ICFAI Tech School (ITS) offers the following Campus based fulltime Programs.
The world of technology is rapidly evolving. In the last 20 years, scientific and
technological advancements have fundamentally altered the living and lifestyle.
Everything from electronics to information sciences to nanotechnology have
caused drastic changes in the technological and engineering environment around
the globe.
The world needs leaders who understand science and technology to keep up the
pace of innovation. ICFAI Group is focused on creating the leaders of tomorrow
in the field of science and technology.
Pass with 60% and above aggregate
marks in Class X and Class XII or its
equivalent with Mathematics / Physics
/ Chemistry (M.P.C.) and English as
subjects.
Class XII (or its equivalent) students
awaiting examination results may also
apply.
YEAR  FIRST SEMESTER  SECOND SEMESTER 
I 


YEAR  THIRD SEMESTER  FOURTH SEMESTER 
II 


YEAR  FIFTH SEMESTER  SIXTH SEMESTER 
Summer Term  Internship Program I  
III 


Summer Term  Internship Program I  
YEAR  SEVENTH SEMESTER  EIGHTH SEMESTER 
IV 


Based on percentage in 10+2 exam / Ranks secured in JEE (Main) 2017 / State Level Engineering Entrance Tests 2017. Additionally, merit scholarships are also offered in each semester based on semesterwise performance.
Admission is through an All India Admission Test (ITSAT 2017). Alternatively, scores of JEE (Main) 2017 / State Level / Other National Level Engineering Entrance Tests 2017 are also accepted.
On successful completion of the course of studies, students will be awarded a B.Tech. from ICFAI Foundation for Higher Education, Hyderabad.
Advances in VLSI have today enabled most systems to become
compact, highly reliable and deliver data at high speed. The
requirement of improved solutions for miniaturization,
high speed, reliability, and high performance computers,
necessitates skilled engineers. There is an urgent need to
produce quality engineers who can conceive, design and
develop VLSI systems.
The Program aims at preparing students to develop knowledge
and skills in VLSI design methodology with systems perspective
in order to facilitate the use of computeraided design tools
for the analysis and design of specialpurpose digital and
analog circuits and systems. The Program will help students
understand the requirements of EDA development, library
design, analog and mixed signal design, semiconductor chip
design, design and verification of ICs, FPGA development and
SOC design. Analysis, design and implementation of integrated
circuits using standard tools .
The VLSI program will focus on the development of handson
skills in designing semiconductor devices and circuits,
architecting systems using embedded components such as
CPU, memory and peripherals. Students will learn several
topics starting from the lowest level of physical devices to the
top level of application development involving FPGA and ASICS.
To develop world class professionals equipped with all
aspects of VLSI and Embedded design methodologies.
To expose students to the complexities and design
methodologies of current and advanced IC designs.
To develop engineers trained in both hardware and design
tools VLSI.
To disseminate VLSI design including both the low level
circuit and high level algorithmic details
Minimum 60% or equivalent in the qualifying examination of
Bachelor’s degree in Electronics & Communication / Electronics
& Instrumentation Engineering/Instrumentation Technology/
Telecommunication Engineering / Electrical & Electronics /
AMIE in appropriate branch mentioned above.
The program curriculum is aimed at VLSI system design
(both Front end & Back end designs) covering algorithms,
Hardware description Languages, System Architectures,
Physical designs, Verification techniques, Simulation &
Synthesis, Low power design techniques and mixed mode
design methodologies.
Students will have access to well equipped VLSI Lab setup
with industrial collaboration.
Institute is having the collaboration with Industry giants
Mentor Graphics, Xilinx.
All students are assigned a designated supervisor, an
academic member of staff who will provide formal
supervision and support on a daily basis.
Year 
Semester I 
Semester II 
I 

System Hardware Design  CMOS Analog VLSI Design  
CMOS Analog Circuits  VLSI Technology  
Digital VLSI Design  Low Power Design  
CAD for VLSI  Elective I  
Physics of Transistors 
Elective II  
Language Lab  
Year  Semester IV  Semester IV 
II  Elective III  Project and Viva Voice 
Elective IV  
Elective V  
Elective VI  
Pre Project Study & Seminar 
Digital Signal Processing; Electronic Systems Design; Sensors Interfacing; Microelectronics Chip Design; System Design; Introduction to MEMS; Testing and Verification of VLSI Circuits; Embedded Systems Design; Mixed Signal VLSI Design; Nanoelectronics; Microelectronics Simulation Laboratory; Processor Design; Advanced Computer Organization.
