RTMNU M.Sc Mathematics Sem 1 New Syllabus 2020<\/strong> RTM Nagpur University M.Sc Semester New Revised Syllabus is given below for Downloading. The students can Download<\/a> the respective Syllabus from following given details. Just go through the given links & read the given syllabus<\/a> carefully. Nagpur University First Year New Semester Online Detail syllabus given below.<\/p>\n Permutation Group. Group of Symmetry. Dihedral group. Commutator group. Isomorphism,Theorems. Automorphisms. Characteristic subgroup. Conjugacy and G-Sets.<\/p>\n Normal Series. Solvable groups. Nilpotent groups. Cyclic decomposition of permutation group. Alternating groups. Simplicity of An.<\/p>\n Direct product, semi-direct product of groups. Sylows theorems. Groups of order 2 p and pq.<\/p>\n Ideals and Homomorphisms. Sum and direct sum of ideals. Maximal and prime ideals. Nilpotent and Nil ideals. Modules. Submodules. Direct sums. R-homomorphisms and quotient modules. Completely reducible modules. Free modules.<\/p>\n Basic Abstract Algebra :Bhattacharya, Jain, and Nagpal ,Second Edition, Cambridge University Press.<\/p>\n 1. Topics in Algebra, I. N. Herstein, Second Edition, John Wiley. _______________________________________________________________________________<\/p>\n Uniform convergence. Uniform convergence and continuity. Uniform convergence and integration. Uniform convergence and differentiation. Equicontinuous families of functions. The Stone-Weierstrass theorem.<\/p>\n Differentiation. The Contraction Principle. The Inverse Function Theorem. The Implicit Function Theorem. The Rank Theorem. Partitions of unity.<\/p>\n The space of tangent vectors at a point of Rn. Another definition of Ta (Rn). Vector fields on open subsets of Rn. Topological manifolds. Differentiable manifolds. Real Projective space. Grassman manifolds. Differentiable functions and mappings.<\/p>\n Rank of a mapping. Immersion. Sub manifolds. Lie groups. Examples of Lie groups.<\/p>\n 1. Principles of Mathematical Analysis (Third Edition): Walter Rudin Mc GRAW \u2013 HILL Book Company. 1. Methods of Real Analysis: R.R. Goldberg, John Wiley. _______________________________________________________________________________<\/p>\n Countable and Uncountable sets. Examples and related Theorems. Cardinal Numbers and related Theorems. Topological Spaces and Examples.<\/p>\n Open sets and limit points. Derived Sets. Closed sets and closure operators. Interior, Exterior and boundary operators. Neighbourhoods, bases and relative topologies.<\/p>\n Connected sets and components. Compact and countably compact spaces. Continuous functions and<\/p>\n homeomorphisms.<\/p>\n To and T1-spaces, T2-spaces and sequences. Axioms of countability. Separability. Regular and normal spaces.<\/p>\n Foundations of General Topology: W.J. Pervin, Academic press, 1964.<\/p>\n 1. Topology: J.R. Munkres, (second edition), Prentice Hall of India, 2002. ________________________________________________________________________________<\/p>\n Matrices and operators, Subspaces, Bases and Dimension. Determinants, trace, and Rank. Direct sum decomposition. Real Eigen Values. Differential equations with Real Distinct Eigen values. Complex Eigen values.<\/p>\n Complex vector spaces. Real operators with Complex Eigen values. Application of complexlinear algebra to differential equations. Review of topo\u0000ogy in Rn. New norms for old.Exponential of operators.<\/p>\n Homogeneous linear systems. A non-homogeneous equation. Higher order systems. The primary decomposition. The S+N decomposition. Nilpotent canonical orms.<\/p>\n Jordan and real canonical forms. Canonical forms and differential equations. Higher order linear equations on function spaces. Sinks and sources. Hyperbolic flows. Generic properties of operators. Significance of genericity.<\/p>\n Differential equations, dynamical systems and linear algebra: M.W. Hirsch and S. Smale, Academic Press, 1975.<\/p>\n Dynamical systems: V.I. Arnold, Springer Verlag, 1992.<\/p>\n ______________________________________________________________________________<\/p>\n Preliminary concepts of integral equations. Some problems which give rise to integral equations. Conversion of ordinary differential equations into integral equations. Classification of linear integral equations. Integro-differential equations.