P Kalika

A Site for Higher Mathematics


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CSIR-NET Mathematics Details Syllabus

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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Free Maths Handwritten Study Materials (Donated)

To help students for their academics and competitive exams, we have started ‘Let’s Do’ Program in which anyone can take Notes FREELY and anyone can contribute*.

The following mathematical notes are contributed by students(mentioned below). These notes are available on FREE OF COST, You may download and share them.

We encourage you (BSc/MSc Students) to contribute your notes (Only scanned, Not hardcopy), your little contribution can help many people. Those who wish to contribute can send scanned notes on maths.whisperer@gmail.com.

(Notes are arranged in Alphabetical order(A-Z) )

  1. Classical Mechanics (New): Download PDF
    • (by  Rakhee Kumari, MSc, CUJ)
  2. Linear Algebra: Download PDF
    • (by  M. Sarojini, MSc, CUJ)
  3. Metric Space: Download PDF
    • (by  M. Sarojini, MSc, CUJ)
  4. Number Theory: Download PDF
    • (by  M. Sarojini, MSc, CUJ)
  5. Probability & Statistics: Download PDF
    • (by  M. Sarojini, MSc, CUJ)
  6. Real Analysis
    • Sequence(by Laxmi, MSc, Ranchi Univ.): Download PDF
    • Sequence, Series & Uniform Continuity(Rahul Anand, MSc, NIT Jalandhar): Download PDF
    • Point set Topology(Rahul Anand, MSc, NIT Jalandhar): Download PDF
  7. Ring Theory(Rahul Anand, MSc, NIT Jalandhar)Download PDF
  8. Free Study Materials(by P Kalika): Download Here

*Term & conditions for Contribution

  1. Notes will be Scanned in PDF Format
  2. Writing Should be Clear/Clean
  3. No Copyright Materials
  4. Only Notes Related to Mathematics
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MSc Entrance Exams Que. Papers (JAM, CUCET, BHU, …etc)

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.

  1. BHU PET Que Paper(Maths): Download PDF
  2. BHU PET Que Paper(Stats.): Download PDF
  3. CUCET MSc Maths (2019-2016+Sample): Download PDF
  4. JAM Mathematics (2020-2007): Download PDF
  5. JAM Statistics(2020-2008): Uploading Soon
  6. NBHM MSc Que Paper(2019-2008): Uploading Soon
  7. SAU MSc Entrance Que. Papers (2019-2014): Uploading Soon
  8. TIFR Mathematics Que Paper(2019-2010): Download PDF
  9. University of Delhi(Central University): Uploading Soon
  10. University of Hyderabad(Central University): Download PDF
  11. Any other: On-demand

Credit:

  • Jay Prakash, Neha & Shambhu (MSc, CUJ): CUCET, BHU Related Papers:
  • Guddu Kumar(Patna University, BSc): UOH, BHU Related Papers

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If you wish to send any question papers, we welcome you. Kindly send it to help@pkalika.in


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CSIR NET Previous Yr. Que. Papers

FREE PDF Download Question Papers of CSIR-NET (Mathematical Science) year-wise upto 2020 (Latest).

  1. Nov-2020 (Que.+Ans, 26 Nov): Download PDF
  2. Dec-2019 (Que. Paper+Key): Download PDF
  3. Dec-2019(Assam)(Que. Paper+Key): Download PDF 
  4. June-2019 (Que. Paper+Key): Download PDF
  5. Dec-2018 (Que. Paper+Key): Download PDF
  6. June-2018 (Que. Paper+Key): Download PDF
  7.  Dec-2017 (Que. Paper+Key): Download PDF
  8. June-2017 (Que. Paper+Key): Download PDF
  9. Dec-2016 (Que. Paper+Key): Download PDF
  10. June-2016 (Que. Paper+Key): Download PDF
  11. Dec-2015 (Que. Paper+Key): Download PDF
  12. June-2015 (Que. Paper+Key): Download PDF
  13. Dec-2014 (Que. Paper): Download PDF
  14. June-2014 (Que. Paper+Key): Uploading Soon
  15. Dec-2013 (Que. Paper): Download PDF
  16. June-2013 (Que. Paper+Key): Download PDF
  17. Dec-2012(Que. Paper+Key): Download PDF
  18. June-2012 (Que. Paper+Key): Download PDF
  19. CSIR-NET June-2011: Download PDF
  20. CSIR-NET Dec-2011: Download PDF
  21. CSIR-NET 2008:  Download Paper-1 and Download Paper-2

