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Old June 11th, 2014, 03:37 PM
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Join Date: May 2011
Default Re: TIFR Ph.D Computer Science Entrance Syllabus

Here I am sharing the Ph.D Computer & Systems Sciences Exam Syllabus of TIFR

Computer Science----

1. Discrete Mathematics: Sets and Relations, Combinatorics (Counting) and Ele-
mentary Probability Theory, Graph Theory, Propositional and Predicate Logic.

2. Formal Languages, Automata Theory and Computability.

3. Data Structures and Algorithms: Arrays, Lists and Trees, Sorting and Searching, Graph algorithms, Complexity of problems and NP-completeness.

4. Fundamentals of Programming Languages and Compilers: Control structures,
Parameter passing mechanisms, Recursion, Parsing and type checking, Memory
management.

5. Operating Systems and Concurrency

6. Switching Theory and Digital Circuits

7. Theory of Databases

Systems Science----

1. Engineering Mathematics: Complex Analysis, Linear Algebra, Elementary Nu-
merical Analysis, Basic Optimization Theory and Algorithms, Introduction to
Probability Theory and Statistics.

2. Electrical and Computer Sciences: Introduction to Signals and Linear Systems
Analysis, Control Systems, Digital Signal Processing, Basic Circuit Theory,
Introduction to Digital Communications, Digital Computer Fundamentals, Introduction to Computer Programming.
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  #3  
Old October 20th, 2015, 03:56 PM
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Default Re: TIFR Ph.D Computer Science Entrance Syllabus

I want the syllabus of Ph.D Computer Science of Tata Institute of Fundamental Research (TIFR) Graduate School Admission so can you provide me?
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  #4  
Old October 20th, 2015, 03:58 PM
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Join Date: Dec 2011
Default Re: TIFR Ph.D Computer Science Entrance Syllabus

Ok, as you want the syllabus of Ph.D Computer Science of Tata Institute of Fundamental Research (TIFR) Graduate School Admission so here I am providing you.

TIFR GS Computer Science Syllabus


There are two streams in the School of Technology and Computer
Science:

1. Computer Science.
2. Systems Science.

Topics covered in the two streams

Computer Science

1. Discrete Mathematics: Sets and Relations, Combinatorics (Counting) and Ele-
mentary Probability Theory, Graph Theory, Propositional and Predicate Logic.

2. Formal Languages, Automata Theory and Computability.

3. Data Structures and Algorithms: Arrays, Lists and Trees, Sorting and Search-ing, Graph algorithms, Complexity of problems and NP-completeness.

4. Fundamentals of Programming Languages and Compilers: Control structures,
Parameter passing mechanisms, Recursion, Parsing and type checking, Memory
management.

5. Operating Systems and Concurrency

6. Switching Theory and Digital Circuits

7. Theory of Databases

TIFR GS Computer Science Syllabus
Sample Questions [Computer Science]
1. A function f : f0; 1gn ! f0; 1g is called symmetric if for every x1; x2; : : : ; xn 2
f0; 1g and every permutation _ of f1; 2; : : : ; ng, we have
f(x1; x2; : : : ; xn) = f(x_(1); x_(2); : : : ; x_(n)):
The number of such symmetric functions is:
(a) 2n+1 (b) 2n (c) 22n=n! (d) 22n (e) n!
2. Let r, s and t be regular expressions. Which of the following is wrong?
(a) (r + s)_ = (r_s_)_ (b) r(s + t) = rs + rt
(c) (r + s)_ = (s + r)_ (d) (rs + r)_r = r(sr + r)_ (e) All are correct.
3. Consider the following program
x:=0; y:=1; z:=1;
while y <= N do
begin
x:=x+1; y:=y+z+2; z:=z+2;
end
Which of the following holds on termination of the program?
(a) (x + 1)2 = N (b) x = pN
(c) x2 = N (d) x2 _ N < (x + 1)2 (e) x2 < N _ (x + 1)2.
4. The maximum height of a rooted binary tree (all nodes have either two children
or none) with N nodes is
(a) N (b) logN (c) (N _ 1)=2 (d) (N2)=2 (e) N(N _ 1)=2.
5. If a graph G has n vertices and m edges then the depth _rst traversal of G can
be carried out in time
(a) O(n + m) (b) O(nm) but not O(n + m)
(c) O(n2) but not O(n + m) (d) O(n) (e) O(m)
Systems Science
1. Engineering Mathematics: Complex Analysis, Linear Algebra, Elementary Nu-
merical Analysis, Basic Optimization Theory and Algorithms, Introduction to
Probability Theory and Statistics.
2. Electrical and Computer Sciences: Introduction to Signals and Linear Systems
Analysis, Control Systems, Digital Signal Processing, Basic Circuit Theory,
Introduction to Digital Communications, Digital Computer Fundamentals, In-
troduction to Computer Programming.
Sample Questions [Systems Science]
1. The probability density of a random variable is
f(x) = ax2 exp_kx (k > 0; 0 _ x _ 1)
Then, the coe_cient a equals
(a) k3=2 (b) k3 (c) k2 (d) k (e) 2k=_.
2. Discrete sequences x(n) is non-zero for 0 _ n _ Nx and y(n) for 0 _ n _ Ny.
The sequence z(n) is obtained by convolving x(n) and y(n). z(n) assumes
nonzero values for N1 _ n _ N2, where N1 and N2 can be expressed in terms
of Nx and Ny as,
(a) N1 = 0;N2 = MAX(Nx;Ny)
(b) N1 = Nx;N2 = Ny
(c) N1 = MIN(Nx;Ny);N2 = Nx + Ny
(d) N1 = 0;N2 = Nx + Ny
(e) N1 = MIN(Nx;Ny);N2 = MAX(Nx;Ny)
3. This is a portion of FORTRAN-77 program for assigning values to a N _ N
matrix A:
DO I=1,N
DO J=I,N
A(I,J) = ABS(I_J)+1
ENDDO
ENDDO
What is the matrix A called ?
(a) Anti-symmetric (b) Sparse (c) Upper triangular (d) Toeplitz
(e) Irregular.
4. logb(logbx) equals
(a) (ln ln x _ ln ln b)= ln b
(b) (ln x _ ln b)= ln b
(c) (ln ln x _ ln ln b)
(d) (ln x _ ln b)=[(ln x)(ln b)]
(e) None of the Above.
5. The Laplace Transform G(s) of the transfer function of a linear time invariant
system is given by
G(s) =
(s + a)2 + b2
For the system to be stable it is necessary that
(a) a < 0 (b) a _ 0 (c) a = b (d) b = 0 (e) a = _b.

Contact Address

Tata Institute of Fundamental Research
Dr. Homi Bhabha Road, Navy Nagar, Near Navy Canteen
Mandir Marg, Colaba
Mumbai, Maharashtra 400005

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For complete syllabus here is the attachment;
Attached Files Available for Download
File Type: pdf TIFR GS Computer Science Syllabus.pdf (65.3 KB, 26 views)
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