DAC-201 Discrete Structures
Autumn 2025-26
Instructor: Balasubramanian Raman
Other Instructor: Sanjeev Kumar
Office: S-227, CSE Building
Class Meeting Time: Tuesdays (11 am to 12 noon), Wednesdays and Fridays (12 noon to 1 pm).
Class Room: APJ 509
Office Hours: Mondays, Thursdays 11:00 a.m. - 1:00 p.m. and by appointment
TAs: TBA
Email: first four letters of first name at cs dot ac dot in
Announcements
September 23, 2025: Second session has begun.
Course Objectives, Learning Outcomes and Prerequisites
To understand the basic concepts of Set Theory, Graph Thory, Logic, Abstract Algebra and Number Theory.
To analyze logical propositions via truth tables.
To prove mathematical theorems using mathematical induction.
To understand sets and perform operations and algebra on sets.
To determine properties of relations, identify equivalence and partial order relations, sketch relations.
To Identify functions and determine their properties.
To Define graphs, digraphs and trees, and identify their main properties.
To evaluate combinations and permutations on sets.
Prerequisites: NIL.
Evaluation Components
- Term tests/quizzes (10%)
- Assignments (10%)
- Class participation (5%)
- Mid-Term Examination (25%)
- End Term Examination (50%)
Lecture Notes
01. Introduction to Linear Graphs and Applications, Incidence, Adjacent, Degree (26/09/2025)
02. Graph Isomorphism, Subgraph, Walk, Paths, Circuits, Connected & Disconnected Graphs, Components and Related Theorems (27/09/2025)
03. Components and Related Theorems, Euler Graphs, Representation of Graphs, Eigenvalues of a graph and Bipartite Graphs (30/09/2025)
04. Complete Bipartite Graphs (07/10/2025)
05. Operations on Graphs and Arbitrary Traceable Vertices ( (08/10/2025)
06. Eulerian, Hamiltonian graphs and related theorems, Introduction to Trees ( (10/10/2025)
07. Trees and Related Theorems, Distance and Centers in a Tree ( (14/10/2025)
Assignments
01. Assignment 1 (Posted on 09/10/2025)
- There will be three to five assignments.
- Late assignments will be accepted, with a 10% penalty per day, up to five days.
- Submission procedure and other requirements will be stated in individual assignments.
- Students are responsible for backing up and protecting their work.
Examinations
Recommended Study Material
The following will be used as a reference/text book for this course:
1. Herstein, I., Abstract Algebra, Pearson Education. 2005.
2. Harary, F., Graph Theory, Narosa Publishing House. 2001.
3. Huth, M. and Ryan, M., Logic in Computer Science: Modeling and
Reasoning About Systems, Cambridge University Press. 2005.
4. Narsingh Deo, Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall, 1979.
Instructor: Balasubramanian Raman
Other Instructor: Sanjeev Kumar
Office: S-227, CSE Building
Class Meeting Time: Tuesdays (11 am to 12 noon), Wednesdays and Fridays (12 noon to 1 pm).
Class Room: APJ 509
Office Hours: Mondays, Thursdays 11:00 a.m. - 1:00 p.m. and by appointment
TAs: TBA
Email: first four letters of first name at cs dot ac dot in
Other Instructor: Sanjeev Kumar
Office: S-227, CSE Building
Class Meeting Time: Tuesdays (11 am to 12 noon), Wednesdays and Fridays (12 noon to 1 pm).
Class Room: APJ 509
Office Hours: Mondays, Thursdays 11:00 a.m. - 1:00 p.m. and by appointment
TAs: TBA
Email: first four letters of first name at cs dot ac dot in
Announcements
September 23, 2025: Second session has begun.Course Objectives, Learning Outcomes and Prerequisites
To understand the basic concepts of Set Theory, Graph Thory, Logic, Abstract Algebra and Number Theory.
To analyze logical propositions via truth tables.
To prove mathematical theorems using mathematical induction.
To understand sets and perform operations and algebra on sets.
To determine properties of relations, identify equivalence and partial order relations, sketch relations.
To Identify functions and determine their properties.
To Define graphs, digraphs and trees, and identify their main properties.
To evaluate combinations and permutations on sets.
Prerequisites: NIL.
To analyze logical propositions via truth tables.
To prove mathematical theorems using mathematical induction.
To understand sets and perform operations and algebra on sets.
To determine properties of relations, identify equivalence and partial order relations, sketch relations.
To Identify functions and determine their properties.
To Define graphs, digraphs and trees, and identify their main properties.
To evaluate combinations and permutations on sets.
Prerequisites: NIL.
Evaluation Components
- Term tests/quizzes (10%)
- Assignments (10%)
- Class participation (5%)
- Mid-Term Examination (25%)
- End Term Examination (50%)
Lecture Notes
01. Introduction to Linear Graphs and Applications, Incidence, Adjacent, Degree (26/09/2025)02. Graph Isomorphism, Subgraph, Walk, Paths, Circuits, Connected & Disconnected Graphs, Components and Related Theorems (27/09/2025)
03. Components and Related Theorems, Euler Graphs, Representation of Graphs, Eigenvalues of a graph and Bipartite Graphs (30/09/2025)
04. Complete Bipartite Graphs (07/10/2025)
05. Operations on Graphs and Arbitrary Traceable Vertices ( (08/10/2025)
06. Eulerian, Hamiltonian graphs and related theorems, Introduction to Trees ( (10/10/2025)
07. Trees and Related Theorems, Distance and Centers in a Tree ( (14/10/2025)
Assignments
01. Assignment 1 (Posted on 09/10/2025)
- There will be three to five assignments.
- Late assignments will be accepted, with a 10% penalty per day, up to five days.
- Submission procedure and other requirements will be stated in individual assignments.
- Students are responsible for backing up and protecting their work.
Examinations
Recommended Study Material
The following will be used as a reference/text book for this course:1. Herstein, I., Abstract Algebra, Pearson Education. 2005.
2. Harary, F., Graph Theory, Narosa Publishing House. 2001.
3. Huth, M. and Ryan, M., Logic in Computer Science: Modeling and Reasoning About Systems, Cambridge University Press. 2005.
4. Narsingh Deo, Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall, 1979.