The Admission Modalities are with reference to the campusbased PG Programs offered by IcfaiTech (ICFAI Tech School) of The ICFAI Foundation for Higher Education (IFHE), Hyderabad. The medium of instruction is English.
Admission into the M.Tech (Manufacturing Systems
Engineering), M.Tech (VLSI) and M.Sc (Data Analytics)
programs is common to all 3 PG Programs:
GATE Qualified candidates / IcfaiTech Master’s
Entrance Exam (IMEE 2016).
Candidates who have Qualified in GATE (2014 onwards)
need not write the IcfaiTech Master’s Entrance Exam
2016. They can directly appear for Interview.
IcfaiTech Master’s Entrance Examination (IMEE 2016) is an aptitude test conducted by IcfaiTech of IFHE for students seeking admission into the PG Programs of IcfaiTech. The test is of One hour duration. The question paper consists of 50 multiple choice questions with duration of 60 minutes.
Candidates based on the performance in GATE (from 2014 onwards) / IMEE 2016 will be called for Personal Interview at IcfaiTech, IFHE, Hyderabad on August 26, 2016.
The completed Application Form should be sent /
submitted at:
Coordinator, Post Graduate Programs (PGP),
ICFAI Tech School,
The ICFAI Foundation for Higher Education (IFHE),
Donthanpally, Shankarpally Rd, Hyderabad 501203,
Telangana State, India, Ph: 04023479801
Email ID: pgprograms.fst@ifheindia.org
www.ifheindia.org
ADMISSION CALENDAR 

Last Date for Submission of completed Application Form  August 01, 2016 
IcfaiTech Master’s Entrance Examination (IMEE 2016)*  August 10, 2016 
IMEE 2016 Results  August 16, 2016 
Dispatch of Interview Letters  August 20, 2016 
Personal Interview  August 26, 2016 
Issue of Admission Letters  August 26, 2016 onwards 
Payment of First Semester Fee  on or before September 19, 2016 
Reporting & Registration for First Semester  September 19, 2016 
Commencement of Classes  Septemebr 19, 2016 
* GATE Scores (from 2014 onwards) are accepted in place of IMEE 2016, and they can directly appear for Interview
Selected candidates are required to pay an Admission Fee of Rs 20,000 on or before September 19, 2016.
The Program fee of Rs 2.50 lakhs is to be paid in four equal installments of Rs 62,500, payable at the begining of each semester.
A refundable Caution Deposit of Rs 10,000 is to be paid
along with the 1st installment of the program fee. The
Caution Deposit will be refunded without interest
(after adjusting for dues, if any) on completion of the
program.
Students are expected to have their own laptops at
the time of reporting to IcfaiTech.
All payments should be made by way of Demand
Draft, drawn in favour of:
“IFHEFee Collection A/c M.Tech (2016)”,
payable at Hyderabad, for M.Tech (MSE) & M.Tech
(VLSI).
September 19, 2016.
On successful completion of specified courses and projects, the candidates will be awarded the M.Tech / M.Sc Degree in respective disciplines by IFHE, a DeemedtobeUniversity.
IcfaiTech (ICFAI Tech School), IFHE Hyderabad offers a two year PG program, M.Tech. in Manufacturing Systems Engineering. The program provides advanced building blocks for conceptualizing, understanding manufacturing systems integrated with computer based applications. These include core courses: Unified Approach to Manufacturing systems Engineering, Manufacturing processes, Engineering Economy, Computer based simulation methods & applications, Optimization Methods & their applications, Quality & Reliability Engineering, Facilities Planning & Material Handling. Besides these there are a number of relevant electives to choose from. Further, the curriculum includes project work, which helps students understand the concepts and methods and apply to real life situations. The program enables the students to be technically competent to takeup challenging jobs in industries, government and R & D organizations. The program provides a sound platform for undertaking higher studies such as doctoral research in any top ranked university across the globe.
Students will develop an understanding of the concepts of
manufacturing systems engineering, product and process
development with an awareness of strategic management
and operations.
The program helps students acquire manufacturing
techniques and processes and its applications in
manufacturing organizations.
Students completing the program may find job opportunities
as design engineers, manufacturing engineers, production
engineers, engineering managers, systems engineers, or
research and development engineers in companies such
as automotive, appliances manufacturing and discrete
manufacturing intending to adopt advanced manufacturing
technologies.
