# P Kalika

## 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 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 (Read Students Feedback).

8. Linear Programming with Sol. (Sample PDF): Buy Now
13. Numerical Analysis with Sol.

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

## 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

## GATE 2022 || Important Dates, Syllabus, Eligibility, PYQs and Additional Information

Organising Institute for GATE 2022 is Indian Institute of Technology Kharagpur.

## 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.

## 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

9. JNU PhD Mathematics Que. Papers(2018-2015):
15. Any others: On Demand

Questions Paper of  MSc Entrance exams

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

Related Posts:

## I. CSIR-NET, GATE, JAM, SET Study Materials

## III. CSIR-NET Sol. (Year-wise & Topic Wise)

Note: For  ALL-IN-ONE Package/Multiple Notes, Study Material write us on maths.whisperer@gmail.com.

Feedbacks on Our Notes: https://pkalika.in/feedback-on-notes/

## Abstract/Modern Algebra

2. Abstract-2 (Ring Theory): (Buy Now

All Notes of Abstract Algebra (Available Now)

## Linear Algebra

1. Linear(Only Matrix Theory):

## 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.

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

7. Linear Algebra: Available Soon
8. COV + Integral Equation: Available Soon
9. PhD Interviews Questions Collection: Available Soon

Quick Revision Check List

Related Posts:

## GATE Mathematics(MA) Handwritten Study Materials & Solutions

These notes are prepared for self preparing students. Written in an easy way with explanations and tricks.

### GATE Mathematics(MA) Study Materials(View Syllabus)

12. GATE Solution: GATE Problems & Solutions

Detailed syllabus for GATE & JAM:
◆◆ GATE Math, ◆◆GATE Statistics, ◆◆ JAM Math, ◆◆JAM Statistics

## Real Analysis

Real Analysis handwritten study material for CSIR-NET, GATE, SET, JAM, NBHM, TIFR, PSC, PhD Interview, …etc

## GATE-2020 Mathematics(MA) Detailed Syllabus

Calculus: Finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property; Sequences and series, convergence; Limits, continuity, uniform continuity, differentiability, mean value theorems; Riemann integration, Improper integrals; Functions of two or three 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; 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, Sylow’s theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings and irreducibility criteria; Fields, finite fields, field extensions.

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

Complex Analysis: 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 theorem and Laurent’s theorem; residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; conformal mappings, bilinear transformations.

## Complex Analysis Handwritten Study Material

Complex Analysis handwritten study material for CSIR-NET, GATE, SET, NBHM, TIFR, PSC, Lecturer & Asst. Prof. Exams and Interview, …etc.

Weightage of Complex in CSIR-NET : (28 – 34.50Marks).

### Complex Analysis

Some Suggested Book Reading for Complex Analysis:-

1. Functions of Complex Variable by J.K. GOYAL, K.P. GUPTA
2. A First Course Complex Analysis with Applications by D.G. Zill & P.D. Shanahan
3. A First Course in Complex Analysis by M. Beck, G. Marchesi, D. Pixton & L. Sabalka
4. Complex Analysis by Joseph Bak and Donald Newman
5. Complex Variables and Applications, by James Ward Brown, Ruel Churchill

All handwritten notes for NET/GATE: Check here