# 1
| |||

| |||

TIFR Ph.D Computer Science Entrance Syllabus |

# 2
| |||

| |||

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.
__________________ Answered By StudyChaCha Member |

# 4
| |||

| |||

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 SyllabusSample 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 AddressTata Institute of Fundamental Research Dr. Homi Bhabha Road, Navy Nagar, Near Navy Canteen Mandir Marg, Colaba Mumbai, Maharashtra 400005 Map locationFor complete syllabus here is the attachment;
__________________ Answered By StudyChaCha Member |