B23-CAL-104 Mathematical Foundations for Computer Science-I
| Part A – Introduction | |||
| Subject | BCA(AI) | ||
| Semester | I | ||
| Name of the Course | Mathematical Foundations for Computer Science-I | ||
| Course Code | B23-CAL-104 | ||
| Course Type: (CC/MCC/MDC/CC- M/DSEC/VOC/DSE/PC/AEC/ VAC) | CC-M1 | ||
| Level of the course (As per Annexure-I | 100-199 | ||
| Pre-requisite for the course (if any) | |||
| Course Learning Outcomes (CLO): | After learning this course student will be able to:
1. Gain knowledge of set theory, types of sets, and operations on sets. Understand various concepts of matrices and determinants, and acquire the cognitive skills to apply different operations on matrices and determinants. 2. Know the basic concepts of complex numbers and acquire skills to solve linear quadratic equations. 3. Gain the knowledge of the concepts of Arithmetic progression, Geometric progression, and Harmonic progression, and find A.M., G.M., and H.M. of given numbers. 4. Understand the concept of differentiation 5. * Attain the skills to make use of the learned concepts of Introductory Mathematics in multidisciplinary learning contexts and to know their applications |
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| Credits | Theory | Practical | Total |
| 1 | 1 | 2 | |
| Contact Hours | 1 | 2 | 3 |
| Max. Marks:50(30(T)+20(P))
Internal Assessment Marks:15(10(T)+5(P)) End Term Exam Marks:35(20(T)+15(P)) |
Time: 3 Hrs.(T), 3Hrs.(P) | ||
| Part B-Contents of the Course | |||
| Instructions for Paper-Setter
The examiner will set a total of nine questions. Out of which first question will be compulsory. The remaining eight questions will be set from four units, selecting two questions from each. The examination will be of three-hour duration. All questions will carry equal marks. The first question will comprise short answer-type questions covering the entire syllabus. Candidate will have to attempt five questions in all, selecting one question from each unit. The first question will be compulsory. The practicum will be evaluated by an external and an internal examiner. The examination will be of three-hour duration. |
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| Unit | Topics | Contact Hours | |
| I | Sets and their representations, Empty sets, Finite and infinite sets, Subsets, Equal sets, Power sets, Universal sets, Union and intersection of sets, Difference of two sets, Complement of a set, Venn diagram, De-Morgan’s laws and their applications. | 4 | |
| II | An introduction to matrices and their types, Operations on matrices, Symmetric and skew-symmetric matrices, Minors, and Co-factors. Determinant of a square matrix, Adjoint and inverse of a square matrix, Solutions of a system of linear equations up to order 3. | 4 | |
| III | Quadratic equations, Solution of quadratic equations. Arithmetic progression, Geometric progression, Harmonic progression, Arithmetic mean (A.M.), Geometric mean (G.M.), Harmonic mean (H.M.), Relation between A.M., G.M. and H.M. | 3 | |
| IV | The concept of differentiation, differentiation of simple functions, and Use of differentiation for solving problems related to real-life situations. Differentiation of simple algebraic, trigonometric, and exponential functions. | 4 | |
| V* | Practicum:
Students are advised to do laboratory/practical practice not limited to but including the following types of problems: Problem-Solving– Questions related to the practical problems based on t h e following topics will be worked out and a record ofthose will be maintained in the Practical Note Book: · Problems related to union, intersection, difference, andcomplement of sets. · Problems based on De Morgan’s Laws. · Problems related to Venn diagrams. · Problems to find the inverse of a matrix. · Problems to find the determinant of a square matrix oforder 3. · Problems to find nth term of A.P., G.P., and H.P. · Problems to find the sum of n terms of A.P., G.P., and H.P. · Problems to find A.M., G.M., and H.M. of givennumbers. · Problems involving formulation and solution of quadratic equations in one variable. · Problems to find the first derivatives of functions. |
30 |
| Suggested Evaluation Methods | ||
| Internal Assessment:
➢ Theory · Class Participation: 4 · Seminar/presentation/assignment/quiz/class test etc.: NA · Mid-Term Exam: 6 ➢ Practicum · Class Participation: NA · Seminar/Demonstration/Viva-voce/Lab records etc.: 5 · Mid-Term Exam: NA |
End Term Examination:
A three-hour exam for both theory and practicum. |
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| Part C-Learning Resources | ||
| Text /Reference Books:
· C. Y. Young (2021). Algebra and Trigonometry. Wiley. · S.L. Loney (2016). The Elements of Coordinate Geometry (Cartesian Coordinates) (2nd Edition). G.K. Publication Private Limited. · Seymour Lipschutz and Marc Lars Lipson (2013). Linear Algebra. (4th Edition) Schaum’s Outline Series, McGraw-Hill. · C.C. Pinter (2014). A Book of Set Theory. Dover Publications. · J. V. Dyke, J. Rogers and H. Adams (2011). Fundamentals of Mathematics (10th Edition), Brooks/Cole. · A.Tussy, R. Gustafson and D. Koenig (2010). Basic Mathematics for College Students (4th Edition). Brooks Cole |
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