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Algorithms & Data Structures

Algorithms:

• Analysis, Asymptotic notation, Notions of space and time complexity, Worst and average case analysis;
• Design: Greedy approach, Dynamic programming, Divide-and-conquer;
• Tree and graph traversals, Connected components, Spanning trees, Shortest paths;
• Hashing, Sorting, Searching.
• Asymptotic analysis (best, worst, average cases) of time and space, upper and lower bounds, Basic concepts of complexity classes – P, NP, NP-hard, NP-complete.

Data Structures:

• Abstract data types, Arrays, Stacks, Queues
• Linked Lists
• Trees, Binary search trees, Binary heaps.

Course Videos	Description
Algorithms Shai Simonson, Aduni.org	Aduni.org: before you do any other thing, the first thing to do is watch these videos, you won’t believe how awesome Shai is.
Introduction to Algorithms Leiserson, OCW.MIT	One of the lecturers is C. Leiserson, The “L” in CLRS..
Introduction to Data Structures & Algorithms NPTEL
Coursera Course Kevin Wayne, Robert Sedgewick, Princeton University	Course and slides

Databases

• ER-model, Relational model (relational algebra, tuple calculus)
• Database design (integrity constraints, normal forms)
• Query languages (SQL)
• File structures (sequential files, indexing, B and B+ trees)
• Transactions and concurrency control

Course Videos	Description
DBMS NPTEL PPC - IIT KGP NPTEL	IIT KGP PPC DBMS lecture is good one
CS145 Introduction to Databases Stanford	Course and slides for DBMS

Compiler Design

• Lexical analysis, Parsing
• Syntax directed translation, Runtime environments
• Intermediate and target code generation, Basics of code optimization.

Course Videos	Description
CS143 Compilers Stanford	Best notes and assignment for Compiler Course, no video
Compilers Stanford Alex Aiken, Coursera	Comprehensive

Operating Systems

• Processes, Threads, Inter-process communication
• Concurrency, Synchronization
• Deadlock
• CPU scheduling
• Memory management and virtual memory
• File systems, I/O systems, Protection and security.

Course Videos	Description
Operating Systems P.K.Biswas	Enough for GATE
Computer Science 162 - Lecture 1 UCBerkeley

Theory of Computation

• Regular languages and finite automata
• Context free languages and Push-down automata
• Recursively enumerable sets and Turing machines
• Undecidability.

Course Videos	Description
Theory of Computation Shai Simonson, Aduni.org	If you have not seen these videos, don’t do anything go and see the videos immediately, no excuses.

CO & Architecture

• Machine instructions and addressing modes
• ALU and data-path, CPU control design
• Memory interface, I/O interface (Interrupt and DMA mode)
• Instruction pipelining
• Cache and main memory, Secondary storage.

Course Videos	Description
Computer Architecture Prof. Anshul Kumar, IIT Delhi, NPTEL
Computer Organization Prof. S. Raman, IIT Madras, NPTEL
Computer Architecture David Wentzlaff, Princeton University, Coursera	Full Course

Computer Networks

• ISO/OSI stack, LAN technologies (Ethernet, Token ring)
• Flow and error control techniques, Routing algorithms, Congestion control
• TCP/UDP and sockets, IP(v4), Application layer protocols (icmp, dns, smtp, pop, ftp, http)
• Basic concepts of hubs, switches, gateways, and routers
• Network security – basic concepts of public key and private key cryptography, digital signature, firewalls

Course Videos	Description
Computer Networks NPTEL
Introduction to Computer Networks Jain, WUSTL

Programming

• Programming in C
• Functions, Recursion
• Parameter passing, Scope, Binding

Course Videos	Description
Programming Paradigms Jerry Cain, Stanford	Doesn't cover the entire GATE syllabus in programming but useful
Computer Science 61B - Fall 2006 UCBerkeley	For Data structures

Digital Logic

• Logic functions, Minimization
• Design and synthesis of combinational and sequential circuits
• Number representation and computer arithmetic (fixed and floating point)

Course Videos	Description
Introduction to Digital Circuits Prof. S. Srinivasan, IIT Madras, NPTEL

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.

Course Videos	Description
Introduction to Software Engineering Challenges IIT Bombay, NPTEL

Web technologies

• HTML, XML
• Basic concepts of client-server computing

Course Videos	Description
Web Technologies Basics Telerik Academy	This presentation is enough for GATE.

Engineering Mathematics

Combinatory & Probability

Combinatory

• Permutations, Combinations
• Counting, Summation
• Generating functions, recurrence relations, asymptotics

Probability

• Conditional Probability
• Mean, Median, Mode and Standard Deviation
• Random Variables
• Distributions; uniform, normal, exponential, Poisson, Binomial.

Course Videos	Description
Sets, Counting, and Probability Harvard	Covers the basics
Applied Probability MIT	Advanced course and topics are mostly above GATE syllabus.

Mathematical Logic, Set Theory & Algebra

Mathematical Logic

• Propositional Logic
• First Order Logic

Set Theory & Algebra

• Sets, Relations, Functions
• Groups
• Partial Orders, Lattice
• Boolean Algebra

Course Videos	Description
Discrete Mathematical Structures Prof. Kamala Krithivasan, IIT Madras, NPTEL	Covers Mathematical logic, Set Theory and Algebra syllabus from GATE completely

Graph Theory

• Connectivity, spanning trees
• Cut vertices & edges
• Covering, matching, independent sets
• Colouring, Planarity, Isomorphism

Course Videos	Description
Graph Theory NPTEL	Advanced course, just take what you need from GATE syllabus

Linear Algebra

• Algebra of matrices, determinants
• Systems of linear equations
• Eigen values and Eigen vectors

Course Videos	Description
Linear Algebra Gilbert Strang, OCW.MIT	Straight from the master

Numerical Methods & Calculus

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

Calculus

• Limit, Continuity & differentiability
• Mean value theorems
• Theorems of integral calculus, evaluation of definite & improper integrals
• Partial derivatives, Total derivatives, maxima & minima

Course Videos	Description
Single Variable Calculus David Jerison, OCW.MIT	Very good videos

General Aptitude

Numerical Ability

• Numerical computation
• Numerical estimation
• Numerical reasoning and data interpretation

Verbal Ability

• English grammar, sentence completion
• Verbal analogies, word groups
• Instructions, critical reasoning and verbal deduction