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1. REAL ANALYSIS
Real numbers - Rational numbers - finite and infinite sets - countable and
uncountable sets -open and closed sets - limit points sequence and series of real numbers
convergence of sequence and series of real numbers - limits of sequence and series -
continuous functions - compactness -Riemann integrals - beta and gamma functions —
cantor set
2. ALGEBRA
Integers - divisibility - prime numbers - congruence - Fermat’s theorem - Euler’s
theorem -Matrices - rank of a matrix - characteristic values and characteristic vectors -
symmetric , skew symmetric , Hermition , skew Hermition , and orthogonal matrices -
Roots of polynomials – Cardan’s solution of cubic equation - Ferrari’s solution of
biquadratic equation - Descartes’ rule of signs
3. MODERN ALGEBRA
Binary compositions - Groups - Rings - Integral domains - Fields - Vector spaces -
Basis of finite dimensional vector spaces - Dimension of a vector space - linear
transformations- definition of Boolean Algebra
4. CALCULUS
Functions and graphs - algebraic ,trigonometric and exponential limits -
derivability and derivative - concavity and points of inflection - curvature - asymptotes -
Hyperbolic Functions - Mean value theorems - higher derivatives -Partial derivatives -
Applications of Integration - Differential equations
5. COMPLEX ANALYSIS
Complex Numbers - Polar form - Analytic Functions - Power series - Zeroes of an
analytic Function - Residues and contour integration
PART. II - STATISTICS
1. BASICS OF DATA COLLECTION:
Collection of data-Methods of data collection-Primary and Secondary data—
Classification and Tabulation—Frequency distribution— Diagrammatic and Graphic
presentation of data — Ogives.
2. DESCRIPTIVE STATISTICS:
Measures of central values (AM,GM,HM, Median, Mode)-Measures of variations
(QD, MD, SD, coefficient of variation)- partition values- skewness and kurtosis.
3. CORRELATION AND REGRESSION:
Pearson’s correlation coefficient and rank correlation coefficient - coefficient of
determination- Regression — simple linear regression, the two regression lines,
regression coefficients and their properties.
4. PROBABILITY THEORY:
Definitions of probability- Addition and multiplication theorem - Conditional
probability- Bayes’ Theorem.
5. RANDOM VARIABLE AND PROBABILITY DISTRIBUTION:
Probability density function and cumulative distribution- marginal and conditional
distributions, independence of random variables- Expectation of a random variable,
moments, moment generating function.
6. STANDARD DISTRIBUTIONS:
Bernoulli, Binomial, Poisson — Geometric- Uniform-Normal distributions.
7. SAMPLING THEORY:-
Population and sample— advantages of sampling over census —Random Sampling
and non-random sampling- methods of drawing random samples from a finite
population (SRS, Systematic, Stratified, Multistage and Cluster sampling)- sampling
error and non-sampling error.
8. SAMPLING DISTRIBUTIONS:
Sampling from a normal population, sampling distributions of the sample mean and
variance. Chi-square, student’s t and F distributions
9. ESTIMATION THEORY:
Parameter and Statistic- Point estimation, unbiased ness, consistency, sufficiency,
Fisher Neyman factorization criterion, efficiency. - Methods of estimation, method of
moments, method of maximum likelihood Interval estimates of mean, difference of
means, variance.
1O. TESTING OF HYPOTHESIS:
Simple and composite hypotheses, null and alternative hypotheses, type I and, type II
errors, critical region, level of significance and power of a test Neymann-Pearson
approach-Large sample tests concerning mean, equality of means. Small sample tests
based on t distribution for mean, equality of means and paired t-test for paired data.
Tests based on F distribution for ratio of variances. Test based on chi squaredistribution for variance, goodness of fit and for independence of attributes. One-way
ANOVA.
PART. III - COMPUTER PROGRAMMING
1. BASIC SCIENCES & MATHEMATICS
Binomial series - coordinate geometry - differential equations - eigen values &
eigen vectors - relations & functions - graph connectedness - planarity -
Hamiltonian / Eulerian graph.
Operations Research - linear programming - game theory.
2. HARDWARE & MICROPROCESSORS
Passive components - Semiconductors - Transistors.
Number systems - logic families - sequential circuits - flip-flops - counters - RAM
and ROM.
