Foundations of Mathematics

Paper Code: 
25GBCA101
Credits: 
03
Periods/week: 
03
Max. Marks: 
100.00
Objective: 

Course Objective:

The course will enable the students to

1.   Understand the basics of mathematics.

2.   This module is introductory in nature and focuses on numerical aspects, keeping           those students in mind who did not have mathematics at 10+2 level.

 

Course Outcomes: 

Course

Learning Outcome (at course level)

Learning and teaching

strategies

Assessment

Strategies

Course

Code

Course

Title

 

 

 

 

 

 

 

 

 

 

 

 

25GBCA

101

 

 

 

 

 

 

 

 

 

 

 

Foundations of Mathematics (Theory)

CO25.  Build a basic mathematical concepts and solve applied problems using matrices.

CO26.Evaluate problems related to set theory, relation and functions. CO27.Compute limits and derivatives of algebraic, logarithmic and exponential functions.

CO28.Compute anti- derivatives of general functions.

CO29. Interpret and solve problems related to permutations and combinations of a set and basic coordinate geometry. CO30.Contribut effectively in course-specific interaction.

Approach in teaching: Interactive Lectures, Discussion, Reading

assignments, Demonstration.

 

Learning activities for the students: Self- learning assignments, Problem based learning, Giving tasks.

Class test, Semester end examinations, Quiz, Assignments,

Presentation, Solving problems.

 

9.00
Unit I: 

Matrices and Determinants:

Matrices, Types of Matrices, Operations of addition, Scalar Multiplication and Multiplication of Matrices, Determinant of a Square Matrix, Minors and Cofactors. Transpose, adjoint and inverse of a matrix. Solving system of linear equations in two or three variables using inverse of amatrix.

 

9.00
Unit II: 

Sets, Relation & Functions:

Definition of Set, Type of Sets, Operations on Sets, Venn diagram, Cartesian Product, Relations, Functions, Types of function, Some elementary functions with their graphs (Exponential, logarithmic, modulus). Limit & continuity of a function (Simple Problems).

9.00
Unit III: 

Differentiation:  

Derivative  and  its  meaning,  Differentiation  of  algebraic,  trigonometric, exponential & logarithmic functions, Rules of Differentiation, Differentiation by substitution, Second order differentiation, Maxima and Minima of simple functions.

9.00
Unit IV: 

Integration: -

Indefinite Integrals, Rules of Integration, Integration by substitution, Integration by Partial Fractions, Definite Integration, Properties of Definite Integral, finding areas of simple closed curves.

9.00
Unit V: 

Permutation and Combination:  Fundamental Principles of Counting, Addition Principle, Factorial, Permutations, Combinations.

Coordinate Geometry: - 2D Cartesian Co-ordinate system. Straight line (Equation & Slope of aline). Circle: basic equation of Circle.

 

ESSENTIAL READINGS: 

SUGGESTED TEXT BOOKS

1. G. C. Sharma & Madhu Jain, “Mathematics for BCA”, Oscar Publication.

2. R.S.Agarwal, “Mathematics for class 12”, Bharati Bhavan, New Delhi.

3. S. L. Loney, “The Elements of Co-ordinate Geometry Part-I”, Book Palace, New Delhi.

 

REFERENCES: 

SUGGESTED REFERENCE BOOKS

1. Tom M. Apostol, “Calculus Volume II”, Second edition, John-Wiley & Sons, 2002.

2. S. Balachandra Rao, C.K. Shantha, “Differential Calculus”,New Age                            International(P) Ltd.

3. R.D. Sharma, “Mathematics for class 12 part-1”, Dhanpat Rai and Co. New Delhi.

4. R.D. Sharma, “Mathematics for class 12 Part-2”, Dhanpat Rai and Co. New Delhi.

e-RESOURCES:

1. Khan academy, mathematics 11 level: https://www.khanacademy.org/math/in-in-        grade-11- ncert

2. Khan academy, mathematics 11 level: https://www.khanacademy.org/math/in-in-        grade-12- ncert

JOURNALS:

1. Journal of Mathematics and Mathematical Sciences.

2. https://www.hindawi.com/journals/ijmms/

3. https://mathscinet.ams.org/mathscinet/

 

Academic Year: 
2025-26
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