________________________________<\/p>\n Unit 1:<\/strong> Unit 2:<\/strong> Unit 3:<\/strong> Unit 4:<\/strong> Compact surfaces whose points are umbilics. Hilbert\u2019s lemma. Compact surfaces of constant Gaussian or mean curvature. Complete surfaces. Characterisation of complete surfaces. Hilbert\u2019s theorem. Conjugate points on geodesics. Intrinsically defined surfaces. Triangulation. Two dimensional Riemannian manifolds. Problem of metrization. Problem of continuation.<\/p>\n Text Book:<\/strong> Reference Book:<\/strong> ____________________________________________________________________________<\/p>\n Unit 1:<\/strong> Unit 2:<\/strong> Legendre transformations and the Hamilton equations of motion. Cyclic coordinates and conservation theorems. Routh\u2019s procedure and oscillations about steady motion, The Hamiltonian formulation of relativistic mechanics, The Principle of least action.<\/p>\n Unit 3:<\/strong> Unit 4:<\/strong> Text Book:<\/strong> References:<\/strong> <\/p>\n","protected":false},"excerpt":{"rendered":" RTMNU M.Sc. Sem 2 New Syllabus 2020 | RTMNU M.Sc. Revised Sem 2 Syllabus 2020 | Nagpur University M.Sc. Syllabus Part 1 | RTMNU First Year M.Sc. Syllabus RTM Nagpur University M.Sc Semester New Revised Syllabus is given below for Downloading. The students can Download the respective Syllabus from following given details. Just go through […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-355","post","type-post","status-publish","format-standard","hentry","category-rtmnu-syllabus"],"_links":{"self":[{"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/posts\/355","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/comments?post=355"}],"version-history":[{"count":0,"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/posts\/355\/revisions"}],"wp:attachment":[{"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/media?parent=355"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/categories?post=355"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/tags?post=355"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nUnique factorization domains. Principal Ideal domains. Euclidean domains. Polynomial rings over unique factorization domains.<\/p>\n
\nIrreducible polynomials and Eisenstein criterion. Adjunction of roots. Algebraic extensions. Algebraically closed fields. Splitting fields. Normal extensions. Multiple roots.<\/p>\n
\nFinite fields. Separable extensions. Automorphism groups, and fixed fields. Fundamental theorem of Galois theory. Fundamental theorem of algebra.<\/p>\n
\nRoots of unity and Cyclotomic polynomials. Cyclic extensions. Polynomials solvable by radicals. Ruler and compass constructions.<\/p>\n
\nBasic Abstract Algebra: Bhattacharya, Jain, Nagpaul; Second Edition, Cambridge University Press.<\/p>\n
\n1. Topics in Algebra, I. N. Herstein, Second Edition, John Wiley.
\n2. Abstract Algebra, David S.Dummit and Richard M.Foote, John Wiley.<\/p>\nSyllabus\u00a0 Semester -II\u00a0<\/strong>
\nM. Sc. Mathematics<\/strong>
\nPaper – VII<\/strong><\/h3>\nReal Analysis -II<\/strong><\/h3>\n
\nOuter measure.Measurable sets and Lebesgue measure. Anon-measurable set, Measurable functions, Littlewood\u2019s three principles.<\/p>\n
\nThe Riemann integral. Lebesgue integral of a bounded function over a set of finite measure. Integral of a non-negative function. General Lebesgue integral. Convergence in measure. Differentiation of monotone functions. Functions of bounded variation. Differentiation of an integral.<\/p>\n
\nAbsolute continuity.Convex functions. Lp-spaces. Holder and Minkowski inequality. Riesz Fischer theorem. Approximation in Lp. Bounded linear functionals on Lp-spaces.<\/p>\n
\nCompact metric spaces. Baire category theorem. Arzela Ascoli theorem. Locally compact spaces. Sigma compact spaces.<\/p>\n
\nReal Analysis, H.L. Royden, Third edition, Prentice Hall, 1988.<\/p>\n
\n1. Measure theory and Integration, G. de Barra Wiley Eastern Limited, 1981.