Minimum 60% or equivalent in the qualifying examination
of Bachelor’s degree in Mechanical Engineering
/Automobile Engineering/Production Engineering/ Industrial
Engineering/ Manufacturing Engineering/ Mechatronics.
The two year program is organized into four semesters. Every student is required to take a minimum of 6 elective courses in the second and third semester. The elective courses are chosen in consultation with the thesis supervisor to match the student’s interest as well as his project requirements. The fourth semester is dedicated for the project work.
Year 
Semester I 
Semester II 
I 

Unified Approach to Manufacturing Systems Engineering  Computer Based Simulation Methods & Applications  
Manufacturing Processes  Quality Engineering & Management  
Engineering Economy  Facilities Planning & Material Handling  
Applied Statistics and Probability  Elective I  
Optimization Methods & Their Applications  Elective II  
Year  Semester IV  Semester IV 
II  Elective III  Project and Viva Voice 
Elective IV  
Elective V  
Elective VI  
Pre Project Study & Seminar  
(Literature Survey and Project definition) 
Advances in Industrial Systems Engineering, Flexible Manufacturing Systems, Industrial Robotics, Automation in Manufacturing, Manufacturing Strategy, Supply Chain Management, Project Management, Advances in Production and Inventory Control, Intelligent Manufacturing Systems, Advances in Manufacturing Technology, Sustainable Manufacturing Systems, Product Design & Development, Technology Management, Venture Management, Micro Electronic Mechanical Systems, Advances in Optimization Techniques, Advance Topics in Manufacturing System Engineering, Reliability Engineering & Management
The Admission Modalities are with reference to the campusbased PG Programs offered by IcfaiTech (ICFAI Tech School) of The ICFAI Foundation for Higher Education (IFHE), Hyderabad. The medium of instruction is English.
Admission into the M.Tech (Manufacturing Systems
Engineering), M.Tech (VLSI) and M.Sc (Data Analytics)
programs is common to all 3 PG Programs:
GATE Qualified candidates / IcfaiTech Master’s
Entrance Exam (IMEE 2016).
Candidates who have Qualified in GATE (2014 onwards)
need not write the IcfaiTech Master’s Entrance Exam
2016. They can directly appear for Interview.
IcfaiTech Master’s Entrance Examination (IMEE 2016) is an aptitude test conducted by IcfaiTech of IFHE for students seeking admission into the PG Programs of IcfaiTech. The test is of One hour duration. The question paper consists of 50 multiple choice questions with duration of 60 minutes.
Candidates based on the performance in GATE (from 2014 onwards) / IMEE 2016 will be called for Personal Interview at IcfaiTech, IFHE, Hyderabad on August 26, 2016.
The completed Application Form should be sent /
submitted at:
Coordinator, Post Graduate Programs (PGP),
ICFAI Tech School,
The ICFAI Foundation for Higher Education (IFHE),
Donthanpally, Shankarpally Rd, Hyderabad 501203,
Telangana State, India, Ph: 04023479801
Email ID: pgprograms.fst@ifheindia.org
www.ifheindia.org
ADMISSION CALENDAR 

Last Date for Submission of completed Application Form  August 01, 2016 
IcfaiTech Master’s Entrance Examination (IMEE 2016)*  August 10, 2016 
IMEE 2016 Results  August 16, 2016 
Dispatch of Interview Letters  August 20, 2016 
Personal Interview  August 26, 2016 
Issue of Admission Letters  August 26, 2016 onwards 
Payment of First Semester Fee  on or before September 19, 2016 
Reporting & Registration for First Semester  September 19, 2016 
Commencement of Classes  Septemebr 19, 2016 
* GATE Scores (from 2014 onwards) are accepted in place of IMEE 2016, and they can directly appear for Interview
Selected candidates are required to pay an Admission Fee of Rs 20,000 on or before September 19, 2016.
The Program fee of Rs 2.50 lakhs is to be paid in four equal installments of Rs 62,500, payable at the begining of each semester.
A refundable Caution Deposit of Rs 10,000 is to be paid
along with the 1st installment of the program fee. The
Caution Deposit will be refunded without interest
(after adjusting for dues, if any) on completion of the
program.
Students are expected to have their own laptops at
the time of reporting to IcfaiTech.
