MATHEMATICAL FUNDAMENTALS

Paper Code: 
24MCA(B)120C
Credits: 
04
Periods/week: 
04
Max. Marks: 
100.00
Objective: 

This course enable student to

  1. Define the concepts and operations of matrix algebra.
  2. Understand the concepts of probability, Bayes’ theorem and independence problems.
  3. Illustrate the basic concepts of sets, relations and functions.
  4. Differentiate between Differentiation and Integration.
  5. Evaluate the understanding of the concepts by applying them in different domains.
  6. Develop the skills to solve the problem using mathematical ability.

 

Course Outcomes: 

  

Course

Learning Outcome (at course level)

Learning and teaching strategies

Assessment Strategies

Course Code

Course

Title

 

24MCA(B) 120(C)

Mathematical Fundamentals

(Theory)

  1. Analyse the concepts and operations of matrix algebra.
  2. Evaluate and apply basic concepts of probability and theorems.
  3. Demonstrate and apply the concepts of differentiation and integration.
  4. Examine the use of data representation in computer science.
  5. Evaluate and analyze the problem using sets and relations.
  6. Contribute effectively in course-specific interaction

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstration, Team teaching

Learning activities for the students:

Self-learning assignments, Effective questions, Simulation, Seminar presentation, Giving tasks, Field practical

  • Assignments
  • Written test in classroom
  • Classroom activity
  • Written test in classroom
  • Semester End Examination

 

12.00
Unit I: 
Introduction to Matrices

  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.

12.00
Unit II: 
Sets, Relations & Functions

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).

12.00
Unit III: 
Differentiation and Integration

Differentiation: Derivative and its meaning, Differentiation of algebraic, trigonometric, exponential & logarithmic functions, Rules of Differentiation.

Integration: - Integral as Anti-derivative process, Indefinite Integrals, Rules of Integration.

12.00
Unit IV: 
Data Representation

Data Representation - Floating point Arithmetic – Addition, Subtraction, Multiplication and Division operation. Pitfall of floating point representation, Errors in numerical computation Iterative Methods, Measurement of Accuracy by using Absolute Error and Relative Error.

 

12.00
Unit V: 
Probability & Statistics

Probability Classical, relative frequency and axiomatic definitions of probability, addition rule and conditional probability, multiplication rule, total probability, Bayes’ Theorem and independence problems. Introduction to Statistics- Population, Sample, Variable, Descriptive Statistics-Mean, Mode, Median, Variance, Standard Deviation, Correlation, Regression.

 

ESSENTIAL READINGS: 

  

  1. R. D. Sharma, “Mathematics Vol-2”, Dhalpat Raj & Sons, 2021
  2. Seymour Lipschutz, Marc Laras Lipson,  “ Discrete Mathematics (Schaum's Outlines) (SIE)”, McGraw Hill, 4th Edition, 2021.
  3. Santosh Kumar Sengar “Computer Based Numerical and Statistical Techniques Paperback”, S. Chand Publishing, 4th Edition (1 January 2019)
REFERENCES: 

   Suggested Reading:

  1. David Makinson, “Sets, Logic and Maths for Computing”, Springer Indian Reprint, 2011.
  2. Edgar Goodaire ,”Discrete Mathematics with Graph Theory” Pearson Education, 2019.

      

  E- Resources

  1. Mathematics XII by NPTEL(https://onlinecourses.swayam2.ac.in/nce19_sc11/preview)
  2. Foundation in Mathematics and Statistics (http://egyankosh.ac.in/bitstream/123456789/20431/1/Introduction.pdf)
  3. Basic Calculus-1 by SWAYAM(https://www.classcentral.com/course/swayam-basic-calculus-1-22910)
  4. Mathematical Foundations of Computing (http://web.stanford.edu/class/archive/cs/cs103/cs103.1184/)

Journals

1.Foundations of Computational Mathematics, Springer (https://www.springer.com/journal/10208)            2.Mathematical Foundations of Computing, American Institute of Mathematical Sciences (https://www.aimsciences.org/journal/A0000 -0001#:~:text=Mathematical%20Foundations%20of%20Computing%20(MFC,pressing%20challenges%20in%20data%20analysis )                                                                                                     3.International Journal of Foundations of Computer Science, Word Scientific (https://www.worldscientific.com/worldscinet/ijfcs )                                                                       4.Mathematical Foundations of Computing, Web of Science(https://publons.com/journal/250682/mathematical-foundations-of-computing/ )

 

Academic Year: 
2024-25
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