Top Coaching for CSIR NET Mathematics (1)

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CSIR NET
MATHEMATICS

• OFFLINE CLASSES
• ONLINE LIVE INTERACTIVE CLASSES
• RECORDED VIDEO LECTURE
• COURSES
• TEST SERIES
• STUDY MATERIAL
• 98723 11001
• mathsmim_at_gmail.com
• www.onlinemim.comSCO 223, 2nd Floor, Sector 37C,
  Chandigarh 160036

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98723 11001
ABOUT MIM MIM Academy is the oldest institute of
Mathematics in the Northern India with high
Competitive Environment and most Qualified
Faculty including two Ph.Ds. Our hard work,
efforts, quality of teaching is our IDENTITY. MIM
has earned a name and fame for itself by
imparting quality education to its students.
Result of our students always speak of our
dedication and commitment towards excellence.
MIM aims at all round development of Personality
of Students. We not only impart Educational
values but also moral and ethical values. We
believe in WISDOM CANT BE INHERITED BUT MUST
BE ACQUIRED. MIM aims to achieve
satisfaction in pioneering new efforts to spread
best Education in the imperative field of
Mathematics and not in profit making. MIM aims to
develop the best Mathematical skills among the
Students. MESSAGE FOR STUDENTS Dear
Students, Earning an academic degree is not the
end of a journey but education is a lifelong
process that requires a lot of hard work and
perseverance on your part. Once you decide that
you want to learn Mathematics and once you have
created faith in yourself that you can learn it,
you have won half of the battle. For the
remaining half of the battle, MIM plays its
role. The study material offered by the highly
qualified MIM faculty is the best of its type not
only in terms of CSIR UGC- NET pattern but also
for various other exams like GATE, DRDO, NBHM
Research award, various TGT/PGT and State
Assitant Professor Public Service Commission
Exams etc. From Director MIM Academy
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CSIR NET MATHEMATICAL SCIENCES EXAM
PATTERNTIME 3 HOURS MAXIMUM MARKS
200CSIR-UGC (NET) Exam for Award of Junior
Research Fellowship and Eligibility for
Lecturership shall be a Single Paper Test having
Multiple Choice Questions (MCQs). The question
paper shall be divided in three parts. Part
'A This part shall carry 20 questions
pertaining to General Science, Quantitative
Reasoning Analysis and Research Aptitude. The
candidates shall be required to answer any 15
questions. Each question shall be of two marks.
The total marks allocated to this section shall
be 30 out of 200. Part 'B This part shall
contain 40 Multiple Choice Questions (MCQs)
generally covering the topics given in the
syllabus. A candidate shall be required to answer
any 25 questions. Each question shall be of three
marks. The total marks allocated to this section
shall be 75 out of 200. Part 'C This part shall
contain 60 questions that are designed to test a
candidate's knowledge of scientific concepts
and/or application of the scientific concepts.
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The questions shall be of analytical nature where
a candidate is expected to apply the scientific
knowledge to arrive at the solution to the given
scientific problem. The questions in this part
shall have multiple correct options. Credit in a
question shall be given only on identification of
ALL the correct options. No credit shall be
allowed in a question if any incorrect option is
marked as correct answer. No partial credit is
allowed. A candidate shall be required to answer
any 20 questions. Each question shall be of 4.75
marks. The total marks allocated to this section
shall be 95 out of 200. NOTE For Part A and
B there will be Negative marking _at_25 for each
wrong answer. No Negative marking for Part C.
NUMBER OF QUESTIONS TO BE ATTEMPTED IN EACH
SECTION
Mathematical Sciences Part A Part B Part C Total
Total Questions 20 40 60 120
Max No of Questions to attempt 15 25 20 60
Marks for each correct answer 2 3 4.75 200
Negative marking 0.5 0.75 0 -
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CSIR NET MATHEMATICAL SCIENCES SYLLABUS (For
Junior Research Fellowship and Lecturer-ship) MAT
HEMATICAL SCIENCES 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.
