Foundations of Mathematics

Paper Code: 
25GBCA101
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

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25GBC A 101

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Foundations of Mathematic s

(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.Comput e               anti derivatives    of general functions. CO29. Interpret    and solve  problems related         to

Approach in teaching:Interacti ve 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 invers e of amatrix.

 

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: 

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 READINGS:

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: 
2025-26
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