VIT M.C.A Entrance

Algebra

9 topics

• Fundamental operations in Algebra
• Expansion
• factorization
• quadratic equations
• indices
• loga- rithms
• arithmetic, geometric and harmonic progressions
• binomial theorem
• permutations and combina- tions

Calculus

10 topics

• Functions of single variable
• limit
• continuity and differentiability
• Mean value theorems
• indetermi- nate forms and L'Hospital rule
• Maxima and minima
• Taylor's series
• Fundamental and mean value-theorems of integral calculus
• total derivatives
• Lagrange method of multipliers

Differential Equations

3 topics

• Differential equations of first order and their solutions
• linear differential equations with constant coefficients
• homogenous linear differential equations

Algorithms

12 topics

• Analysis
• Asymptotic notation
• Notions of space and time complexity
• Worst and average case analysis
• Design: Greedy approach
• Dynamic programming
• Divide-and conquer
• Connected components
• Spanning trees
• Shortest paths
• Asymptotic analysis (best, worst, average cases) of time and space
• upper and lower bounds

Probability

7 topics

• Probability theory
• Dependent and independent events
• frequency distributions, and measures of dispersions
• Skewness and Kurtosis
• random variable and distribution functions
• mathematical expecta- tions
• Binomial, Poisson, normal distributions

Algebra and Complex Analysis

22 topics

• Algebra of matrices
• rank and determinant of matrices
• linear equa- tions
• Eigenvalues and eigenvectors
• Cayley-Hamilton theorem
• Matrix representation of linear trans- formations
• Canonical forms
• diagonal forms
• triangular forms
• Quadratic forms
• reduction and classification of quadratic forms Analytic functions
• Cauchy-Riemann equations
• Contour integral
• Cauchy’s theorem
• Cau- chy’s integral formula
• Taylor series
• Laurent series
• calculus of residues
• Conformal mappings
• Mobius trans- formations
• Fourier series
• harmonics

Calculus and its Applications

10 topics

• Linear ordinary differential equations (ODEs)
• variation of parame- ters
• Sturm-Liouville problem
• Partial differential equations (PDEs) - Classification of second or- der PDEs
• General solution of higher order PDEs with constant coefficients
• Method of separation of variables for Laplace, Heat and Wave equations
• Transformation techniques
• Laplace transfor- mation
• Fourier transforms
• z—transformation to solve differential and difference equations

Numerical Methods

3 topics

• Numerical solutions of algebraic and transcendental equations iteration meth- ods and Newton—Raphson method
• Solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods-Numerical differentiation and integration
• Numerical solu- tions of ODEs and PDEs

Descriptive statistics, Exploratory Data Analysis

17 topics

• 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 distribu- tions
• Characteristic functions
• Standard discrete and continuous univariate distributions
• Corre- lation and simple and multiple linear regression
• Test of hypotheses
• Large and small sample tests confidence intervals
• Chi-square test goodness of fit
• Simple non parametric tests for one and two sample problems
• rank correlation and test for independence
• ANOVA

Date Structures

9 topics

• Arrays
• Stacks
• Queues
• linked Lists
• Sorting techniques
• Searching Techniques
• Trees and Graph terminology and representation in memory
• binary search tree
• traversal techniques of graphs and Trees

Computer Networks

16 topics

• Network models
• Internet model
• OSI model
• Physical Layer - Analog and Digital Signals
• Analog and Digital Transmission
• Coding
• Sampling
• Data Link Layer - Error detection and correction
• Data link control and Protocols
• Stop and wait
• Go-back-n
• Selective repeat
• Network Layer - Inter-networks
• Address- ing
• unicast and multicast routing
• Presentation Layer

Programming in C

9 topics

• Data types
• Declarations
• Expressions
• statements and symbolic constants
• input-Output functions
• Operators and expressions: Arithmetic, unary, logical, bit-wise, assignment and conditional opera- tors
• Control statements: While, do-while, for statements, nested loops, if else, switch, break, Continue, com- ma operators
• Storage types: Automatic, external, register and static variables
• Functions: Defining and ac- cessing, passing arguments, Recursion

Database Management Systems

10 topics

• DBMS architecture
• Data models
• data independence
• E-R model
• normalization
• Relational Model: concepts, constraints, languages
• Data storage
• indexing
• query processing
• design and programming SQL

Operating Systems

13 topics

• Process management
• Process States
• Process Control Block
• Process and Threads
• CPU Scheduling
• Scheduling algorithm
• Process Synchronization and Deadlock
• Memory management
• Virtual memory concepts paging and segmentation File organization
• Blocking and buffering
• file descriptor
• File and Directory structures
• I/O Devices

Computer Architecture

13 topics

• Boolean algebra and computer arithmetic
• flip-flops
• design of combinational and sequential circuits
• instruction formats
• addressing modes
• interfacing peripheral devices
• types of memory and their organization
• interrupts and exceptions
• Von Neumann Computer
• System Bus
• Instruction Cycle
• Data Representation
• Machine instruction and Assembly Language

Grammar

4 topics

• Subject – Verb Agreement
• Tense forms
• Voices
• Conditionals

Writing Technical Instructions

0 topics

Writing Memos & Writing Minutes

0 topics

Transcoding

0 topics

Preparing Questionnaire

0 topics

Proof Reading

0 topics

General vocabulary: Synonyms, Antonyms, Words Often Confused

0 topics

Question Tags

0 topics

Polite Expressions

0 topics