(Created page with " ==Discrete Mathematics== *Propositional and first order logic. *Sets, relations, functions, partial orders and lattices. Groups. * Graphs: connectivity, matching, coloring....")
 
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{{alert| Some missing links for topics do not mean that they were never asked for GATE. I'll add their links soon after correcting the corresponding tags in [http://gateoverflow.in/tags GATE Overflow] |alert-danger}}
  
==Discrete Mathematics==
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==Official Syllabus Links==
*Propositional and first order logic.  
+
[http://www.gate.iisc.ernet.in/wp-content/uploads/2015/06/Computer-Science-and-Information-Technology.pdf Computer Science]
*Sets, relations, functions, partial orders and lattices. Groups.  
 
* Graphs: connectivity, matching, coloring.  
 
* Combinatorics: counting, recurrence relations, generating functions.
 
  
==Linear Algebra==
+
[http://gate.iitk.ac.in/GATE2015/docs/syllabi/GA.pdf General Aptitude]
*Matrices, determinants
+
 
*System of linear equations
+
==[http://www.gatecse.in/gate-subjects/ Discrete Mathematics]==
*Eigenvalues and eigenvectors  
+
*[http://gateoverflow.in/tag/mathematical-logic Propositional and first order logic.]
 +
*[http://gateoverflow.in/tag/set Sets], [http://gateoverflow.in/tag/relations relations], [http://gateoverflow.in/tag/functions functions], [http://gateoverflow.in/tag/partial-order partial orders] and [http://gateoverflow.in/tag/lattice lattices]. [http://gateoverflow.in/tag/groups Groups].
 +
* Graphs: [http://gateoverflow.in/tag/graph-connectivity connectivity], [http://gateoverflow.in/tag/graph-matching matching], [http://gateoverflow.in/tag/graph-coloring coloring].
 +
* [http://gateoverflow.in/tag/combinatory Combinatorics:] [http://gateoverflow.in/tag/counting counting], [http://gateoverflow.in/tag/recurrence recurrence relations], [http://gateoverflow.in/tag/generating-functions generating functions].
 +
 
 +
'''Boolean Algebra''' moved to Digital Logic.
 +
'''[http://gateoverflow.in/tag/permutation Permutations]; [http://gateoverflow.in/tag/combinations Combinations]''' removed from Combinatorics but being basic and counting being there this does not really matter.
 +
'''asymptotics''' removed, but basics are in asymptotic analysis part of Algorithms
 +
'''spanning trees; Cut vertices & edges; covering;  independent sets; [http://gateoverflow.in/tag/planar-embedding Planarity]; [http://gateoverflow.in/tag/isomorphism Isomorphism]''' removed. But based on other topics this just means Planarity and isomorphism are removed (spanning trees are already in algorithms)
 +
 
 +
==[http://www.gatecse.in/linear-algebra/ Linear Algebra]==
 +
*[http://gateoverflow.in/tag/matrices Matrices, determinants]
 +
*[http://gateoverflow.in/tag/system-of-equations System of linear equations]
 +
*[http://gateoverflow.in/tag/eigen-value Eigenvalues and eigenvectors]
 
*LU decomposition
 
*LU decomposition
  
==Calculus==
+
'''LU decomposition''' added here from Numerical methods which was removed as a whole otherwise.  
* Limits, continuity and differentiability.
 
* Maxima and minima. Mean value theorem.
 
* Integration.
 
  
==Probability==
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==[http://www.gatecse.in/calculus/ Calculus]==
* Random variables.  
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* [http://gateoverflow.in/tag/limit Limits], [http://gateoverflow.in/tag/continuity continuity] and [http://gateoverflow.in/tag/differentiability differentiability].
*Uniform, normal, exponential, poisson and binomial distributions.  
+
* [http://gateoverflow.in/tag/maxima-minima Maxima and minima]. Mean value theorem.
*Mean, median, mode and standard deviation.  
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* [http://gateoverflow.in/tag/integration Integration].
 +
'''Theorems of integral calculus, evaluation of definite & improper integrals, Partial derivatives, Total derivatives''' removed and '''Integration''' added. So, this would mean we can expect only simple integration questions.
 +
 
 +
==[http://www.gatecse.in/probability/ Probability]==
 +
*[http://gateoverflow.in/tag/random-variable Random variables].  
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*Uniform, [http://gateoverflow.in/tag/normal-distribution normal], [http://gateoverflow.in/tag/exponential-distribution exponential], [http://gateoverflow.in/tag/poisson-distribution poisson] and [http://gateoverflow.in/tag/binomial-distribution binomial distributions].  
 +
*[http://gateoverflow.in/tag/statistics Mean, median, mode and standard deviation].  
 
