Comprehensive list of Topic-wise Marks distribution for CSIR-NET Exam.
Important Topics of Complex Analysis for CSIR-NET & GATE
CSIR-UGC National Eligibility Test (NET) for JRF & Lecturer-ship
Common Syllabus for PART ‘B’ AND ‘C’
UNIT – 1
Analysis: Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum.
Sequences and series, convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, uniform continuity, differentiability, mean value theorem.
Sequences and series of functions, uniform convergence. Riemann sums and Riemann integral, Improper Integrals. Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral.
Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems.
Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions as examples.
Linear Algebra: Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations.
Algebra of matrices, rank and determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem. Matrix representation of linear transformations. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms. Inner product spaces, orthonormal basis.
Quadratic forms, reduction and classification of quadratic forms
UNIT – 2
Abstract Algebra: Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements. Fundamental theorem of arithmetic, divisibility in Z, Number Theory: Congruences, Chinese Remainder Theorem, Euler’s Ø- function, primitive roots.
Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley’s theorem, class equations, Sylow theorems.
Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain. Polynomial rings and irreducibility criteria.
Fields, finite fields, field extensions, Galois Theory.
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Question Paper of MSc Entrance exams(like JAM, CUCET, BHU, … etc.). Download the PDFs and practice it for your upcoming exams. It will be very very useful and sufficient, no need to join any test series.
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FREE PDF Download Question Papers of CSIR-NET (Mathematical Science) year-wise upto 2020 (Latest).
CSIR NET Mathematical Science Syllabus: Download Syllabus
Some of the useful links for Self-study/e-Learnings. Using contents provided by these organizations, you may prepare for your academic exams(Diploma, Undergraduate and Postgraduate) as well as for entrance and scholarship exams like CSIR-NET, UGC-NET, JAM, PSC, SET, CUCET, Ph.D. Entrance, …etc
Here, you will get the collection of Previous Year Que. Papers (Math & Stat.) for CSIR-NET(JRF), GATE, NBHM, TIFR, IITs, CUCET, …etc and many mores including MSc/PhD Entrance Que. Papers. Practice these questions for your entrance exams. It will be very very helpful and sufficient for qualifying.
Questions Paper of NET, GATE & Ph.D. Entrance
Questions Paper of MSc Entrance exams
Video Lectures and Video Series for CSIR-NET/GATE on Important Topics, Marks Distribution, Cut off Set up, Preparation Strategy, Fast Revision, …etc.
Free Lectures Watch Here: https://www.youtube.com/playlist?list=PLDu0JgProGz55UHLDu7Y1xLd-uWSGxSPQ
Numerical Analysis Free Crash Course for NET, GATE & SET.
Number Theory Crash Course for NET, GATE & SET.
(Fast and Complete Revision of Dynamical System)
(List of Important Topics and their weightage in CSIR-NET exam )
(Where & how Download PDF Que. Papers of CSIR-NET, GATE, BHU, …etc)Continue reading →
Jawaharlal Nehru University Entrance Examination (JNUEE)-2020 Information Bulletin: Download Here
Registration Starts: March 02, 2020
Last date: April 30, 2020(Extended)
Admit card: April 30, 2020
Exam Date: May 11 -14, 2020
Online Application: Apply Here
JNU PhD Maths Prev. Yr. Que. Papers: Download PDF
JNU MSc Maths Prev. Yr. Que. Papers: Download PDF
CUCET released their notifications for admission to academic session 2020-2021 to UG, PG and PhD Programs in Central Universities. Check here List of all participating Universities
Registration Start: March 16, 2020
May 23, 2020, Again Extended till June 06, 2020)
Exam date: Mentioned below in Poster.
Result date: Notify Later.
Online Application: Apply here
How to Apply: Click here
For More Details: Visit here
CUCET MSc-2020 Mathematics Solution: Download Here
CUCET PhD-2019 Mathematics Solution: Download Here
Deadline to submit application: April 27, 2020.
Online Application: Click Here
About Google PhD Fellowship: This highly competitive program will award up to four named fellowships. The fellowship recipient will be supported for a maximum period of four years with a monthly fellowship, a contingency grant for expenses like books, stationery etc and a travel grant for attending conferences.
Each fellowship recipient will be assigned a Google Sponsor who will mentor the PhD fellow over the research period. Engagement with the Google Sponsor will include discussions on research direction, research progress updates etc.
Internship opportunities are frequently available at Google. Based on mutual interest between the fellowship recipient and Google Sponsor, the fellowship recipient can do an internship at Google after successfully clearing the internship interview process. Please note that awarding of the fellowship does not guarantee a Google internship.
For current PhD Students
For current UG/PG Students and Professionals Continue reading →
Full Notification: Download Here
Last Date for Application : March 04, 2020
Last Date with late fine: March 09, 2020
Exam Date: April 12, 2020
Detail Eligibility Criteria : Click Here
Old year Question Paper :
Syllabus of MH-SET-2020: Download Syllabus
More Details about Karnataka-SET 2020 : Visit Here
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