CSIR NET Mathematical Science Syllabus: Download Syllabus

CSIR-NET Solutions(Upto 2020 June): Click Here

GATE Maths Solution(Upto 2021): Click Here

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UGC/AICTE Provided Important links for Self-study/e-Learning

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

  1. e-PG Pathshala (https://epgp.inflibnet.ac.in/)
    • Contents/Course: 70 subjects across all disciplines of social sciences, arts, fine arts and humanities, natural & mathematical sciences.
    • Format:  e-text more than 20k and videos more than 19k available here.
  2. UP-PG MOOCS (http://ugcmoocs.inflibnet.ac.in/ugcmoocs/moocs_courses.php)
    • Contents/Course: UG Course(222) and PG Course(86)
  3. SWAYAM (https://www.swayam.gov.in/)
    • Contents/Course: From School level to PG-level, Can be accessed by anyone, anywhere at any time.
  4. Consortium For Education Communication (CEC) (http://cec.nic.in/cec/)
    • Contents/Course: e-Contents available for more than 85 UG courses and more than 24k e-content modules available. Visit Youtube Channel.
  5. National Digital Library of India (https://ndl.iitkgp.ac.in/)
    • Students/readers may get contents online in all languages, which are available in different libraries of India.
  6. Shodh Ganga (https://shodhganga.inflibnet.ac.in/)
    • ShodhGanga@INFLIBNET Centre provides a platform for research students to deposit their PhD theses and make it available to the entire scholarly community in open access.
  7. e-Shodh Sindhu (https://ess.inflibnet.ac.in/)
    • e-Shodh Sindhu provides current as well as archival access to more than 15,000 core and peer-reviewed journals and a number of bibliographic, citation, and factual databases in different disciplines from a large number of publishers and aggregators.
  8. VIDWAN (https://vidwan.inflibnet.ac.in/)
    • This website is for faculty. VIDWAN is the premier database of profiles of scientists/researchers and other faculty members working at leading academic institutions and other R & D organization involved in teaching and research in India.
  9. SWAYAM PRABHA (https://swayamprabha.gov.in/)
    • SWAYAM PRABHA is a group of 32 DTH channels devoted to telecasting of high-quality educational programs on a 24*7 basis using the GSAT-15 satellite. The contents are provided by NPTEL, IITs, UGC, CEC, IGNOU, NCERT, and NIOS.

Important Links:


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Que. Papers of CSIR-NET, GATE, JAM, CUCET, BHU, JNU, IIT, NBHM, DU, …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

  1. CSIR-NET Mathematics Que. Paper+Ans (2019-2011): Download Here
  2. CUCET PhD Mathematics Que. Paper+Ans (2020-2016): Download PDF
  3. Delhi University PhD Entrance Test(2015-2019): Download PDF
  4. GATE Mathematics Que Paper+Ans (2020-2010): Download PDF
  5. IIT Bombay PhD Screening Test(Dec 2015-May 2019): Download PDF
  6. IIT Kanpur PhD Screening Test(Dec 2015-May 2019): Uploading Soon
  7. IISc Banglore Int. PhD Test(178Pages): Uploading Soon
  8. ISI PhD Entrance Test(2015-2019): Uploading Soon
  9. JNU PhD Mathematics Que. Papers(2018-2015): Download PDF
  10. NBHM PhD Que Paper+Ans (2020-2005): Download PDF
  11. SAU PhD Admission Que. Paper(115 Pages): Download PDF
  12. TIFR Mathematics Que Paper(2020-2010): Download PDF
  13. BHU RET Que Paper(Math & Statistics): Uploading Soon
  14. P Kalika Practices Sets(52Pages): Download Practice Sets
  15. Any others: On Demand