*Conditional probability and Bayes theorem.
 
*Conditional probability and Bayes theorem.
 +
'''Bayes theorem''' newly added but it was implicitly part of conditional probability
 +
 +
==[http://www.gatecse.in/digital-logic/ Digital Logic]==
 +
 +
*[http://gateoverflow.in/tag/boolean-expressions Boolean algebra].
 +
*[http://gateoverflow.in/tag/circuit-output Combinational and sequential circuits.] [http://gateoverflow.in/tag/canonical-normal-form Minimization].
 +
*[http://gateoverflow.in/tag/number-representation Number representations] and computer arithmetic (fixed and [http://gateoverflow.in/tag/floating-point-representation floating point]).
 +
'''Boolean algebra''' added to here from set theory & algebra
 +
 +
==[http://www.gatecse.in/co-architecture/ Computer Organization and Architecture]==
 +
 +
*[http://gateoverflow.in/tag/machine-instructions Machine instructions] and [http://gateoverflow.in/tag/addressing-modes addressing modes].
 +
*[http://gateoverflow.in/tag/microprogramming ALU, data‐path and control unit].
 +
*[http://gateoverflow.in/tag/pipeline Instruction pipelining.]
 +
* [http://gateoverflow.in/tag/cache-memory Memory hierarchy: cache, main memory and secondary storage;]
 +
* [http://gateoverflow.in/tag/io-handling I/O interface]. ([http://gateoverflow.in/tag/interrupts Interrupt] and [http://gateoverflow.in/tag/dma DMA mode])
 +
'''[http://gateoverflow.in/tag/ram Memory interface]''' part is removed. So, questions on RAM would not be there.
 +
 +
==[http://www.gatecse.in/data-structures/ Programming and Data Structures]==
 +
*[http://gateoverflow.in/tag/programming-in-c Programming in C.] [http://gateoverflow.in/tag/recursion Recursion].
 +
*[http://gateoverflow.in/tag/arrays Arrays], [http://gateoverflow.in/tag/stack stacks], [http://gateoverflow.in/tag/queues queues], [http://gateoverflow.in/tag/linked-lists linked lists], [http://gateoverflow.in/tag/trees trees], [http://gateoverflow.in/tag/binary-tree binary search trees], [http://gateoverflow.in/tag/heap binary heaps], graphs.
 +
'''Functions, Parameter passing, Scope, [http://gateoverflow.in/tag/variable-binding Binding]; Abstract data types''' removed. So, questions like pass by reference, static-dynamic scopes, etc would not be there.
 +
'''Graphs''' added here.
 +
 +
==[http://www.gatecse.in/algorithms/ Algorithms]==
 +
*[http://gateoverflow.in/tag/binary-search Searching], [http://gateoverflow.in/tag/sorting sorting], [http://gateoverflow.in/tag/hashing hashing].
 +
*[http://gateoverflow.in/tag/time-complexity Asymptotic worst case time] and [http://gateoverflow.in/tag/space-complexity space complexity.]
 +
*Algorithm design techniques: [http://gateoverflow.in/tag/greedy-algorithm greedy], [http://gateoverflow.in/tag/dynamic-programming dynamic programming] and divide‐and‐conquer.
 +
*[http://gateoverflow.in/tag/graph-search Graph search], [http://gateoverflow.in/tag/spanning-tree minimum spanning trees], [http://gateoverflow.in/tag/shortest-path shortest paths].
 +
'''Space and time complexity''' restricted to only worst case.
 +
'''[http://gateoverflow.in/tag/connected-components Connected components]''' removed here, but they are in Graph theory anyway
 +
'''Tree and graph traversals''' removed. But these are implied in Data Structure portion and other algorithm portions.
 +
'''Basic concepts of complexity classes – [http://gateoverflow.in/tag/p-np-npc-nph P, NP, NP-hard, NP-complete]. ''' removed. So, these definitions need not be studied but reduction is there in Theory of Computation anyway.
 +
 +
==[http://www.gatecse.in/theory-of-computation/ Theory of Computation]==
 +
*[http://gateoverflow.in/tag/regular-expressions Regular expressions] and [http://gateoverflow.in/tag/finite-automata finite automata].
 +
*[http://gateoverflow.in/tag/grammar Context-free grammars] and [http://gateoverflow.in/tag/pda push-down automata].
 +
*[http://gateoverflow.in/tag/regular-set Regular] and [http://gateoverflow.in/tag/context-free context-free languages], pumping lemma.
 +
*[http://gateoverflow.in/tag/turing-machine Turing machines] and [http://gateoverflow.in/tag/decidability undecidability].
 +
'''pumping lemma''' newly added. So, questions based on pumping length or some examples can be asked.
