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# Study BSc - Modern Algebra

UNIT I: Matrices : Introduction – Transpose of a matrix – Inverse matrix – Symmetric and Skew – Symmetric matrices - Hermitian and Skew-Hermitian Matrices – Orthogonal and Unitary Matrices – Rank of a Matrix –Characteristic Roots and Characteristic Vectors of a Square Matrix. UNIT II: Sets – Relations and binary operations – Groups – Symmetric Group definitions and Examples – Subgroups – Index of a group – Fermat theorem - Normal subgroups and quotient groups. UNIT III: Homomorphisms – Cauchy’s theorem, Sylow’s theorem for Abelian groups Automorphisms – permutation groups – Rings : Definition and Examples – Some special classes of Rings Anx.18 D - B.Sc Maths (SDE) 2007-08 Page 12 of 26 UNIT IV: Field – Integral domain - Homomorphisms of Rings. - Ideals and Quotient Rings – Vector space: Subspace of a Vector space - Homomorphism – Isomorphism - Linear Independence and Bases. UNIT V: Dual spaces – Innerproduct spaces – Orthonormal set – Linear transformations – Characteristic roots and characteristic vectors of a square matrix

## BSc Subjects

 Applied Electronics Atomic Physics and Nuclear Physics Classical Algebra and Calculus CLIENT SERVER COMPUTING Climatology and Oceanography Complex Analysis DATA COMMUNICATION AND NETWORKS DATA STRUCTURES AND C PROGRAMMING Differential Equation Lap lace Transforms DIGITAL FUNDAMENTALS AND ARCHITECTURE Economic geography Geography of India Geomorphology Heat Thermodynamics Mechanics Properties of Matter and Sound Human geography INTERNET and JAVA PROGRAMMING MATHEMATICAL FOUNDATION FOR COMPUTER Mathematical Physics Mechanics Modern Algebra OBJECT ORIENTED PROGRAMMING WITH C++ Optics Electricity and Magnetism Principles of cartography Quantum Mechanics and Relativity Real Analysis SOFTWARE ENGINEERING Solid State Physics Statistics for geographers Statistics for Mathematics SYSTEM SOFTWARE AND OPERATING SYSTEM Trigonometry Vector Calculus and Analytical Geometry VISUAL PROGRAMMING WEB TECHNOLOGY Business Economics Business Management Business Organisation and Office Management Business Statistics Commercial Law and Company Law Company law and secretarial practice I Company law and Secretarial practice II Corporate Accounting Cost and Management Accounting Executive Communication Financial Accounting Industrial law Life Office Management Managerial Economics Mathematics for Business Principles of Accountancy Principles of Life Insurance Principles of Management Principles of Marketing Priniciples of Reinsurance Statistics

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