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A Site for Higher Mathematics

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NBHM PhD Scholarship Scheme 2021: Important Dates, Eligibility Criteria, Question Papers & Related Queries.

  • Exam Date: August 18, 2021
  • Selection procedure for the scholarship

    Candidates shall be shortlisted for an interview based on their performance in the test. Final selection for the scholarship shall primarily be on the basis of performance in the test and the subsequent interview, although the selection committee may take into account other aspects of the candidate’s academic track record.

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    TIFR Graduate School Admissions (GS-2021)

    Tata Institute of Fundamental Research PhD & Int. PhD Admissions (GS-2021)

    GS2021: Selection Process for Mathematics

    Selection process for admission in 2021 to the various programs in Mathematics at the TIFR centers – namely, the PhD and Integrated PhD programs at TIFR, Mumbai as well as the programs conducted by TIFR CAM, Bengaluru and ICTS, Bengaluru – will be held in two stages.
    Stage I. A nation-wide test will be conducted in various centers on March 7, 2021. For the PhD and Integrated PhD programs at the Mumbai Center, this test will comprise the entirety of Stage I of the evaluation process. For more precise details about Stage I of the selection process at other centers (TIFR CAM, Bengaluru, and ICTS, Bengaluru) we refer you to the websites of those centers.
    The nation-wide test on March 7 will be an objective test of three hours duration, with 20 multiple choice questions and 20 true/false questions. The score in this test will serve as qualification marks for a student to progress to the second step of the evaluation process. The cut-off marks for a particular program will be decided by the TIFR center handling that program. Additionally, some or all of the centers may consider the score in Stage I (in addition to the score in Stage II) towards making the final selection for the graduate program in 2021.
    Stage II. The second stage of the selection process varies according to the program and the center. More details about this stage will be provided at a later date

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    RPSC Assistant Professor/Lecturer Exam Syllabus, Study Materials and Free Video Lectures.

    We suggest you to solve problems of other states PSC/Lecturer exams questions for your RPSC practice. Also try to solve easy level problems from NET/GATE.


    Click on the subject to download the notes.

    Topics According to New Syllabus

    1. Differential and Integral Calculus:
    2. 2-D Coordinate Geometry

    (Catesian and Polar coordinates)
    3. 3-D Coordinate Geometry
    4. Vector Calculus
    5. Ordinary Differential Equations
    6. Partial Differential Equations
    7. Mechanics
    8. Abstract Algebra
    9. Linear Algebra
    10. Complex Analysis

    # Maximum Marks : 75
    # Number of Questions : 150

    # Duration of Paper : Three Hours
    1– Special Functions
    2- Integral Transforms
    3- Differential and Integral Equations
    4- Metric spaces and Topology
    5- Differential Geometry
    6- Tensors
    7- Mechanics
    8- Numerical Analysis
    9- Operations Research
    10- Mathematical Statistics

    # Maximum Marks : 75
    # Number of Questions : 150

    # Duration of Paper : Three Hours

    Suggested Books Reading: https://pkalika.in/suggested-books-for-mathematics/

    Download Study Materials For RPSC Maths Lecturer: Click Here

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    GATE Mathematics(MA) Solutions (Topic-wise & Year-wise)

    Handwritten Solution of GATE Mathematics for self preparation. We provide best quality notes for self preparation of GATE Mathematics for those who can not afford coaching. Best way to prepare for GATE 2022 is to do practice of problems from Previous Yr. Questions of GATE Mathematics. Start your preparation of GATE 2022 with P Kalika Notes and make a path to success.

    Year-wise Solution

    GATE Topic-wise Solution

    Buy All PDF Study Materials & Solutions for GATE: Click Here

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    CSIR-NET (Maths) Topic-wise & Year-wise Solutions

    Handwritten Solutions of CSIR-NET Mathematics Prev. Yr. Que. Papers (Upto November-2020) is available here. Very very helpful in preparation of CSIR-NET, SET, GATE, PSC, …. and other equivalent exams. Self preparation materials(No need of any coaching).

    Note: CSIR NET(JRF) Exam of June-2020 has been done in Nov-2020 and Exam for Dec-2020 and June-2021 still not held and also no any information out.

    1. Sol. of Linear algebra(Upto Nov-2020, Pages:205): Download PDF
    2. Sol. of Abstract algebra(Upto Nov-2020, Pages:107): Download PDF
    3. Sol. of Real Analysis(Upto Nov-2020, Pages:210): Download PDF
    4. Sol. of Complex Analysis(Upto June-2020, Pages:118): Download PDF
    5. Sol. of NT, NA, LPP & DS (Upto 2021, Pages:118)Download PDF
    6. Sol. of ODE, PDE, IE & COV(Upto Nov 2020, Pages:205): Download PDF
    7. Combined Solutions (All above Sr. No. 1 – 6): Click Here

    CSIR-NET Year wise Complete Solution

    1. CSIR-NET 26 Nov 2020: Download Here
    2. CSIR-NET Dec-2019: Download Here
    3. CSIR-NET June-2019: Download PDF
    4. CSIR-NET Dec-2018: Download PDF
    5. CSIR-NET June-2018: Download PDF
    6. Combined Solutions of 2017D, 2018J, 2018D, 2019J, 2019D & 2020Nov Download Here
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    GATE-2021 Mathematics(MA) Modified Syllabus (New)

    Note: Syllabus of GATE-2021 have been revised. New Syllabus is presented here. (Check Old Syllabus of GATE-2020)

    Calculus: Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications to area, volume and surface area; Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.

    Abstract Algebra: Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups, Group action,Sylow’s theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions,algebraic extensions, algebraically closed fields.

    Linear Algebra: Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, minimal polynomial, Cayley-Hamilton Theorem, Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric, Hermitian, skew-Hermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms.

    Complex Analysis: Functions of a complex variable: continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle, Morera’s theorem; zeros and singularities; Power series, radius of convergence, Taylor’s series and Laurent’s series; Residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations.

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    Learn LaTeX with P Kalika (From very beginning)

    An initiative towards learning. Don’t worry, no need of any programming skill. We have started from very beginning and for practice purpose we also uploaded some symbols and content writing. You may practice them.

    Recorded videos for your practice purpose: Click here

    Contents for “LaTeX Learning”

    Bemar(Presentation) in LaTeXDownload .tex File & Download PDF
    LaTeX Practice-1LaTeX Short Math Guide Download
    LaTeX Practice-2LaTeX_Symbols Download
    LaTeX Practice-3Math into LaTeX Download
    LaTeX Practice-4Latex All SymbolsDownload
    DescriptionDownload .Tex File
    LaTeX Workshop (Day-1):Download File (tex & PDF)
    LaTeX Workshop (Day-2):Download .tex file and Download PDF
    LaTeX Workshop (Day-3):Download .tex File and Download PDF

    Videos of LaTeX Learning

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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


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

    Related Posts:

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


    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: