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A Site for Higher Mathematics


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GATE Mathematics Prev. Yr. Cut-offs and Ranks

Here, we have provided GATE Mathematics Prev. Yr. Cut offs and Ranks shared GATE qualified candidates.

Credit: Thanks to all those students who helped me to collect these data.

If possible, kindly share the following GATE Survey form among your circle to collect the data to help GATE-2022 aspirants.
Google Form Link: https://forms.gle/h1JWvqH5WC5SoLYm8

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Latest Handwritten PDF Notes for CSIR-NET, GATE, SET, JAM, PCS, MSc/PhD Exams in Mathematics

Here we have prepared the subject-wise handwritten study materials (PDF Notes) based on the latest syllabus of CSIR-NET, GATE, SET, JAM, PSC, CUCET, BHU, …etc exams. These notes are very very helpful in self-preparation, written in an easy way so that you can easily understand the concepts and be ready for your exams(Read Students Feedback).

  1. Abstract AlgebraCLICK HERE
  2. Calculus: Download PDF
  3. Calculus of Variation: Download PDF
  4. Complex Analysis:  CLICK HERE
  5. Functional Analysis: Download PDF
  6. Integral Equation with Solutions: Download PDF
  7. Linear Algebra(VVICLICK HERE
  8. Linear Programming with Sol. (Sample PDF): Buy Now
  9. Markov Chain with Solution: Click Here
  10. Measure Theory: Download Here
  11. Metric Space: Download Here
  12. Number Theory with Sol.: Download PDF
  13. Numerical Analysis with Sol.: Download PDF
  14. Probability & Prob. Distribution: Download Here
  15. Ordinary Differential Equations: Download PDF
  16. Partial Differential Equation: Download PDF
  17. Real Analysis(VVI)CLICK HERE
  18. Sum of Series, Power Series & ROC: Download Here
  19. Topology: Download PDF

For INSTANT Downloading any PDF Visit Here.

Important Link: Fast Revision Notes for CSIR-NET, GATE CSIR NET Mathematics Solution

Not only read theory & solve problems but also make a strategy for exam a/c to your preparation. Keep in mind that, it is not necessary to solve all problems in exams, your guessing power should also be strong which comes by solving a lot of problems.

CSIR-NET Exam Tips/Trick for scoring marks easily: Visit 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) are available here. Very very helpful in the preparation of CSIR-NET, SET, GATE, PSC, …. and other equivalent exams. Self-preparation materials(No need for any coaching).

Note: CSIR NET(JRF) June-2020 exam was held in Nov-2020 and June-2021 will be held in Feb 2022.

  1. General Aptitude Solution (CSIR-NET 26 Nov 2020 & GATE 2021-2016): Download PDF
  2. Sol. of Abstract algebra(Upto Nov-2020, Pages:107): Download PDF
  3. Sol. of Complex Analysis(Upto June-2020, Pages:118): Download PDF
  4. Sol. of Linear algebra(Upto Nov-2020, Pages:205): 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. Sol. of Real Analysis(Upto Nov-2020, Pages:210): Download PDF
  8. Combined Solutions (All above Sr. No. 2 – 7): 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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Quick Revision Notes for CSIR-NET, GATE, SET, JAM, Lecturer & Asst. Prof. Exams

Followings Quick Revision notes are VERY VERY helpful in Quick revision of concepts and refreshing your knowledge before starting practicing problems for NET/GATE/PSC and also before an exam. These notes are also useful in concepts revision before an interview of Ph.D./Asst. Prof./Lecturer Exams.

These notes are specially prepared for CSIR-NET, GATE, SET, JAM, Lecturer & Asst. Prof. Exams.

  1. Complex Analysis: Download PDF
  2. Group Theory: Download PDF
  3. Ring Theory: Download PDF
  4. ODE Quick Revision: Download PDF
  5. PDE Quick Revision: Download PDF
  6. Probability & Distribution: Download PDF
  7. Real Analysis: Download PDF
  8. Linear Algebra(Sample): Download PDF
  9. COV + Integral Equation: Download PDF
  10. PhD Interviews Questions Collection: Available Soon

Quick Revision Package

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

Handwritten Solution of GATE Mathematics for self-preparation. We provide the best quality notes for self preparation of GATE Mathematics for those who can not afford coaching. The best way to prepare for GATE 2022 is to do the practice of problems from Previous Yr. Questions of GATE Mathematics. Start your preparation for 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: Check Here

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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.


    SYLLABUS FOR COMPETITIVE EXAMINATION FOR THE POST OF ASSISTANT PROFESSOR IN MATHEMATICS FOR COLLEGE EDUCATION DEPARTMENT

    Click on the subject to download the notes.

    Topics According to New Syllabus

    PAPER – IPAPER – II
    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

    Note:
    # 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


    Note:
    # 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-2021 Mathematics(MA) Modified Syllabus (New)

    Note: The syllabus of GATE-2021 has 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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