Course Name
BCA (Bachelor of Computer Application)
Subject Code BC0033 (Basic Mathematics)
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PART  A
PART  B
PART  C
Basic Mathematics Syllabus.
Unit 1 Set Theory
Sets, types of sets, operation on sets, Venn diagrams, Cartesians product of
two sets, Distributive laws
Unit 2 Mathematical logic
Proposition or statements, converse, inverse and contrapositive of an
implication
Unit 3 Modern algebra
Binary operation, semi groups, monoid, group
Unit 4 Subgroups and other groups
Subgroups, cosets, cyclic groups, group of permutations
Unit 5 Basic graph theory
Definition of graphs, multigraphs, complete graphs, null graphs, bigraphs,
degrees, degree sequences
Unit 6 Data analysis
Data and statistical data, Frequency distribution, graphical representation,
measures of central tendency, measures of dispersion
Unit 7 Permutation and combination
Fundamental principles, Permutation and Combination, Permutation of n
different things taken r at a time, Permutation of things of which some are
alike, circular permutation,
combinations, complementary combinations
Unit 8 Probability
Random experiment, sample space, event, probability additional theorem,
classical approach, conditional probability, independent events, multiplication
theorem, empirical
approach
Unit 9 Elements of trigonometry
Radian and circular measure, trigonometric functions, identities,
trigonometrical ratios of certain standard angles, allied angles, compound
angles, multiple and sub multiple angles
Unit 10 Limits
Definition of limits, continuity, evaluation of limits, some of the standard
limits with their derivations, exponential limit
Unit11 Continuity and differential calculus
Differentiation, equations of tangent and normal, pedal equations, polar
coordinates, angle between radius vector and tangent, successive
differentiation, indeterminate forms, partial
differentiation
Unit 12 Integral Calculus
Integration by parts, integral as the limit of a sum, reduction formulae,
integration of algebraic rational functions, integration of irrational
functions, definite integrals and
evaluation.
Unit 13 Complex Trigonometry
Complex number definition, De Moivre’s theorem, Roots of a complex number,
Exponential function of a complex variable, hyperbolic functions, logarithmic
function of a
complex variable.
Unit 14 Matrices and determinants
Matrices, related matrices, matrix method of solution of simultaneous
equations, elementary transformation of a matrix.
Unit 15 Infinite series
Convergence and divergence, series of positive terms, Binomial series,
exponential series, logarithmic series.
Unit 16 Differential equations
First order differential equations, Practical approach to differential
equations, first order and first degree differential equations, homogeneous
equations, linear equations, Bernoulli’s
equations, exact differential equations.