\n2. An introduction to Measure & Integration, Inder K. Rana, Narosa Publishing House<\/p>\nSyllabus\u00a0 Semester -II\u00a0<\/strong>
\nM. Sc. Mathematics<\/strong>
\nPaper – VIII<\/strong><\/h3>\nTopology-II<\/strong><\/h3>\n
\nUrysohn\u2019s lemma. Tietze extension theorem. Completely regular spaces.Completely normal
\nspaces. Compactness for metric spaces. Properties of metric spaces.<\/p>\n
\nQuotient topology. Nets and filters.<\/p>\n
\nProduct topology : Finite products, product invariant properties, metric products, Tichonov
\ntopology, Tichonov theorem.<\/p>\n
\nLocally finite and discrete families in topological spaces. Paracompact spaces, Urysohn\u2019s metrization theorem.<\/p>\n
\n1. Foundations of General Topology: W.J. Pervin, Academic press, 1964.
\n2. Introduction to general Topology: K.D. Joshi, Wiley Eastern Ltd. 1983.<\/p>\n
\n1. Topology: J.R.. Munkres, second edition, Prentice Hall of India, 2002.
\n2. Introduction to topology and modern analysis :G.F. Simmons, Mc Graw Hill 1963.
\n3. General Topology: J.L. Kelley, Van Nostrand, 1995.<\/p>\nSyllabus\u00a0 Semester -II\u00a0<\/strong>
\nM. Sc. Mathematics<\/strong>
\nPaper – IX<\/strong><\/h3>\nDifferential Geometry<\/strong><\/h3>\n
\nDefinition of surface. Curves on a surface. Surfaces of revolution. Helicoids. Metric. Direction coefficients. Families of curves. Isometric correspondence. Intrinsic properties. Geodesics. Canonical geodesic equations.<\/p>\n
\nNormal property of geodesics. Existence theorems. Geodesic parallels. Geodesic curvature. Gauss Bonnet theorem. Gaussian curvature. Surfaces of constant curvature. Conformal mapping. Geodesic mapping.<\/p>\n
\nSecond fundamental form. Principal curvatures. Lines of curvature. Developable. Developable associated with space curves. Developable associated with curves on surfaces. Minimal surfaces and ruled surfaces. Fundamental equations of Surface theory. Parallel surfaces.<\/p>\n
\nAn introduction to Differential Geometry: T.J. Wilmore; Oxford University Press<\/p>\n
\nGeometry of curves and surfaces: do Carmo, Academic Press.<\/p>\nSyllabus\u00a0 Semester -II\u00a0<\/strong>
\nM. Sc. Mathematics<\/strong>
\nPaper – X<\/strong><\/h3>\nClassical Mechanics<\/strong><\/h3>\n
\nVariational Principle and Lagrange\u2019s equations; Hamilton\u2019s Principle, some techniques of calculus of variations, Derivation of Lagrange equations from Hamilton\u2019s principle. Extension of principle to nonholonomic systems. Conservation theorems and symmetry properties.<\/p>\n
\nThe equations of canonical transformation. Examples of canonical transformation. The symplectic approach to canonical transformations. Poisson brackets and other canonical invariants.<\/p>\n
\nEquations of motion. Infinitesimal canonical transformations and conservation theorems in the Poisson bracket formulation, the angular momentum, Poisson bracket relations, symmetry groups of mechanical systems. Liouville\u2019s theorem.<\/p>\n
\nClassical Mechanics: By H. Goldstein, Second Edition Narosa publishing house, New Delhi.<\/p>\n
\n1. Lectures in Analytic Mechanics: F. Gantmacher, MIR Publishers, Moscow, 1975.
\n2. Classical Mechanics: Narayan Chandra Rana and Pramod Sharad Chandra Jog, Tata Mc Graw Hill.
\n3. Lecture on Advanced Mechanics, Sonu Nilu Publication (2004) by T M Karade and G S Khadekar<\/p>\n