 +
'''Recursively enumerable sets''' removed but Turing machines are there. So, this should not really matter.
 +
 +
==[http://www.gatecse.in/compiler-design/ Compiler Design]==
 +
*[http://gateoverflow.in/tag/lexical-analysis Lexical analysis], [http://gateoverflow.in/tag/parsing parsing], [http://gateoverflow.in/tag/syntax-directed-translation syntax-directed translation].
 +
*[http://gateoverflow.in/tag/runtime-environments Runtime environments].
 +
*[http://gateoverflow.in/tag/intermediate-code Intermediate code generation].
 +
'''[http://gateoverflow.in/tag/code-generation target code generation], [http://gateoverflow.in/tag/optimization Basics of code optimization].''' removed. This is quite a good removal for students. Questions like register allocation, optimizations like code motion  etc. would not be there
 +
 +
==[http://www.gatecse.in/operating-systems/ Operating System]==
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*[http://gateoverflow.in/tag/fork Processes], [http://gateoverflow.in/tag/threads threads], [http://gateoverflow.in/tag/semaphore inter‐process communication], [http://gateoverflow.in/tag/process-synchronization concurrency and synchronization.]
 +
*[http://gateoverflow.in/tag/resource-allocation Deadlock.]
 +
*[http://gateoverflow.in/tag/process-schedule CPU scheduling.]
 +
*[http://gateoverflow.in/tag/memory-management Memory management] and [http://gateoverflow.in/tag/virtual-memory  virtual memory.]
 +
*[http://gateoverflow.in/tag/disk-scheduling File systems.] [http://gateoverflow.in/tag/disk Disks is also under this]
 +
'''I/O systems, Protection and security''' removed. Rarely questions like size of graphic card required etc have been asked.
 +
 +
==[http://www.gatecse.in/databases/ Databases]==
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*[http://gateoverflow.in/tag/er-model ER‐model]. Relational model:[http://gateoverflow.in/tag/relational-algebra relational algebra], [http://gateoverflow.in/tag/relational-calculus tuple calculus],[http://gateoverflow.in/tag/sql SQL].
 +
*[http://gateoverflow.in/tag/referential-integrity Integrity constraints],
 +
*[http://gateoverflow.in/tag/database-normalization normal forms.]
 +
*[http://gateoverflow.in/tag/indexing File organization], [http://gateoverflow.in/tag/b-tree indexing (e.g., B and B+ trees)].
 +
*[http://gateoverflow.in/tag/transactions Transactions and concurrency control].
 +
No change
 +
 +
==[http://www.gatecse.in/computer-networks/ Computer Networks]==
 +
*[http://gateoverflow.in/tag/network-layering Concept of layering]. [http://gateoverflow.in/tag/lan-technologies LAN technologies (Ethernet)].
 +
*[http://gateoverflow.in/tag/sliding-window Flow] and [http://gateoverflow.in/tag/error-detection error control] techniques,
 +
*[http://gateoverflow.in/tag/network-switching switching].
 +
*[http://gateoverflow.in/tag/ip-packet IPv4]/IPv6,
 +
*[http://gateoverflow.in/tag/routing routers and routing algorithms (distance vector, link state)].
 +
*[http://gateoverflow.in/tag/tcp TCP]/[http://gateoverflow.in/tag/udp UDP] and [http://gateoverflow.in/tag/sockets sockets], [http://gateoverflow.in/tag/congestion-control congestion control].
 +
*[http://gateoverflow.in/tag/application-layer-protocols Application layer protocols (DNS, SMTP, POP, FTP, HTTP)].
 +
*Basics of Wi-Fi.
 +
*[http://gateoverflow.in/tag/network-security Network security: authentication, basics of public key and private key cryptography, digital signatures and certificates], [http://gateoverflow.in/tag/firewall firewalls].
 +
'''IPv6''' added
 +
'''[http://gateoverflow.in/tag/token-ring Token Ring]''' removed
 +
'''Basics of Wi-Fi''' added
 +
'''[http://gateoverflow.in/tag/routers-bridge-hubs-switches Basic concepts of hubs, switches, gateways, and routers]''' removed
 +
'''[http://gateoverflow.in/tag/subnettting Subnetting]''' is an important part under IP.
 +
 +
==General Aptitude==
 +
*No change in [http://www.gatecse.in/numerical-ability/ Numerical Ability] as well as [http://www.gatecse.in/verbal-ability/ Verbal Ability].
 +
 +
==Removals==
 +
Except LU decomposition, all portions of Web Technologies, IS & Software Engineering and Numerical Methods are removed.
  