<\/p>\n Fredholm equations. Degenerate kernels. Hermitian and symmetric kernels. The Hilbert Schmidt theorem. Hermitization and symmetrization of kernels. Solutions of integral equations with Green\u2019s function type kernels.<\/p>\n Types of Voltera equations. Resolvent kernel of Voltera equations, Convolution type kernels. Some miscellaneous types of Voltera equations. Non-linear Voltera equations. Fourier integral equations. Laplace integral equations.<\/p>\n Hilbert transform. Finite Hilbert transforms. Miscellaneous integral transforms. Approximate methods of solutions for linear integral equations. Approximate evaluation of Eigen values and Eigen functions.<\/p>\n Integral Equations: A short course: LI. G Chambers: International text book company Ltd, 1976.<\/p>\n","protected":false},"excerpt":{"rendered":" RTMNU M.Sc Mathematics Sem 1 New Syllabus 2020 RTMNU M.Sc Mathematics Sem 1 New Syllabus 2020 | RTMNU M.Sc. Revised Sem 1 Syllabus 2020 | Nagpur University M.Sc. Syllabus Part 1 | RTMNU First Year M.Sc. Syllabus RTMNU M.Sc Mathematics Sem 1 New Syllabus 2020 RTM Nagpur University M.Sc Semester New Revised Syllabus is given […]<\/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-347","post","type-post","status-publish","format-standard","hentry","category-rtmnu-syllabus"],"_links":{"self":[{"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/posts\/347","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=347"}],"version-history":[{"count":0,"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/posts\/347\/revisions"}],"wp:attachment":[{"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/media?parent=347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/categories?post=347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mahabharti.in\/university\/wp-json\/wp\/v2\/tags?post=347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}RTMNU M.Sc Mathematics Sem 1 New Syllabus 2020<\/h2>\n
Syllabus\u00a0 Semester -I\u00a0<\/strong>
\nM. Sc. Mathematics<\/strong>
\nPaper – I\u00a0<\/strong><\/h3>\nAlgebra -I<\/strong><\/h3>\n
Unit 1:<\/strong><\/h4>\n
Unit 2:<\/strong><\/h4>\n
Unit 3:<\/strong><\/h4>\n
Unit 4:<\/strong><\/h4>\n
Text Book:<\/strong><\/h4>\n
Reference Books:<\/strong><\/h4>\n
\n2. Abstract Algebra: David S.Dummit and Richard M. Foote, John Wiley.<\/p>\nRTMNU M.Sc Mathematics Sem 1 New Syllabus 2020<\/h2>\n
Syllabus\u00a0 Semester -I\u00a0<\/strong>
\nM. Sc. Mathematics<\/strong>
\nPaper – II\u00a0<\/strong><\/h3>\nReal Analysis-I<\/strong><\/h3>\n
Unit 1:<\/strong><\/h4>\n
Unit 2:<\/strong><\/h4>\n
Unit 3:<\/strong><\/h4>\n
Unit 4:<\/strong><\/h4>\n
Text Books:<\/strong><\/h4>\n
\n2. An Introduction to Differentiable Manifolds and Riemannian Geometry: W. Boothby, Academic Press, 1975.<\/p>\nReference Books:<\/strong><\/h4>\n
\n2. Calculus of Several Variables: C Goffman, Harper and Row.<\/p>\nRTMNU M.Sc Mathematics Sem 1 New Syllabus 2020<\/h2>\n
Syllabus\u00a0 Semester -I\u00a0<\/strong>
\nM. Sc. Mathematics<\/strong>
\nPaper – III<\/strong><\/h3>\nTopology-I<\/h3>\n
Unit 1:<\/strong><\/h4>\n
Unit 2:<\/strong><\/h4>\n
Unit 3:<\/strong><\/h4>\n
Unit 4:<\/strong><\/h4>\n
Text Book:<\/strong><\/h4>\n
Reference Books:<\/strong><\/h4>\n
\n2. Introduction to Topology and Modern Analysis: G.F. Simmons, Mc Graw Hill 1963.
\n3. General Topology: J.L. Kelley, Van Nostrand, 1995.
\n4. Introduction to general Topology: K.D. Joshi, Wiley Eastern Ltd. 1983<\/p>\nRTMNU M.Sc Mathematics Sem 1 New Syllabus 2020<\/h2>\n
Syllabus\u00a0 Semester -I\u00a0<\/strong>
\nM. Sc. Mathematics<\/strong>
\nPaper – IV<\/strong><\/h3>\nLinear Algebra and Differential Equations<\/h3>\n
Unit 1:<\/strong><\/h4>\n
Unit 2:<\/strong><\/h4>\n
Unit 3:.<\/strong><\/h4>\n
Unit 4:<\/strong><\/h4>\n
Text Book :<\/strong><\/h4>\n
Reference Book :<\/strong><\/h4>\n
RTMNU M.Sc Mathematics Sem 1 New Syllabus 2020<\/h2>\n
Syllabus\u00a0 Semester -I\u00a0<\/strong>
\nM. Sc. Mathematics<\/strong>
\nPaper – V<\/strong><\/h3>\nIntegral Equations<\/strong><\/h3>\n
Unit 1:<\/strong><\/h4>\n
Unit 2:<\/strong><\/h4>\n
Unit 3:<\/strong><\/h4>\n
Unit 4:<\/strong><\/h4>\n
Text Book:<\/strong><\/h4>\n