Questions Paper of  MSc Entrance exams

  1. BHU PET Que Paper(Mathematics): Download PDF
  2. BHU PET Que Paper(Statistics): Download PDF
  3. CMI PG Entrance Papers(2010-2019): Uploading Soon
  4. CUCET MSc Maths Que. Paper(2019-2016+Sample): Download PDF
  5. JAM Mathematics(2020-2007): PDF Download
  6. NBHM MSc Que Paper(2019-2008): Uploading Soon
  7. TIFR Mathematics Que Paper(2019-2010): Download PDF
  8. University of Delhi(Central University): Uploading Soon
  9. University of Hyderabad(Central University): Download PDF
  10. Others: On demand

Note:

  • If you need any other Exam paper, write here.
  • If you want to share any Que. Paper, then send it to help@pkalika.in

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Youtube Videos on CSIR-NET/GATE

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

Online Classes Started Now, Check here:

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)

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JNU Entrance Exam- 2020

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

Results(tentatively): 31 May 2020
Note: The Test will be conducted in the Computer Based Test (CBT) mode only by NTA.

JNU PhD Maths Prev. Yr. Que. Papers: Download PDF
JNU MSc Maths Prev. Yr. Que. Papers: Download PDF

FileHandle

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CUCET-2020 admission to UG, PG and PhD

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
Last Date: 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

Sample Que. Paper Downloads(PDF Download)
UG Math, PG Math & Statistics, PG Math, PhD Math, Phd Statistics

Participating Institutions

  1. National Institute of Technology Tiruchirappalli (NIT-T)
  2. Central University of Andhra Pradesh
  3. Assam University
  4. Central University of Gujarat
  5. Central University of Haryana
  6. Central University of Jammu
  7. Central University of Jharkhand
  8. Central University of Karnataka
  9. Central University of Kashmir
  10. Central University of Kerala
  11. Central University of Odisha
  12. Central University of Punjab
  13. Central University of Rajasthan
  14. Central University of South Bihar
  15. Central University of Tamil Nadu
  16. Mahatma Gandhi Central University, Bihar

State University

  1. Baba Ghulam Shah Badshah University, Rajouri
  2. Bengaluru Dr B R Ambedkar School of Economics (BASE)
  3. Khallikote University, Berhampur
  4. Sardar Patel University of Police, Security & Criminal Justice, Jodhpur
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Google PhD Fellowship India 2020

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.

Eligibility Criteria
For current PhD Students

  1. Applicants must have been enrolled at an Indian University, in a full-time PhD program, on or after 1-Jan-2019. For any questions about this criterion, please email research-programs-in@google.com.
  2. Students must remain enrolled in the PhD program for the duration of the Fellowship or forfeit the award.
  3. Applicants must be pursuing a PhD in Computer Science or related areas.
  4. Google employees and family members of Google employees are not eligible
  5. Students who are already receiving another corporate fellowship are not eligible.

For current UG/PG Students and Professionals Continue reading


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Karnataka State Eligibility Test (KSET)-2020 For Assistant Professor

Full Notification: Download Here
Important Dates

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

Note: The candidates must read the conditions of eligibility carefully and must satisfy
themselves regarding their eligibility for the test before filling the online application form.
Candidate who became eligible in Previous KSETs are not eligible to apply again in the same subject.

Note: For study materials(Only Mathematics) related to Karnataka-SET, contact us on maths.whisperer@gmail.com. or Visit here.