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98723 11001
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 Complex Analysis Algebra of complex numbers,
the complex plane, polynomials, power series,
transcendental functions such as exponential,
trigonometric and hyperbolic functions. Analytic
functions, Cauchy-Riemann equations. Contour
integral, Cauchys theorem, Cauchys integral
formula, Liouvilles theorem, Maximum modulus
principle, Schwarz lemma, Open mapping
theorem. Taylor series, Laurent series, calculus
of residues. Conformal mappings, Mobius
transformations. Algebra Permutations,
combinations, pigeon-hole principle,
inclusion-exclusion principle, derangements. Funda
mental theorem of arithmetic, divisibility in Z,
congruences, Chinese Remainder Theorem, Eulers
Ø- function, primitive roots. Groups, subgroups,
normal subgroups, quotient groups, homomorphisms,
cyclic groups, permutation groups, Cayleys
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.
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Fields, finite fields, field extensions, Galois
Theory.Topology basis, dense sets, subspace
and product topology, separation axioms,
connectedness and compactness. UNIT
3 Ordinary Differential Equations
(ODEs) Existence and uniqueness of solutions of
initial value problems for first order ordinary
differential equations, singular solutions of
first order ODEs, system of first order
ODEs. General theory of homogenous and
non-homogeneous linear ODEs, variation of
parameters, Sturm-Liouville boundary value
problem, Greens function.Partial Differential
Equations (PDEs) Lagrange and Charpit methods
for solving first order PDEs, Cauchy problem for
first order PDEs. Classification of second order
PDEs, General solution of higher order PDEs with
constant coefficients, Method of separation of
variables for Laplace, Heat and Wave
equations. Numerical Analysis Numerical
solutions of algebraic equations, Method of
iteration and Newton-Raphson method, Rate of
convergence, Solution of systems of linear
algebraic equations using Gauss elimination and
Gauss-Seidel methods, Finite differences,
Lagrange, Hermite and spline interpolation,
Numerical differentiation and integration,
Numerical solutions of ODEs using Picard, Euler,
modified Euler and Runge-Kutta methods.
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Calculus of Variations Variation of a
functional, Euler-Lagrange equation, Necessary
and sufficient conditions for extrema.
Variational methods for boundary value problems
in ordinary and partial differential
equations.Linear Integral Equations Linear
integral equation of the first and second kind of
Fredholm and Volterra type, Solutions with
separable kernels. Characteristic numbers and
eigenfunctions, resolvent kernel. Classical
Mechanics Generalized coordinates, Lagranges
equations, Hamiltons canonical equations,
Hamiltons principle and principle of least
action, Two-dimensional motion of rigid bodies,
Eulers dynamical equations for the motion of a
rigid body about an axis, theory of small
oscillations. UNIT 4 Descriptive statistics,
exploratory data analysis Sample space, discrete
probability, independent events, Bayes theorem.
Random variables and distribution functions
(univariate and multivariate) expectation and
moments. Independent random variables, marginal
and conditional distributions. Characteristic
functions. Probability inequalities (Tchebyshef,
Markov, Jensen). Modes of convergence, weak and
strong laws of large numbers, Central Limit
theorems (i.i.d. case).Markov chains with
finite and countable state space, classification
of states, limiting behaviour of n-step
transition probabilities,
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stationary distribution, Poisson and
birth-and-death processes. Standard discrete and
continuous univariate distributions. sampling
distributions, standard errors and asymptotic
distributions, distribution of order statistics
and range. Methods of estimation, properties of
estimators, confidence intervals. Tests of
hypotheses most powerful and uniformly most
powerful tests, likelihood ratio tests. Analysis
of discrete data and chi-square test of goodness
of fit. Large sample tests. Simple nonparametric
tests for one and two sample problems, rank
correlation and test for independence. Elementary
Bayesian inference. Gauss-Markov models,
estimability of parameters, best linear unbiased
estimators, confidence intervals, tests for
linear hypotheses. Analysis of variance and
covariance. Fixed, random and mixed effects
models. Simple and multiple linear regression.
Elementary regression diagnostics. Logistic
regression. Multivariate normal distribution,
Wishart distribution and their properties.
Distribution of quadratic forms. Inference for
parameters, partial and multiple correlation
coefficients and related tests. Data reduction
techniques Principle component analysis,
Discriminant analysis, Cluster analysis,
Canonical correlation. Simple random sampling,
stratified sampling and systematic sampling.
Probability proportional to size sampling. Ratio
and regression methods. Completely randomized
designs, randomized block designs and
Latin-square designs. Connectedness and
orthogonality of block designs, BIBD. 2K
factorial experiments confounding and
construction.