Section 2: Digital Logic
+
'''Web technologies:''' HTML, XML, basic concepts of client-server computing.  
Boolean algebra. Combinational and sequential circuits. Minimization. Number
 
representations and computer arithmetic (fixed and floating point).
 
Section 3: Computer Organization and Architecture
 
Machine instructions and addressing modes. ALU, data‐path and control unit. Instruction
 
pipelining. Memory hierarchy: cache, main memory and secondary storage; I/O
 
interface (interrupt and DMA mode).
 
Section 4: Programming and Data Structures
 
Programming in C. Recursion. Arrays, stacks, queues, linked lists, trees, binary search
 
trees, binary heaps, graphs.
 
Section 5: Algorithms
 
Searching, sorting, hashing. Asymptotic worst case time and space complexity.
 
Algorithm design techniques: greedy, dynamic programming and divide‐and‐conquer.
 
Graph search, minimum spanning trees, shortest paths.
 
Section 6: Theory of Computation
 
Regular expressions and finite automata. Context-free grammars and push-down
 
automata. Regular and contex-free languages, pumping lemma. Turing machines and
 
undecidability.
 
Section 7: Compiler Design
 
Lexical analysis, parsing, syntax-directed translation. Runtime environments. Intermediate
 
code generation.
 
Section 8: Operating System
 
Processes, threads, inter‐process communication, concurrency and synchronization.
 
Deadlock. CPU scheduling. Memory management and virtual memory. File systems.
 
Section 9: Databases
 
ER‐model. Relational model: relational algebra, tuple calculus, SQL. Integrity constraints,
 
normal forms. File organization, indexing (e.g., B and B+ trees). Transactions and
 
concurrency control.
 
Section 10: Computer Networks
 
Concept of layering. LAN technologies (Ethernet). Flow and error control techniques,
 
switching. IPv4/IPv6, routers and routing algorithms (distance vector, link state). TCP/UDP
 
and sockets, congestion control. Application layer protocols (DNS, SMTP, POP, FTP, HTTP).
 
Basics of Wi-Fi. Network security: authentication, basics of public key and private key
 
cryptography, digital signatures and certificates, firewalls.  
 
  
 +
'''Information Systems and Software Engineering: ''' information gathering, requirement and feasibility analysis, data flow diagrams, process specifications, input/output design, process life cycle, planning and managing the project, design, coding, testing, implementation, maintenance
  
 +
'''Numerical Methods:''' LU decomposition for systems of linear equations; numerical solutions of non-linear algebraic equations by Secant, Bisection and Newton-Raphson Methods; Numerical integration by trapezoidal and Simpson’s rules.
  
 +
{{Template:FBD}}
 
[[Category:GATE]]
 
[[Category:GATE]]

Latest revision as of 15:40, 29 November 2015

Heads Up! Some missing links for topics do not mean that they were never asked for GATE. I'll add their links soon after correcting the corresponding tags in GATE Overflow

Official Syllabus Links

Computer Science

General Aptitude

Discrete Mathematics

Boolean Algebra moved to Digital Logic. 
Permutations; Combinations removed from Combinatorics but being basic and counting being there this does not really matter. 
asymptotics removed, but basics are in asymptotic analysis part of Algorithms
spanning trees; Cut vertices & edges; covering;  independent sets; Planarity; Isomorphism removed. But based on other topics this just means Planarity and isomorphism are removed (spanning trees are already in algorithms)

Linear Algebra

LU decomposition added here from Numerical methods which was removed as a whole otherwise. 

