COL202: Discrete Mathematical Structures
I semester: 2019-20
Amitabha Bagchi
Pre-Major Totals. Includes all evaluations apart from Major and Reminor. Posted 18 Nov 2019.
All registrants must read:
Timings and Venues
Lecture
Mon Thu 9:30AM to 10:50AM, LH 310.
Tutorial
- Group 1. Thu 2-3PM. Supervised by: Sudeep Agarwal (cs5150295@iitd.ac.in)
- Group 2. Fri 2-3PM. Supervised by: Shubhani (anz168046@iitd.ac.in)
- Group 3. Mon 2-3PM. Supervised by: Raj Kamal (csz188013@iitd.ac.in)
- Group 4. Tue 2-3PM. Supervised by: Mehreen Jabbeen (csz187551@iitd.ac.in)
All tutorials will be conducted in Room LH 604.
Topics
- Basic logic: Propositional logic: logical connectives;
truth tables; normal forms (conjunctive and disjunctive); validity;
predicate logic; limitations of predicate logic, universal and
existential quantification; modus ponens and modus tollens. Proof
techniques: Notions of implication, converse, inverse,
contrapositive, negation, and contradiction; the structure of formal
proofs; direct proofs; proof by counterexample; proof by
contraposition; proof by contradiction; mathematical induction;
strong induction; recursive mathematical definitions; well
orderings.
- Basics of counting: Counting arguments; pigeonhole
principle; permutations and combinations; inclusion-exclusion,
recurrence relations, generating functions.
- Fundamental structures; Functions (surjections, injections, inverses,
composition); relations (reflexivity, symmetry, transitivity,
equivalence relations); sets (Venn diagrams, complements, Cartesian
products, power sets); pigeonhole principle; cardinality and
countability.
- Introduction to probability: Events, probability, probability of unions and intersections of events, independence and conditional probabilities, random variables, expectations, variances, basic tail inequalities.
- Intro to graph theory.
Texts
The primary text book for this class will be:
[LLM10] E. Lehman, F. T. Leighton, and A. R. Meyer. Mathematics for Computer Science, Lecture notes from Fall 2010, MIT Open Courseware.
Other Texts
- [BSD05] K. Bogart, S. Drysdale, C. Stein. Discrete Math for Computer Science Students.
For the purposes of this class the book has been mirrored locally.
- [GKP94] R. L. Graham, D. E. Knuth, O. Patashnik. Concrete Mathematics: A foundation for computer science, 2nd ed. Pearson, 1994. (Available in the Central Library and in affordable Indian edition).
- [Die16] Reinhard Diestel. Graph Theory, 5e, 2016.
- [SAK02] S. Arun-Kumar. Introduction to Logic for Computer Science (WWW draft), IIT Delhi, September 2002. Posted 5 September 2019.
- [Gallier08] Jean Gallier. Discrete Mathematics for Computer Science: Some Notes. arXiv:0805.0585, 2008. Posted 18 September 2019.
- [Wilf94] Herbert S. Wilf. generatingfunctionology, Academic Press, 1994. Posted 20 October 2019.
- [Goemans15] Michael Goemans. Generating functions, Lecture Notes for {\em Principles of Discrete Mathematics}, MIT, 2015. Posted 24 October 2019.
- [Bagchi17] Mutual independence, pairwise independence and
$k$-wise independence: Events versus random variables, Notes for COL202, I Sem 2017-18, September 2017. Posted 7 November 2019.
Miscellaneous
Course calendar
Regarding this calendar please note
- All the material given in the portions of the texts mentioned under "Source" may not have been covered in lecture. Nevertheless it is all in the syllabus.
- Tutorial sheets will generally be based on the material covered in the previous week.
Tutorials
Tutorial sheets
- Tut 12. Posted 7 November 2019.
- Tut 11. Posted 31 October 2019.
- Tut 10. Posted 24 October 2019.
- Tut 9. Posted 17 October 2019.
- Tut 8. Posted 10 October 2019.
- Tut 7. Posted 18 September 2019.
- Tut 6. Posted 12 September 2019.
- Tut 5. Posted 4 September 2019.
- Tut 4. Posted 29 August 2019.
- Tut 3. Posted 8 August 2019.
- Tut 2. Posted 2 August 2019.
- Tut 1. Posted 25 July 2019.
Tutorial guidelines
- Tutorial sheets will be posted in the week before the tutorial is scheduled.
- One or two problems will be marked as for submission. You have to solve this problem and bring it to the tutorial. Write your solution on a plain piece of paper and put your name, entry number and the Tutorial number on top of the page.
- Your tutorial submission will be graded for effort and clarity (not necessarily correctness). You will get marked out of 3 based on the grader's subjective judgment on whether you have put in effort or not and on the level of clarity in what you have written.
- Your tutorial submission will not be accepted if you don't attend the tutorial, i.e. you cannot send your submission with a friend. Your tutorial submission will be graded only if you attend the relevant tutorial.
- The tutorial schedule and the sheets associated with each tutorial are given in the course calendar above.
Evaluation
- 8%: Quizzes. 4% per quiz. Only the best two will be counted.
- 12%: Tutorial exercises. 1.5% per tutorial exercise. Only the best eight will be counted.
- 22%: I Minor Exam.
- 22%: II Minor Exam.
- 36%: Major Exam.
Policies
- Attendance. 75% attendance is an institute requirement for getting an I grade or for being allowed to take a remajor in case of getting an E. There is no other attendance-based restriction in this course. Attendance will be through Timble and Timble issues will not be discussed (take them up with Timble admin).
- Missed minors. For missed minors there will be a single reminor held after the major at an announced time. The syllabus will be the entire course.
- Missing other evaluations. There will be no re-quizzes or make-up tutorials for any reason even illness. We will have enough of both to ensure that you will not suffer for missing up to 2 of each.
- Re-grading policy for quizzes and exams.
- No regrading requests by email, only through gradescope.
- Ask for regrading only if you think your solution is right but has been marked as wrong.
- No regrading for partial marks, i.e., if you have been given marks for attempting, that is a subjective decision and will not be reviewed.
- Frivolous regrading requests will get -0.5.
- You need to describe in detail why you think your marks should be increased. Saying "Recheck Q2" will be considered a frivolous request and treated accordingly.
Amitabha Bagchi