8085 microprocessor - direct memory access - 8051 microcontroller and
applications -
8051 programming - 8251, 8253, 8255, 8257, 8259 and 8279 chips - 8086
microprocessor. 3. DATA STRUCTURES, OBJECT ORIENTED CONCEPTS &
PROGRAMMING
C Programming - pointers - doubly linked lists - dynamic memory allocation -
stack, queue, double-ended queue, tree, graph operations - in-order, pre-order,
post-order traversals - binary search tree - DFS, BFS - shortest path algorithm -
bubble sort, insertion sort, quicksort, heapsort, merge sort - linear search - binary
search - object-oriented programming concepts - C++ programming - multiple
inheritance - files and streams - Java programming - exception handling -
multithreading - applets -servlets.
4. SYSTEM SOFTWARE, DBMS & SOFTWARE ENGINEERING
Data-models- relational model -functional dependency- normalization - SQL. -
Assembler - macro - linker - loader - compiler - lexical analyser - syntax analyser
-storage assignment - code generation.
Operating Systems - CPU scheduling - synchronization - deadlock - address
binding -memory allocation methods - page replacement - virtual memory - file
systems - disk scheduling.
Software life cycle models - SRS - principles of software design - project
management - cost estimation.
5. COMPUTER NETWORKS & WEB TECHNOLOGIES
Data communication - network topologies - LAN, MAN, WAN – ISO/OSI model
-manchester encoding - ASK, FSK, PSK - Quadrature Amplitude Modulation -
transmission media - multiplexing - IEEE 802 standards. -
Data link layer protocols - CSMA - point-to-point protocol - ATM - bridge -
router -distance vector routing - link state routing - TCPIIP - UDP - DHCP -
domain name service - FTP, TFTP, telnet, SMTP, POP, SNMP, HTTP - mobile
computing— wireless LAN - bluetooth.
Socket programming - remote method invocation - proxy server – internet
security -firewall - IIS and Apache server - HTML - XML - style sheet -
javascript - PHP – web design - flash - dreamweaver - web hosting.
NOTE: - It may be noted that apart from the topics
detailed above, questions from other topics
prescribed for the educational qualification of the
post may also appear in the question paper. There is
no undertaking that all the topics above may be
covered in the question paper.
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FULL SYLLABUS OF PROGRAMMER
KERALA STATE PLANNING BOARD
(CATEGORY NO. 441/2009)
PART. I - MATHEMATICS1. REAL ANALYSIS
Real numbers - Rational numbers - finite and infinite sets - countable and
uncountable sets -open and closed sets - limit points sequence and series of real numbers
convergence of sequence and series of real numbers - limits of sequence and series -
continuous functions - compactness -Riemann integrals - beta and gamma functions —
cantor set
2. ALGEBRA
Integers - divisibility - prime numbers - congruence - Fermat’s theorem - Euler’s
theorem -Matrices - rank of a matrix - characteristic values and characteristic vectors -
symmetric , skew symmetric , Hermition , skew Hermition , and orthogonal matrices -
Roots of polynomials – Cardan’s solution of cubic equation - Ferrari’s solution of
biquadratic equation - Descartes’ rule of signs
3. MODERN ALGEBRA
Binary compositions - Groups - Rings - Integral domains - Fields - Vector spaces -
Basis of finite dimensional vector spaces - Dimension of a vector space - linear
transformations- definition of Boolean Algebra
4. CALCULUS
Functions and graphs - algebraic ,trigonometric and exponential limits -
derivability and derivative - concavity and points of inflection - curvature - asymptotes -
Hyperbolic Functions - Mean value theorems - higher derivatives -Partial derivatives -
Applications of Integration - Differential equations
5. COMPLEX ANALYSIS
Complex Numbers - Polar form - Analytic Functions - Power series - Zeroes of an
analytic Function - Residues and contour integration
PART. II - STATISTICS
1. BASICS OF DATA COLLECTION:
Collection of data-Methods of data collection-Primary and Secondary data—
Classification and Tabulation—Frequency distribution— Diagrammatic and Graphic
presentation of data — Ogives.
2. DESCRIPTIVE STATISTICS:
Measures of central values (AM,GM,HM, Median, Mode)-Measures of variations
(QD, MD, SD, coefficient of variation)- partition values- skewness and kurtosis.
3. CORRELATION AND REGRESSION:
Pearson’s correlation coefficient and rank correlation coefficient - coefficient of
determination- Regression — simple linear regression, the two regression lines,
regression coefficients and their properties.