All payments should be made by way of Demand
Draft, drawn in favour of:
“IFHEFee Collection A/c M.Tech (2016)”,
payable at Hyderabad, for M.Tech (MSE) & M.Tech
(VLSI).
at Hyderabad, for M.Sc (Data Analytics).
September 19, 2016.
On successful completion of specified courses and projects, the candidates will be awarded the M.Tech / M.Sc Degree in respective disciplines by IFHE, a DeemedtobeUniversity.
There is a growing demand across all industry sectors for
graduates who are trained to analyze raw data and extract
insights that can help businesses to plan strategically.
Data Analytics is used for many purposes, such as fraud
detection, credit risk modeling, forecasting, developing pricing
models, monitoring personal health, etc. For the past few
years it has become an area of strategic importance nationally
and internationally. The need for data analytics is due to the
massive accumulation of “Big Data” in all industries to include
but not limited to healthcare, finance, government (central,
state, and local), and cyber defense.
In this context a new specialist program “MSc in Data Analytics”
is conceived, designed and developed by the Faculty of ICFAI Tech School (ITS), IFHE, Hyderabad to meet the demand of
new age Data Analysts.
To develop professionals as data analysts and data
scientists by equipping them with statistical applications
and other computational methods and technology to
handle big data
To incorporate analytical practices to extend the value of
business intelligence and analytics far beyond traditional
practices of handling data and unlocking the value residing
in firms’ vast stores of data.
The Program introduces the complete cycle of data
analysis in business applications.
It deals with the Big Data Analysis which cannot fit
in the computer’s memory and application of such
analysis to various applications
Electives to specialize different data analytic
techniques required for specific industries.
The industrylinked internship will provide an
opportunity to analyze and provide solutions to
today’s realworld data analytic problems.
Following graduates with 60% or above marks:
B.Tech / B.E. Graduates
BSc (Maths)/ BSc (Physics) / BSc (Statistics) / MCA
Other graduates are also eligible provided they
have a strong grounding in following areas:
Mathematics, Statistics, and Computer Programming at
their 10+2 level. Such candidates are required to undergo
a Foundation Course administered by us during the
course of the Program.
The two year program is organized into four semesters. Every student is required to take a minimum of 6 elective courses in the second and third semester. The elective courses are chosen in consultation with the thesis supervisor to match the student’s interest as well as his project requirements. The fourth semester is dedicated for the project work.
Year 
Semester I 
Semester II 
I 

Databases & Information Retrieval  Data Mining  
Statistical Methods for Data Analysis  Predictive Analytics  
Optimization and Heuristics  Text Analytics  
Java Programming  Social Networks Analysis  
Topics in Analytics with R  Topics in Analytics with Python  
Programming Lab Courses/ Project Courses  I  Programming Lab Courses/ Project Courses  II  
Year  Semester IV  Semester IV 
II  Data Visualization  Internship Program in Industries/organizations where already Data Analytics is implemented 
Analytics for Big Data  
Data Warehousing  
Elective I, II, III 
The Admission Modalities are with reference to the campusbased PG Programs offered by IcfaiTech (ICFAI Tech School) of The ICFAI Foundation for Higher Education (IFHE), Hyderabad. The medium of instruction is English.
Admission into the M.Tech (Manufacturing Systems
Engineering), M.Tech (VLSI) and M.Sc (Data Analytics)
programs is common to all 3 PG Programs:
GATE Qualified candidates / IcfaiTech Master’s
Entrance Exam (IMEE 2016).
Candidates who have Qualified in GATE (2014 onwards)
need not write the IcfaiTech Master’s Entrance Exam
2016. They can directly appear for Interview.
IcfaiTech Master’s Entrance Examination (IMEE 2016) is an aptitude test conducted by IcfaiTech of IFHE for students seeking admission into the PG Programs of IcfaiTech. The test is of One hour duration. The question paper consists of 50 multiple choice questions with duration of 60 minutes.
Candidates based on the performance in GATE (from 2014 onwards) / IMEE 2016 will be called for Personal Interview at IcfaiTech, IFHE, Hyderabad on August 26, 2016.
