Discrete Mathematics and Statistics

Unit

Contents

Hours

1

Set Theory and Logic

Sets– Set Theory, Need for Sets, Representation of Sets, Set Operations, cardinality of set, Types of Sets – Bounded and Unbounded Sets, Countable and Uncountable Sets, Finite and Infinite Sets, Countably Infinite and Uncountably Infinite Sets, power set, Propositional Logic- logic, Propositional Equivalences, Application of Propositional Logic-Translating English Sentences, Proof by Mathematical Induction and Strong

Mathematical Induction.

06

2

Relations and Functions

Relations: Properties, n-ary Relations and Applications, Representing Relations, Closures of Relations, Equivalence Relations, Partial Orderings, partitions, Hasse Diagram, Lattices, Chains and Anti-Chains, Transitive Closure and Warshall‘s Algorithm.

Functions- Surjective, Injective and Bijective functions, Inverse Functions and Compositions of Functions.

06

3

Counting and Probability

The Basics of Counting, rule of Sum and Product, Permutations and Combinations, Binomial Coefficients and Identities, Generalized Permutations and Combinations, The

Pigeonhole Principle.

Probability: Basic Concepts, Definition, Addition and Multiplication Theorems, Conditional probability and Bayes’ Theorem

06

4

Data Presentation and Aggregation

Data Types: Attribute, variable, discrete and continuous variable, Data presentation: frequency distribution, histogram, ogive, box-plot, bar plots. Measures of Central Tendency: Arithmetic Mean (AM), Weighted Arithmetic Mean, Arithmetic Mean Computed from Grouped Data, Concept of Median, Mode, Geometric Mean (GM), Harmonic Mean (HM), Quartiles, Deciles, and Percentiles. Measures of Dispersion: Standard Deviation, Root Mean Square, Variance, Absolute and Relative Dispersion.

06

5

Correlation Theory and Sampling

Correlation: Bivariate data scatter plots, Linear Correlation, Correlation of Attributes, Coefficient of correlation, Regression: Concept, Linear Regression, Prection. Elementary Sampling Theory : Sampling Theory, Random Samples, Sampling With and Without Replacement, Stratified Sampling

06

Unit

Contents

Hours

1

Set Theory and Logic

Sets– Set Theory, Need for Sets, Representation of Sets, Set Operations, cardinality of set, Types of Sets – Bounded and Unbounded Sets, Countable and Uncountable Sets, Finite and Infinite Sets, Countably Infinite and Uncountably Infinite Sets, power set, Propositional Logic- logic, Propositional Equivalences, Application of Propositional Logic-Translating English Sentences, Proof by Mathematical Induction and Strong Mathematical Induction.

06

2

Relations and Functions

Relations: Properties, n-ary Relations and Applications, Representing Relations, Closures of Relations, Equivalence Relations, Partial Orderings, partitions, Hasse Diagram, Lattices, Chains and Anti-Chains, Transitive Closure and Warshall’s Algorithm.

Functions- Surjective, Injective and Bijective functions, Inverse Functions and Compositions of Functions.

06

3

Counting and Probability

The Basics of Counting, rule of Sum and Product, Permutations and Combinations, Binomial Coefficients and Identities, Generalized Permutations and Combinations, The Pigeonhole Principle. Probability: Basic Concepts, Definition, Addition and Multiplication Theorems, Conditional  probability and Bayes’ Theorem

06

4

Data Presentation and Aggregation

Data Types: Attribute variable, discrete and continuous variable, Data presentation: frequency distribution, histogram, ogive, box-plot, bar plots. Measures of Central Tendency: Arithmetic Mean (AM), Weighted Arithmetic Mean, Arithmetic Mean Computed from Grouped Data, Concept of Median, Mode, Geometric Mean (GM), Harmonic Mean (HM), Quartiles, Deciles, and Percentiles. Measures of Dispersion: Standard Deviation, Root Mean Square, Variance, Absolute and Relative Dispersion

06

5

Correlation Theory and Sampling

Correlation: Bivariate data, scatter plots, Linear Correlation, Correlation of Attributes, Coefficient of correlation. Regression: Concept, Linear Regression, Prection. Elementary Sampling Theory : Sampling Theory, Random Samples, Sampling With and Without Replacement, Stratified Sampling

06

Unit

Contents

Hours

1

Set Theory and Logic

Sets– Set Theory, Need for Sets, Representation of Sets, Set Operations, cardinality of  set, Types of Sets – Bounded and Unbounded Sets, Countable and Uncountable Sets, Finite and Infinite Sets, Countably Infinite and Uncountably Infinite Sets, power set, Propositional Logic- logic, Propositional Equivalences, Application of Propositional, Logic-Translating English Sentences, Proof by Mathematical Induction and Strong

Mathematical Induction.

06

2

Relations and Functions

Relations: Properties, n-ary Relations and Applications, Representing Relations, Closures of Relations, Equivalence Relations, Partial Orderings, partitions, Hasse Diagram, Lattices, Chains and Anti-Chains, Transitive Closure and Warshall’s Algorithm. Functions- Surjective, Injective and Bijective functions, Inverse Functions and  Compositions of Functions.

07

3

Counting and Probability

The Basics of Counting, rule of Sum and Product, Permutations and Combinations, Binomial Coefficients and Identities, Generalized Permutations and Combinations, The Pigeonhole Principle.  Probability: Basic Concepts, Definition, Addition and Multiplication Theorems, Conditional probability and Bayes’ Theorem

05

4

Data Presentation and Aggregation

Data Types: Attribute, variable, discrete and continuous variable, Data presentation:  frequency distribution, histogram, ogive, box-plot, bar plots. Measures of Central Tendency: Arithmetic Mean (AM), Weighted Arithmetic Mean,  Arithmetic Mean Computed from Grouped Data, Concept of Median, Mode, Geometric Mean (GM), Harmonic Mean (HM), Quartiles, Deciles, and Percentiles Measures of Dispersion: Standard Deviation, Root Mean Square, Variance, Absolute  and Relative Dispersion.

06

5

Correlation Theory and Sampling

Correlation: Bivariate data, scatter plots, Linear Correlation, Correlation of Attributes, Coefficient of correlation Regression: Concept, Linear Regression, Prection, Elementary Sampling Theory : Sampling Theory, Random Samples, Sampling With

and Without Replacement, Stratified Sampling

06