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A Site for Higher Mathematics


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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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JAM Mathematics Study Materials and Syllabus

JAM Mathematics(MA/MS) Study materials

  1. Calculus(Updated): Download Here
  2. Differential Equations: PDE and ODE
  3. Group Theory(Sample): Download Here
  4. Linear Algebra(Sample): Download Here
  5. Real Analysis(Sample): Download Here
  6. Statistics(For JAM Statistics): Download PDF
  7. Matrices(For JAM Statistics): Download Here
  8. Linear Algebra & Group Theory Solution: Download Here
  9. ALL AVAILABLE NOTES OF JAM: contact: help@pkalika.in

JAM 2020 Maths Solution: Click Here


Syllabus Mathematics (MA)

Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, maxima and minima.

Functions of Two or Three Real Variables: Limit, continuity, partial derivatives, Differentiability, maxima and minima.

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Free Test Series for CSIR-NET, SET, GATE, PSC

We have started providing topic-wise FREE test series for CSIR-NET, GATE, SET Aspirants. After the topic-wise test, we will start full tests. Test your knowledge here.

Note/Instruction:

  1. The result will be released on 08:00 PM on respective days of tests. The result will be sent on your email id which you will enter in a test.
  2. Related information will be shared on Telegram Channel: https://t.me/pkalika_mathematics
  3. We welcome those who are interested in questions setting for a test, write to us on maths.whisperer@gmail.com.
  4. Next Test: ODE+PDE+COV+IE Test-1 on 30/05/2020
  5. Next Test: Abstract Algebra on 01/06/2020

CSIR-NET, SET & PhD Entrance Test(07/06/2020): Attend Test

Algebra(Abstract+Linear) Tests:-

Analysis(Real+Complex) Tests

  • Complex Test-1(28/05/20): Attend Test-1
  • Complex Test-2: – – – – – – – – – – –


Applied Part(ODE+PDE+LPP+NA) Tests

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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. (New) Classical Mechanics: Download PDF
    • by  Rakhee Kumari, (MSc, CUJ)
  2. Linear Algebra: Download PDF
    • by  M. Sarojini, (MSc, GATE)
  3. Metric Space: Download PDF
    • by  M. Sarojini, (MSc, GATE)
  4. Number Theory: Download PDF
    • by  M. Sarojini, (MSc, GATE)
  5. Probability & Statistics: Download PDF
    • by  M. Sarojini, (MSc, GATE)
  6. (New) Partial Differential Equations (PDE): Download PDF
    • by  M. Sarojini, (MSc, GATE)
  7. 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
  8. Ring Theory(Rahul Anand, MSc, NIT Jalandhar)Download PDF
  9. 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

Previous Year Question Papers of CSIR-NET (Mathematical Science) year-wise up to 2022 (Latest). FREE PDF Download.

  1. Feb-2022 (Que.+Ans Key): Download PDF
  2. Nov-2020 (Que.+Ans, 26 Nov): Download PDF
  3. Dec-2019 (Que. Paper+Key): Download PDF
  4. Dec-2019(Assam)(Que. Paper+Key): Download PDF 
  5. June-2019 (Que. Paper+Key): Download PDF
  6. Dec-2018 (Que. Paper+Key): Download PDF
  7. June-2018 (Que. Paper+Key): Download PDF
  8.  Dec-2017 (Que. Paper+Key): Download PDF
  9. June-2017 (Que. Paper+Key): Download PDF
  10. Dec-2016 (Que. Paper+Key): Download PDF
  11. June-2016 (Que. Paper+Key): Download PDF
  12. Dec-2015 (Que. Paper+Key): Download PDF
  13. June-2015 (Que. Paper+Key): Download PDF
  14. Dec-2014 (Que. Paper): Download PDF
  15. June-2014 (Que. Paper+Key): Uploading Soon
  16. Dec-2013 (Que. Paper): Download PDF
  17. June-2013 (Que. Paper+Key): Download PDF
  18. Dec-2012(Que. Paper+Key): Download PDF
  19. June-2012 (Que. Paper+Key): Download PDF
  20. CSIR-NET June-2011: Download PDF
  21. CSIR-NET Dec-2011: Download PDF
  22. CSIR-NET 2008:  Download Paper-1 and Download Paper-2

CSIR NET Mathematical Science Syllabus: Download Syllabus

CSIR-NET Solutions (Upto Latest Exam): Click Here

GATE Maths Solution (Upto Latest Exam): 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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