4. PROBABILITY THEORY:
Definitions of probability- Addition and multiplication theorem - Conditional
probability- Bayes’ Theorem.
5. RANDOM VARIABLE AND PROBABILITY DISTRIBUTION:
Probability density function and cumulative distribution- marginal and conditional
distributions, independence of random variables- Expectation of a random variable,
moments, moment generating function.
6. STANDARD DISTRIBUTIONS:
Bernoulli, Binomial, Poisson — Geometric- Uniform-Normal distributions.
7. SAMPLING THEORY:-
Population and sample— advantages of sampling over census —Random Sampling
and non-random sampling- methods of drawing random samples from a finite
population (SRS, Systematic, Stratified, Multistage and Cluster sampling)- sampling
error and non-sampling error.
8. SAMPLING DISTRIBUTIONS:
Sampling from a normal population, sampling distributions of the sample mean and
variance. Chi-square, student’s t and F distributions
9. ESTIMATION THEORY:
Parameter and Statistic- Point estimation, unbiased ness, consistency, sufficiency,
Fisher Neyman factorization criterion, efficiency. - Methods of estimation, method of
moments, method of maximum likelihood Interval estimates of mean, difference of
means, variance.
1O. TESTING OF HYPOTHESIS:
Simple and composite hypotheses, null and alternative hypotheses, type I and, type II
errors, critical region, level of significance and power of a test Neymann-Pearson
approach-Large sample tests concerning mean, equality of means. Small sample tests
based on t distribution for mean, equality of means and paired t-test for paired data.
Tests based on F distribution for ratio of variances. Test based on chi squaredistribution for variance, goodness of fit and for independence of attributes. One-way
ANOVA.
PART. III - COMPUTER PROGRAMMING
1. BASIC SCIENCES & MATHEMATICS
Binomial series - coordinate geometry - differential equations - eigen values &
eigen vectors - relations & functions - graph connectedness - planarity -
Hamiltonian / Eulerian graph.
Operations Research - linear programming - game theory.
2. HARDWARE & MICROPROCESSORS
Passive components - Semiconductors - Transistors.
Number systems - logic families - sequential circuits - flip-flops - counters - RAM
and ROM.
8085 microprocessor - direct memory access - 8051 microcontroller and
applications -
8051 programming - 8251, 8253, 8255, 8257, 8259 and 8279 chips - 8086
microprocessor. 3. DATA STRUCTURES, OBJECT ORIENTED CONCEPTS &
PROGRAMMING
C Programming - pointers - doubly linked lists - dynamic memory allocation -
stack, queue, double-ended queue, tree, graph operations - in-order, pre-order,
post-order traversals - binary search tree - DFS, BFS - shortest path algorithm -
bubble sort, insertion sort, quicksort, heapsort, merge sort - linear search - binary
search - object-oriented programming concepts - C++ programming - multiple
inheritance - files and streams - Java programming - exception handling -
multithreading - applets -servlets.
4. SYSTEM SOFTWARE, DBMS & SOFTWARE ENGINEERING
Data-models- relational model -functional dependency- normalization - SQL. -
Assembler - macro - linker - loader - compiler - lexical analyser - syntax analyser
-storage assignment - code generation.
Operating Systems - CPU scheduling - synchronization - deadlock - address
binding -memory allocation methods - page replacement - virtual memory - file
systems - disk scheduling.
Software life cycle models - SRS - principles of software design - project
management - cost estimation.
5. COMPUTER NETWORKS & WEB TECHNOLOGIES
Data communication - network topologies - LAN, MAN, WAN – ISO/OSI model
-manchester encoding - ASK, FSK, PSK - Quadrature Amplitude Modulation -
transmission media - multiplexing - IEEE 802 standards. -
Data link layer protocols - CSMA - point-to-point protocol - ATM - bridge -
router -distance vector routing - link state routing - TCPIIP - UDP - DHCP -
domain name service - FTP, TFTP, telnet, SMTP, POP, SNMP, HTTP - mobile
computing— wireless LAN - bluetooth.
Socket programming - remote method invocation - proxy server – internet
security -firewall - IIS and Apache server - HTML - XML - style sheet -
javascript - PHP – web design - flash - dreamweaver - web hosting.
NOTE: - It may be noted that apart from the topics
detailed above, questions from other topics
prescribed for the educational qualification of the
post may also appear in the question paper. There is
no undertaking that all the topics above may be
covered in the question paper.
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