Syllabus of Pre Ph. D. - Dr. D. Y. Patil Vidyapeeth, Pune.
Syllabus -Course-Work. FUNDAMENTAL OF ECONOMICS. Total Credit: 04 Subject Code: ECPhD01. The objective of this course is the make the students aware of the fundamentals of economics and also the contemporary issues. This course will help the student in deciding their.
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Syllabus for Pre PhD Qualifying Exam. Module - 1. Algebra: Vector spaces, subspaces, linear dependence, basis and dimension, Linear transformation, range space, null space, rank and nullity, Matrix representation of a linear transformation. Change of basis, Eigenvalues and eigenvectors, Inner product, orthogonality, Gram-Schmidt process, orthogonal expansion, Quadratic forms, reduction to.
Syllabus for Advanced Real Analysis For IXth Semester Integrated Mathematics (and Pre-PhD) Text for Reference: Real and Complex Analysis, Walter Rudin. Chapter I: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in (0, 00) Integration of positive functions Integration of complex functions.
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