Foundations of Mathematics (Theory)

Paper Code: 
24GBCA101
Credits: 
03
Periods/week: 
03
Max. Marks: 
100.00
Objective: 

The course will enable the students to

  1. Understand the basics of mathematics.This course 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

24GBCA 101

Foundations of Mathematics

(Theory)

 

CO25.  Build a foundation of 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 Contribute   effectively in

 course-specific interaction

Approach in teaching: Interactive Lectures, Discussion, Reading assignments, Demonstration.

 

Learning activities for the students: Self learning assignments, Effective questions, Seminar presentation

Class test, Semester end examinations, Quiz, Assignments, Presentation.

 

9.00
Unit I: 
Matrices and Determinant

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 a matrix.

 

9.00
Unit II: 
Set Theory

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 a line). 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. https://www.hindawi.com/journals/ijmms/
  2. https://mathscinet.ams.org/mathscinet/

 

Academic Year: 
2024-25
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