The completed Application Form should be sent /
submitted at:
Coordinator, Post Graduate Programs (PGP),
ICFAI Tech School,
The ICFAI Foundation for Higher Education (IFHE),
Donthanpally, Shankarpally Rd, Hyderabad 501203,
Telangana State, India, Ph: 04023479801
Email ID: pgprograms.fst@ifheindia.org
www.ifheindia.org
ADMISSION CALENDAR 

Last Date for Submission of completed Application Form  August 01, 2016 
IcfaiTech Master’s Entrance Examination (IMEE 2016)*  August 10, 2016 
IMEE 2016 Results  August 16, 2016 
Dispatch of Interview Letters  August 20, 2016 
Personal Interview  August 26, 2016 
Issue of Admission Letters  August 26, 2016 onwards 
Payment of First Semester Fee  on or before September 19, 2016 
Reporting & Registration for First Semester  September 19, 2016 
Commencement of Classes  Septemebr 19, 2016 
* GATE Scores (from 2014 onwards) are accepted in place of IMEE 2016, and they can directly appear for Interview
Selected candidates are required to pay an Admission Fee of Rs 20,000 on or before September 19, 2016.
The Program fee of Rs 2.50 lakhs is to be paid in four equal installments of Rs 62,500, payable at the begining of each semester.
A refundable Caution Deposit of Rs 10,000 is to be paid
along with the 1st installment of the program fee. The
Caution Deposit will be refunded without interest
(after adjusting for dues, if any) on completion of the
program.
Students are expected to have their own laptops at
the time of reporting to IcfaiTech.
All payments should be made by way of Demand
Draft, drawn in favour of:
“IFHEFee Collection A/c M.Sc (2016)”, payable
at Hyderabad, for M.Sc (Data Analytics).
September 19, 2016.
On successful completion of specified courses and projects, the candidates will be awarded the M.Tech / M.Sc Degree in respective disciplines by IFHE, a DeemedtobeUniversity.
Ph.D. Program in Basic Sciences (Fulltime and Parttime) 
Apply Online 
Download Appl. Kit 
The ICFAI Tech School (ITS), offers Doctoral Programs in Chemistry, Mathematics and Physics. The program provides scholars with opportunities to undertake research in emerging areas of Chemistry, Mathematics and Physics.
Objectives of the Program
Chemistry 
Analytical chemistry, coordination chemistry 
Mathematics 
Number theory, Boolean Algebra, Fluid Dynamics 
Physics 
Mathematical Physics, NonLinear Dynamics, Experimental Computational Condensed Matter Physics 
The selected candidates have to pay an Admission fee of Rs 40,000. The Program fee is Rs 60,000 per Semester. The Program fee is provided as financial assistance and is waived for full time research scholars, subject to meeting minimum academic requirements as specified by ITS.
A refundable Caution Deposit of Rs 10,000 is to be paid along with the admission fee. The Caution Deposit will be refunded without interest (after adjusting for dues, if any) on completion of the program.
Full time Ph.D. scholars who do not receive any other fellowship, will be awarded the University fellowship of Rs 25,000 per month, from the date of admission, up to a period of four years that include one year of course work plus three years of thesis work. Continuation of scholarship is subject to satisfactory research progress shown by the scholar. A professional development grant of Rs 20,000 per annum is also given to fulltime research students for the four years.
Parttime students are not eligible for Institute scholarship.
In the event, the student withdraws from the program, the student is liable to refund the fellowship and the program fee provided as financial assistance by ITS. To this end, the student is required to execute a financial assistance agreement along with a guarantor for the financial assistance provided by ITS and submit the same on the day of registration.
The duration of Ph.D. program is a minimum period of four years to a maximum period of eight years from the date of registration. All fulltime students admitted into the Ph.D. program must successfully complete the preparatory course work of two semesters duration before registration.
Parttime students must complete Ph.D. course work conducted in two spells in the first year of the program before registration.
Extension beyond the above limits or early submissions (before 4 years) will be governed by the decision of the competent authority and ratification by the Academic Council.
