**COURSE DETAILS**

MCA Syllabus

**Syllabus of MCA Entrances**

**MATHEMATICS**

1. ** ALGEBRA**

Sets, Relations, Functions, Elementary Number Theory Including the relation of congruence Modulo, Simultaneous linear / quadratic equations, Indices, Logarithms, Arithmetic, Geometric and Harmonic progressions, Binomial Theorem, Surds, Complex numbers, Demoivre’s theorem and its simple application.

2. ** MATRICES AND DETERMINANTS**

Matrix operations, Definition and properties of determinants, Co-factors, Adjoint, Elementary Transformations, Rank and inverse of a Matrix, Matrix Polynomial, Characteristic Equations, Eigen Values, Latent Vectors, Caylay Hamilton theorem, Linear system of Equations

3. **THEORY OF EQUATIONS**

Polynomials and their characteristics, Roots of an equation, Relations between Roots and Coefficients, Transformation of Equations, Symmetric function etc.

4. ** ABSTRACT ALGEBRA**

Groups, Cyclic groups, Subgroups, Normal Groups, Lagrange’s theorem, Homomorphism, Isomorphism, Ring, Field, Vector Spaces, Linear Independence of Vectors, Basis, Dimension, Linear Transformation and diagonalization of Matrices etc.

5. ** VECTOR ALGEBRA**

Scalar and Vector quantities their representation, Addition and Subtraction of vectors, Scalar and vector product of two vectors, Scalar tripleproduct, Expansion formula of Vector triple product

6. ** TRIGONOMETRY**

Simple identities, trigonometric equations, Properties of triangles, Solution of triangle, Height and distance, Inverse function

7. ** CALCULAS AND REALANALYSIS**

Real number system, Concept of neighborhood and limit points, Continuity and limits, Indeterminate forms, properties of continuous functionsin closed interval, Differentiation, Successive Differentiation, Maxima Minima, Roll’s theorem, Mean value theorems, Maclaurine’s series and Taylor’s series, Integration, definite integral, Evaluation of length, Area and volume of curves, Curvature, Asymptotes, Tracing of curves, Partial Differentiation, Functions of two variables, definition of partial derivatives, Total Differentiation, Sequence, Sequence of real numbers, Convergent Sequences, Cauchy Sequences, Monotonic Sequences, Infinite series of positive terms and their different test of convergence, Alternating infinite series and Leibnitz’stest of convergence, Absolute convergence, Conditional convergence, Uniform Convergence, Multiple integration, Change of order and change of variables, Application to evaluation of Area, Surface and volume.

8. ** DIFFERENTIAL EQUATIONS**

Differential equations of first order and their solutions, Linear differential equations with constant coefficients, Homogenous lineardifferential equations, Orthogonal Trajectories, Singular solutions.

9. ** COORDINATE GEOMETRY**

2-d: Pair of straight lines, Transformation of coordinate system, Circles, Parabola, Ellipse and Hyperbola,Pair of tangents from a point, Chord of contact, Equation of chord in terms of middle point, Diameter of Conic, Conjugate diameter, Classification of curvesof second degree.

3-d: Introduction to lines and planes, Spheres, Quadric Cones and Cylinders

10. **LINEAR PROGRAMMING**

Linear inequalities with two variables, Mathematical formulation of L.P.P, Basic concepts of graphical and Simplex method.

11. **NUMERICAL ANALYSIS**

Interpolation, Extrapolation, Quadrature formula, Simpson’s1/3rd rule, Trapezoidal rule, Solution of non-linear equations using iterative methods, Numerical differentiation.

12. **STATISTICS**

Classifications of Data and frequency distribution, Calculation of measures of Central tendency and measures of dispersion, Skewness and Kurtosis, Permutation and Combination, Probability, Random variables and distribution functions, Mathematical expectations and generating functions, Binomial, Poisson, Geometric, Exponential and Normal distributions, Curve fitting and principal of least square, Correlation and Regression, Index numbers and their importance, Simple Time Series analysis, Sampling and large sample tests, test of significance based on t, Chi-square and F distributions.

**COMPUTER AWARENESS**

1. ** COMPUTER FUNDAMENTALS**

Organization of a computer, Central Processing Unit (CPU),Structure of instructions in CPU, input / output devices, computer Memory, memory organization, back-up devices.

2. ** DATA REPRESENTATION **

Representation of characters, integers, and fractions, binary and Hexadecimal representations

3. ** BINARY ARITHMETIC **

Addition, subtraction, division, multiplication, single arithmetic and two complement arithmetic, floating point representation of numbers, normalized floating point representation, Boolean Algebra, truth tables, Venn diagrams

4. ** COMPUTER ARCHITECTURE**

Block structure of computers, communication between processor and I / O devices, interrupts

5. ** COMPUTER LANGUAGE**

Assembly language and high level language, Multi-programming and time sharing operating systems, Computer Programming in C

6. ** MATHEMATICAL LOGIC**

Venn Diagrams in logic, Logical operators, Negations, Logical Equivalence and Tautology

7. **FLOW CHART ANDALGORITHMS**

8. ** DATA STRUCTURE**

**ANALYTICAL ABILITY ANDLOGICAL REASONING**

1. Logical Reasoning,

2. Quantitative Reasoning

3. Visuo-Spatial Reasoning

4. Analytical Reasoning

5. Data Interpretation

**ENGLISH**

1. Reading Comprehension

2. Grammar

3. Vocabulary