Calculus

Theorems of integral calculus, evaluation of definite & improper integrals, Partial derivatives, Total derivatives removed and Integration added. So, this would mean we can expect only simple integration questions.

Probability

Bayes theorem newly added but it was implicitly part of conditional probability

Digital Logic

Boolean algebra added to here from set theory & algebra

Computer Organization and Architecture

Memory interface part is removed. So, questions on RAM would not be there.

Programming and Data Structures

Functions, Parameter passing, Scope, Binding; Abstract data types removed. So, questions like pass by reference, static-dynamic scopes, etc would not be there. 
Graphs added here.

Algorithms

Space and time complexity restricted to only worst case. 
Connected components removed here, but they are in Graph theory anyway
Tree and graph traversals removed. But these are implied in Data Structure portion and other algorithm portions.
Basic concepts of complexity classes – P, NP, NP-hard, NP-complete.  removed. So, these definitions need not be studied but reduction is there in Theory of Computation anyway.

Theory of Computation

pumping lemma newly added. So, questions based on pumping length or some examples can be asked. 
Recursively enumerable sets removed but Turing machines are there. So, this should not really matter.

Compiler Design

target code generation, Basics of code optimization. removed. This is quite a good removal for students. Questions like register allocation, optimizations like code motion  etc. would not be there

Operating System

I/O systems, Protection and security removed. Rarely questions like size of graphic card required etc have been asked. 

Databases

No change

Computer Networks

IPv6 added
Token Ring removed
Basics of Wi-Fi added
Basic concepts of hubs, switches, gateways, and routers removed
Subnetting is an important part under IP.

General Aptitude

Removals

Except LU decomposition, all portions of Web Technologies, IS & Software Engineering and Numerical Methods are removed. 

Web technologies: HTML, XML, basic concepts of client-server computing.

Information Systems and Software Engineering: information gathering, requirement and feasibility analysis, data flow diagrams, process specifications, input/output design, process life cycle, planning and managing the project, design, coding, testing, implementation, maintenance

Numerical Methods: LU decomposition for systems of linear equations; numerical solutions of non-linear algebraic equations by Secant, Bisection and Newton-Raphson Methods; Numerical integration by trapezoidal and Simpson’s rules.




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Discrete Mathematics[edit]

Linear Algebra[edit]

Calculus[edit]

Probability[edit]

Section 2: Digital Logic Boolean algebra. Combinational and sequential circuits. Minimization. Number representations and computer arithmetic (fixed and floating point). Section 3: Computer Organization and Architecture Machine instructions and addressing modes. ALU, data‐path and control unit. Instruction pipelining. Memory hierarchy: cache, main memory and secondary storage; I/O interface (interrupt and DMA mode). Section 4: Programming and Data Structures Programming in C. Recursion. Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs. Section 5: Algorithms Searching, sorting, hashing. Asymptotic worst case time and space complexity. Algorithm design techniques: greedy, dynamic programming and divide‐and‐conquer. Graph search, minimum spanning trees, shortest paths. Section 6: Theory of Computation Regular expressions and finite automata. Context-free grammars and push-down automata. Regular and contex-free languages, pumping lemma. Turing machines and undecidability. Section 7: Compiler Design Lexical analysis, parsing, syntax-directed translation. Runtime environments. Intermediate code generation. Section 8: Operating System Processes, threads, inter‐process communication, concurrency and synchronization. Deadlock. CPU scheduling. Memory management and virtual memory. File systems. Section 9: Databases ER‐model. Relational model: relational algebra, tuple calculus, SQL. Integrity constraints, normal forms. File organization, indexing (e.g., B and B+ trees). Transactions and concurrency control. Section 10: Computer Networks Concept of layering. LAN technologies (Ethernet). Flow and error control techniques, switching. IPv4/IPv6, routers and routing algorithms (distance vector, link state). TCP/UDP and sockets, congestion control. Application layer protocols (DNS, SMTP, POP, FTP, HTTP). Basics of Wi-Fi. Network security: authentication, basics of public key and private key cryptography, digital signatures and certificates, firewalls.