Discrete Mathematics – Course Handout (MJBC122)
📘 Course Overview
Discrete Mathematics (MJBC122)
Program: BCA General – Semester 2
University: The ICFAI University, Jaipur
This course introduces the key structures and reasoning tools of discrete mathematics with emphasis on computer science applications including logic, sets, counting, relations, functions, graphs, trees, Boolean algebra, and introductory group theory.
👨🏫 Instructor Information
| Role | Name | Room No. | |
|---|---|---|---|
| Instructor In-Charge | Dr. VK Vyas | 008 | vkvyas@iujaipur.edu.in |
| Instructor | Ms. Payal Singhal | – | psinghal@iujaipur.edu.in |
To be announced in class. Students may meet the faculty during consultation hours without prior appointment.
🎯 Objectives & Outcomes
🎯 Course Objectives
- Introduce concepts of mathematical logic, sets, counting principles, relations, and functions
- Build understanding of Boolean algebra, graph theory, and trees
- Provide basics of group theory for discrete modelling
✅ Course Outcomes (COs)
After completing this course, students will be able to:
- CO1: Understand sets, their properties, operations, and applications
- CO2: Apply counting principles & logic for problem solving and proofs
- CO3: Use graphs, trees, Boolean algebra & group theory in discrete modelling
🧭 Visual Roadmap
This roadmap shows the order of topics across the semester.
📅 Lecture-wise Plan
| Lectures | Unit / Theme | Topics Covered | Textbook Ref. | CO |
|---|---|---|---|---|
| 1–5 | Set Theory Basics | Sets, types of sets, subsets, Venn diagram, set operations, algebra of sets | T1: 1.1–1.8 | CO1 |
| 6–10 | Induction | Inclusion–Exclusion principle, mathematical induction | T1: 1.9–1.11 | CO1 |
| 11–14 | Functions & Relations | Cartesian product, relations, functions, composition, types | T1: 2.1–2.9 | CO1 |
| 15–17 | Counting Principles | Counting, factorial, permutation, combination, binomial coefficients | T1: 6.1–6.5 | CO2 |
| 18–20 | Advanced Counting | Pigeonhole, partitions | T1: 6.6–6.8 | CO2 |
| 21–25 | Logic | Propositions, truth tables, connectives, duality | T1: 4.3–4.12 | CO2 |
| 26–28 | Boolean Algebra | Properties, theorem, lattices | T1: 15.1–15.5 | CO3 |
| 29–32 | Graph Basics | Terminologies, degree, Euler graphs, Dijkstra algorithm | T2: C1–C2 | CO3 |
| 33–35 | Paths & Circuits | Connected/disconnected, Euler/Hamilton, graph operations | T2: C3 | CO3 |
| 36–40 | Trees | Rooted/binary trees, spanning trees, MST algorithms | T2: C4 | CO3 |
| 41–42 | Group Theory | Semi-group, group, subgroup, operations | T1: 12.1–12.5 | CO3 |
✅ After every unit, do 10–15 practice questions. ✅ For graphs/trees, always solve with diagrams.
📈 Evaluation Scheme
Continuous assessment + final comprehensive exam.
| Component | Duration | Weightage | Coverage | Mode |
|---|---|---|---|---|
| Test-I / Quiz | 50 min | 10% | Lec 1–10 | Closed Book |
| Mid-Sem Exam | 1 hour | 20% | Lec 1–20 | Closed Book |
| Test-II / Quiz | 50 min | 10% | Lec 21–32 | Closed Book |
| Quiz / Assignment | 50 min | 10% | As announced | Closed Book |
| Comprehensive Exam | 3 hours | 50% | Entire syllabus | Closed Book |
📚 Learning Resources
Textbooks (T)
- T1: Discrete Mathematics – Seymour Lipschutz & Marc Lars Lipson, McGraw-Hill, 3rd Ed (2010)
- T2: Introduction to Graph Theory – Robin J. Wilson, Prentice-Hall India, 5th Ed (2010)
Reference Books (R)
- R1: Discrete Mathematical Structures – Bernard Kolman et al., PHI Learning, 6th Ed (2013)
🔗 CO-PO Mapping
Legend: 3 = Strong, 2 = Medium, 1 = Low, – = NA
| COs | PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO10 |
|---|---|---|---|---|---|---|---|---|---|---|
| CO1 | 3 | 3 | 3 | – | – | – | 1 | 3 | 3 | 3 |
| CO2 | 3 | 3 | 3 | – | – | – | 1 | 3 | 3 | 3 |
| CO3 | 3 | 3 | 3 | – | – | – | 1 | 3 | 3 | 3 |
🗓️ Weekly Study Schedule
- Daily: 45–60 mins study + 15 mins revision
- Weekly: 1 mini test (10 questions)
- Before exams: 2 full-length papers
| Week | Target Unit | Must-Do Topics | Practice Goal |
|---|---|---|---|
| 1 | Sets | Types of sets, operations, Venn diagrams | 20 MCQs |
| 2 | Sets + Induction | Algebra of sets + Induction basics | 15 numericals |
| 3 | Induction | Induction + Inclusion–Exclusion | 25 mixed |
| 4 | Functions & Relations | Relations types, function types | 25 mixed |
| 5 | Counting | Permutations, combinations | 30 numericals |
| 6 | Advanced Counting | Pigeonhole + partitions | 20 mixed |
| 7 | Logic | Truth tables, connectives | 25 mixed |
| 8 | Boolean Algebra | Properties, theorem, lattices | 20 mixed |
| 9 | Graph Basics | Degree, Euler, Dijkstra | 20 graph problems |
| 10 | Paths & Circuits | Euler/Hamilton + graph operations | 25 graph problems |
| 11 | Trees | BST, spanning tree, MST algorithms | 25 tree problems |
| 12 | Group Theory + Revision | Group/subgroup + full revision | 1 mock test |
Graphs, trees, counting & Boolean algebra usually carry high-weight questions. Don’t skip diagrams — they directly increase marks.
⚠️ Important Policies
- Attendance: Minimum 75% attendance required
- Make-up Policy: Only in genuine cases with prior intimation & approval
This handout is meant to help students plan study, revision and exam practice effectively.