Fundamental Mathematics and Statistics

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This book tailored for Computer Science and Management courses. This comprehensive work has been meticulously crafted in alignment with the updated syllabi for BCA, BBA, and BBM programs, focusing on...

Name : Fundamental Mathematics and Statistics
Vendor : Prashant Publication
Type : Sem - III | BCA 301
Barcode : 9788119120895

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This book tailored for Computer Science and Management courses. This comprehensive work has been meticulously crafted in alignment with the updated syllabi for BCA, BBA, and BBM programs, focusing on the realm of Mathematics and Statistics.
Statistics, as a scientific discipline, finds applications in a multitude of diverse fields, spanning agriculture, industry, sociology, economics, business management, insurance, medicine, and more. Indeed, statistics has woven itself into the fabric of human activity, becoming an indispensable component of general education across numerous academic and professional domains.
The primary objective underpinning the creation of this book is to provide a lucid, systematic, and comprehensible exploration of mathematical and statistical concepts. Each topic has been articulated using straightforward language, ensuring that students can easily grasp the material. We have included a profusion of worked examples to elucidate these concepts effectively. Furthermore, the exercise problems have been thoughtfully designed, taking into account the academic backgrounds of students. It is our sincere hope that both students and educators will find this text invaluable in their teaching and learning endeavors.
This book comprises six meticulously organized chapters, thoughtfully structured to meet the requirements of the syllabus.

Chapter – 1

Mathematical Logic
1.1 Meaning of Statement
1.2 Primitive and Compound Statements
1.3 Truth Values of a Statement
1.4 Law of Excluded Middle
1.5 Logical Operations : Negation, Conjunction & Disjunction Implication, Double Implication, Equivalence
1.6 Equivalence of Logical Statements
1.7 Truth Tables & Construction of Truth Tables
1.8 Tautology and Contradiction
1.9 Argument : Valid And Invalid Arguments

Chapter – 2

Sets
2.1 Meaning of a Set
2.2 Methods of Describing a Set
2.2.1. Tabular Form
2.2.2. Set Builder Form
2.3 Types of a Set :
2.3.1. Finite Set, Infinite Set, Empty Set, Subset, Universal Set,
2.3.2. Equal Sets, Overlapping Sets, Disjoint Sets, Complementary Set.
2.4 Operations on Sets
2.4.1. Union of Sets
2.4.2. Intersection of Sets
2.4.3. Difference of Sets
2.5 Demorgan’s Laws (Without Proof)
2.6 Venn Diagrams
2.7 Cartesian Product of Two Sets
2.8 Statement of Following Laws (Without Proof) Relating To Union and Intersection of Sets : Idempotent Laws (ii) Identity Laws (iii) Commutative Laws (iv) Associative Laws (v) Distributive Laws

Chapter – 3

Matrices
3.1 Meaning of a Matrix, Order Of Matrix
3.2 Types of Matrix
3.2.1. Zero Matrix, Column Matrix, Square Matrix, Diagonal Matrix,
3.2.2. Scalar Matrix, Unit Matrix
3.2.3. Symmetric Matrix, Skew-Symmetric Matrix,
3.2.4. Transpose of a Matrix: Singular Matrix & Non-Singular Matrix.
3.3 Algebra of Matrices :
3.3.1. Equality of Matrices
3.3.2. Multiplication of Matrix by A Scalar
3.3.3. Negative of a Matrix
3.3.4. Multiplication of Matrices

Chapter – 4

Introduction to Statistics
4.1 Meaning of Statistics
4.2 Importance and Limitations of statistics
4.3 Meaning of data, Raw data, Primary data, Secondary data
4.4 Variable and attribute, Types of variable : districts and continuous
4.5 Meaning of Population and sample
4.6 Introduction to methods of sampling : simple random sampling and strafied random sampling

Chapter – 5

Measures of Central Tendency
5.1 Meaning and central tendency
5.2 Statement of measures of central tendency : arithmetic mean, geometric mean, harmonic mean, median and mode
5.3 Partition values : quartiles, deciles and percentiles

Chapter – 6

Mathematical and Statistical Calculations using MS-EXCEL
6.1 Step by step procedure to perform basic logical function using MS Excel
6.2 Step by step procedure to perform basic mathematical function using MS Excel
6.3 Step by step procedure to perform basic statistical function using MS Excel