PartA 1. B.Sc. level knowledge of Chemistry, Mathematics, Physics. 2. Awareness on computers covering basic definitions and abbreviations, basic Organization of Computer system, history of Modern Computer, parts of Computer, difference between Hardware and Software, difference between Input and Output Device, MS Office etc. PartB Chemistry I. Physical Chemistry 1. Basic principles and applications of quantum mechanics – hydrogen atom, angular momentum. 2. Variational and perturbational methods. 3. Basics of atomic structure, electronic configuration, shapes of orbitals, hydrogen atom spectra. 4. Theoretical treatment of atomic structures and chemical bonding. 5. Chemical applications of group theory. 6. Basic principles and application of spectroscopy – rotational, vibrational, electronic, Raman, ESR, NMR. 7. Chemical thermodynamics. 8. Phase equilibria. 9. Statistical thermodynamics. 10. Chemical equilibria. 11. Electrochemistry – Nernst equation, electrode kinetics, electrical double layer, DebyeHückel theory. 12. Chemical kinetics – empirical rate laws, Arrhenius equation, theories of reaction rates, determination of reaction mechanisms, experimental techniques for fast reactions. 13. Concepts of catalysis. 14. Polymer chemistry. Molecular weights and their determinations. Kinetics of chain polymerization. 15. Solids  structural classification of binary and ternary compounds, diffraction techniques, bonding, thermal, electrical and magnetic properties 16. Colloids and surface phenomena. 17. Data analysis. II. Inorganic Chemistry 1. Chemical periodicity 2. Structure and bonding in homo and heteronuclear molecules, including shapes of molecules. 3. Concepts of acids and bases. 4. Chemistry of the main group elements and their compounds. Allotropy, synthesis, bonding and structure. 5. Chemistry of transition elements and coordination compounds – bonding theories, spectral and magnetic properties, reaction mechanisms. 6. Inner transition elements – spectral and magnetic properties, analytical applications. 7. Organometallic compounds  synthesis, bonding and structure, and reactivity. Organometallics in homogenous catalysis. 8. Cages and metal clusters. 9. Analytical chemistry separation techniques. Spectroscopic electro and thermoanalytical methods. 10. Bioinorganic chemistry – photosystems, porphyrines, metalloenzymes, oxygen transport, electron transfer reactions, nitrogen fixation. 11. Physical characterisation of inorganic compounds by IR, Raman, NMR, EPR, Mössbauer, UV, NQR, MS, electron spectroscopy and microscopic techniques. 12. Nuclear chemistry – nuclear reactions, fission and fusion, radioanalytical techniques and activation analysis. III. Organic Chemistry 1. IUPAC nomenclature of organic compounds. 2. Principles of stereochemistry, conformational analysis, isomerism and chirality. 3. Reactive intermediates and organic reaction mechanisms. 4. Concepts of aromaticity. 5. Pericyclic reactions. 6. Named reactions. 7. Transformations and rearrangements. 8. Principles and applications of organic photochemistry. Free radical reactions. 9. Reactions involving nucleophotic carbon intermediates. 10 . Oxidation and reduction of functional groups. 11. Common reagents (organic, inorganic and organometallic) in organic synthesis. 12. Chemistry of natural products such as steroids, alkaloids, terpenes, peptides, carbohydrates, nucleic acids and lipids. 13. Selective organic transformations – chemoselectivity, regionselectivity, stereoselectivity, enantioselectivity. Protecting groups. 14. Chemistry of aromatic and aliphatic heterocyclic compounds. 15. Physical characterisation of organic compounds by IR, UV, MS, and NMR. IV. Interdisciplinary topics 1. Chemistry in nanoscience and technology. 2. Catalysis and green chemistry. 3. Medicinal chemistry. 4. Supramolecular chemistry. 5. Environmental chemistry. Mathematics I. 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. 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, CayleyHamilton 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. II. Complex Analysis: Algebra of complex numbers, the complex plane, polynomials, Power series, transcendental functions such as exponential, trigonometric and hyperbolic functions. Analytic functions, CauchyRiemann equations. Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem. Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius transformations. Algebra: Permutations, combinations, pigeonhole principle, inclusionexclusion principle, derangements. Fundamental theorem of arithmetic, divisibility in Z, 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. III. 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 nonhomogeneous linear ODEs, variation of parameters, SturmLiouville boundary value problem, Green’s 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 NewtonRaphson method, Rate of convergence, Solution of systems of linear algebraic equations using Gauss elimination and GaussSeidel methods, Finite differences, Lagrange, Hermite and spline interpolation, Numerical differentiation and integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and RungeKutta methods. Calculus of Variations: Variation of a functional, EulerLagrange 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, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s principle and principle of least action, Twodimensional motion of rigid bodies, Euler’s dynamical equations for the motion of a rigid body about an axis, theory of small oscillations. IV. 