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Hazard function and failure rates, censoring and
life testing, series and parallel
systems. Linear programming problem, simplex
methods, duality. Elementary queuing and
inventory models. Steady-state solutions of
Markovian queuing models M/M/1, M/M/1 with
limited waiting space, M/M/C, M/M/C with limited
waiting space, M/G/1.All students are
expected to answer questions from Unit I.
Students in mathematics are expected to answer
additional question from Unit II and III.
Students with in statistics are expected to
answer additional question from Unit IV.
91 98723 11001
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COURSES /BATCHES AT MIM ACADEMY
MIM Academy offer different modes of coaching
according to convenience of students
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98723 11001
OFFLINE or ONLINE LIVE CLASSROOM COURSES
At MIM Academy, we believe in providing students
with the flexibility to choose their preferred
mode of learning. Whether you're looking to
attend classes in person or participate from the
comfort of your own space, we've got you covered
with our dynamic learning solutions. Classroom
Experience Our state-of-the-art classrooms offer
an immersive and engaging learning environment.
Join your peers in the physical classroom and
interact directly with our expert instructors.
Engage in real-time discussions, ask questions,
and get instant answers to clarify your
doubts. Live Interactive Classes via ZOOM For
those who prefer the convenience of remote
learning, we offer live interactive classes
through ZOOM Meetings. Attend classes from
anywhere, eliminating the constraints of
geographical boundaries. These live sessions are
just as engaging as in-person classes, ensuring
you receive the same quality education. Interact
with instructors, collaborate with fellow
students, and have your questions addressed
promptly. Doubt Resolution in Real Time At MIM
Academy, we understand that doubts can be a
roadblock to effective learning. That's why we
provide a platform for students to discuss their
queries with our dedicated teachers during class.
No more waiting for office hours or struggling to
find solutions on your own. We believe in
providing immediate support to enhance your
understanding. Comprehensive Study Material To
complement your learning experience, we provide
study materials tailored to your course. Live
students benefit from having these materials
posted directly to them, ensuring you have all
the resources needed to succeed. At MIM Academy,
we are committed to empowering our students with
the best education, regardless of their location
or learning preferences. Join us and embark on a
journey of knowledge, interaction, and academic
excellence.
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98723 11001
Best CSIR NET, UGC NET, IIT JAM, GATE, JEE Main
and Advanced Maths Coaching
MIM Academy is your trusted partner on the
journey to qualifying for CSIR NET/ UGC NET/ IIT
JAM/ JEE/ GATE Mathematics. We understand that
effective guidance is the key to conquering
competitive exams, and we are dedicated to making
this journey a breeze for our students. Our
Track Record of Success Year after year,
MIMcians achieve remarkable success in CSIR NET
and GATE examinations. This is a testament to our
unwavering commitment to excellence in delivering
quality education. Our consistent results reflect
our dedication to perfection. Distinctive
Features of MIM Academy Coaching Excellent
Teaching Methodology Our approach to teaching is
exceptional, ensuring that complex concepts are
made understandable and applicable. State-of-the-
Art Classrooms Our classrooms are meticulously
organized and equipped with all the necessary
facilities for an optimal learning
environment. Highly Qualified Faculty Learn
from accomplished instructors with extensive
expertise in the subject matter. Comprehensive
Study Material Our study materials include
synopsis, notes, and assignments tailored to the
examination pattern, facilitating a deep
understanding of concepts and their real-world
applications.
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Motivating Competitive Environment Surround
yourself with like-minded peers who encourage and
challenge you to excel. Strategic and
Well-Designed Program Our curriculum is
strategically crafted to cover all essential
topics and ensure thorough preparation. Varied
Testing Practice with topic-wise tests, full
tests, and mock tests to gauge your progress and
fine-tune your exam skills. Time Management Our
academic planning ensures course completion well
in advance, allowing ample time for
self-revision, enhancing your exam readiness, and
addressing last-minute doubts. Personalized
Attention We maintain limited batch sizes to
ensure each student receives individualized
attention and guidance from our teachers. Join
MIM Academy, where we are committed to unlocking
your potential and helping you reach your
academic aspirations. Choose us CSIR NET, UGC
NET, IIT JAM, GATE, JEE Main and Advanced Maths
Math coaching, and let's embark on this journey
to success together.
Website https//onlinemim.com/ Phone 98723
11001 Email mathsmim_at_gmail.com Address
SCO 223, 2nd Floor, Sector 37C,
Chandigarh, 160036