Bridge Course (MCA-BC- 23-21 Mathematical Foundations for Computer Science)
| MCA-BC-23-21: Mathematical Foundations for Computer Science | |
| Type: Bridge Course (For students who have not studied mathematics at 10+2/graduation)
Course Credits: 00 Contact Hours: 4 hours/week Examination Duration: 3 Hours Mode: Lecture External Maximum Marks: 75 External Pass Marks: 30(i.e. 40%) Internal Maximum Marks: 25 Total Maximum Marks: 100 Total Pass Marks: 40(i.e. 40%) |
Instructions to paper setter for End semester exam:
Total number of questions shall be nine. Question number one will be compulsory and will be consisting of short/objective type questions from complete syllabus. In addition to compulsory first question there shall be four units in the question paper each consisting of two questions. Student will attempt one question from each unit in addition to compulsory question. All questions will carry equal marks. |
| Course Objectives: The objective of this paper is to make the students familiar with the commonly used mathematics and statistics in the field of computer science. | |
| Unit – I
Sets: Set theory: Basic concept, set types, set operations, cardinality, and notation. Relations: Relations and its representations, Properties of binary relation –Reflexive, symmetric, Asymmetric, transitive, Equivalence, Inverse & Composition of a relation, closure of relations, its types, Partial ordering relation, Hasse diagram, minimal elements, upper bound, lower bound, Lattices Functions: definition, floor functions, ceiling functions, surjective, injunctive and bijective functions, Inverse Function, Composition of functions, recursive Functions, Pigeon hole principles and its application. |
|
| Unit – II
Addition and multiplication of matrices, Laws of matrix algebra, Singular and non-singular matrices, Inverse of a matrix, Systems of linear equations, Eigen values and Eigen vectors, Diagonalization of a square matrix. Interpolation, Numerical Integration and Differentiation. |
|
| Unit – III
Statistical Methods: Definition and scope of Statistics, concepts of statistical population and sample. Data: Quantitative and qualitative, attributes, variables, scales of measurement nominal, ordinal, interval and ratio. Presentation: tabular and graphical, including histogram and ogives. Measures of Central Tendency: Mean, Median, Mode. Measures of Dispersion: range, quartile deviation, mean deviation, standard deviation, coefficient of variation, Moments, skewness and kurtosis. |
|
| Unit – IV
Bivariate data: Definition, scatter diagram, simple, partial and multiple correlation (3 variables only), rank correlation. Simple linear regression, principle of least squares and fitting of polynomials and exponential curves. |
|
| Probability: Introduction, random experiments, sample space, events and algebra of events. Definitions of Probability – classical, statistical, and axiomatic. Conditional Probability, laws of addition and multiplication, independent events, theorem of total probability, Bayes’ theorem and its applications. |
| Text Books:
1. Gupta, S. C. and Kapoor, V.K. : Fundamentals Of Mathematical Statistics, Sultan Chand &Sons 2. Seymour Lipschutz, Marc Lars Lipson, Discrete mathematics, McGraw-Hill international editions, Schaum’s series. 3. V. Rajaraman, Computer-Oriented Numerical Methods., PHI |
| Reference Books:
1. Kenneth H. Rosen, Discrete Mathematics and its Applications, Tata McGraw – Hill 2. Hogg, R.V., Tanis, E.A. and Rao J.M. : Probability and Statistical Inference, Seventh Ed, Pearson Education, New Delhi. 3. Goon A.M., Gupta M.K. and Dasgupta B. (2002): Fundamentals of Statistics, Vol. I & II, The World Press, Kolkata. 4. Babu Ram: Discrete Mathematics 5. Shanti Narayana : Differential & Integral calculus |