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 nstep transition probabilities, stationary distribution. 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 chisquare 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. GaussMarkov models, estimability of parameters, Best linear unbiased estimators, tests for linear hypotheses and confidence intervals. 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, randomized blocks and Latinsquare designs. Connected, complete and orthogonal block designs, BIBD. 2K factorial experiments: confounding and construction. Series and parallel systems, hazard function and failure rates, censoring and life testing. Linear programming problem. Simplex methods, duality. Elementary queuing and inventory models. Steadystate 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. PhysicsI. Mathematical Methods of PhysicsDimensional analysis. Vector algebra and vector calculus. Linear algebra, matrices, CayleyHamilton Theorem. Eigenvalues and eigenvectors. Linear ordinary differential equations of first & second order, Special functions (Hermite, Bessel, Laguerre and Legendre functions). Fourier series, Fourier and Laplace transforms. Elements of complex analysis, analytic functions; Taylor & Laurent series; poles, residues and evaluation of integrals. Elementary probability theory, random variables, binomial, Poisson and normal distributions. Central limit theorem. II. Classical Mechanics Newton’s laws. Dynamical systems, Phase space dynamics, stability analysis. Central force motions. Two body Collisions  scattering in laboratory and Centre of mass frames. Rigid body dynamicsmoment of inertia tensor. Noninertial frames and pseudoforces. Variational principle. Generalized coordinates. Lagrangian and Hamiltonian formalism and equations of motion. Conservation laws and cyclic coordinates. Periodic motion: small oscillations, normal modes. Special theory of relativityLorentz transformations, relativistic kinematics and mass–energy equivalence. III. Electromagnetic Theory Electrostatics Gauss’s law and its applications, Laplace and Poisson equations, boundary value problems. Magnetostatics: BiotSavart law, Ampere's theorem. Electromagnetic induction. Maxwell's equations in free space and linear isotropic media; boundary conditions on the fields at interfaces. Scalar and vector potentials, gauge invariance. Electromagnetic waves in free space. Dielectrics and conductors. Reflection and refraction, polarization, Fresnel’s law, interference, coherence, and diffraction. Dynamics of charged particles in static and uniform electromagnetic fields. IV. Quantum Mechanics Waveparticle duality. Schrödinger equation (timedependent and timeindependent). Eigenvalue problems (particle in a box, harmonic oscillator, etc.). Tunneling through a barrier. Wavefunction in coordinate and momentum representations. Commutators and Heisenberg uncertainty principle. Dirac notation for state vectors. Motion in a central potential: orbital angular momentum, angular momentum algebra, spin, addition of angular momenta; Hydrogen atom. SternGerlach experiment. Timeindependent perturbation theory and applications. Variational method. Time dependent perturbation theory and Fermi's golden rule, selection rules. Identical particles, Pauli exclusion principle, spinstatistics connection. V. Thermodynamic and Statistical Physics Laws of thermodynamics and their consequences. Thermodynamic potentials, Maxwell relations, chemical potential, phase equilibria. Phase space, micro and macrostates. Microcanonical, canonical and grandcanonical ensembles and partition functions. Free energy and its connection with thermodynamic quantities. Classical and quantum statistics. Ideal Bose and Fermi gases. Principle of detailed balance. Blackbody radiation and Planck's distribution law. VI. Electronics and Experimental Methods Semiconductor devices (diodes, junctions, transistors, field effect devices, homo and heterojunction devices), device structure, device characteristics, frequency dependence and applications. Optoelectronic devices (solar cells, photodetectors, LEDs). Operational amplifiers and their applications. Digital techniques and applications (registers, counters, comparators and similar circuits). A/D and D/A converters. Microprocessor and microcontroller basics. Data interpretation and analysis. Precision and accuracy. Error analysis, propagation of errors. Least squares fitting. VII. Condensed Matter Physics Bravais lattices. Reciprocal lattice. Diffraction and the structure factor. Bonding of solids. Elastic properties, phonons, lattice specific heat. Free electron theory and electronic specific heat. Response and relaxation phenomena. Drude model of electrical and thermal conductivity. Hall effect and thermoelectric power. Electron motion in a periodic potential, band theory of solids: metals, insulators and semiconductors. Superconductivity: typeI and typeII superconductors. Josephson junctions. Superfluidity. Defects and dislocations. Ordered phases of matter: translational and orientational order, kinds of liquid crystalline order. Quasi crystals. Ph.D. Admission InterviewCandidates who have qualified in the Ph.D. eligibility test shall be called for Ph.D. Admission Interview. After the Ph.D. Admission Interview the list of eligible candidates for registration for full time and part time Ph.D. program will be finalized.Admission Calendar
For more information, contact: Coordinator, Ph.D. Program, ITS cell:9949168287 