Discrete Mathematics for Algorithm and Software Design

(HSE University, CS Faculty, September – October)


NEW: 2024

Materials for the 2024 installation of this course will appear here.

Final Exam

Final exam tasks

The solutions should be submitted by e-mail to slkuznetsov@hse.ru; the deadline is Monday October 28, 20:00 Moscow time.

The exam will be checked Monday evening, and the results will be put in the grading sheet. On Tuesday October 29, 18:00 Moscow time, the grades will be transmitted to the study office, after that no changes will be possible. The final exam is obligatory for all students enrolled in the course, no exceptions.

Grading Formula

Total = 0.5 · (HW1 + HW2 + HW3) + 0.5 · Exam

Maximal grades for home assignments: HW1 — 4, HW2 — 4, HW3 — 2 (giving 4+4+2=10).

The final exam is obligatory for all students enrolled in the course, no exceptions.

Home Assignment #3

Formulation of the task. Submission by GitHub (https://classroom.github.com/a/h5y9w8qP); fallback submission: by e-mail slkuznetsov@hse.ru.

Deadline: October 21, AoE (this means: October 22, 15:00 Moscow time).

Home Assignment #2: Theoretical Midterm

Download [.pdf]

This is a written theoretical assignment. Deadline: October 19, 2024, AoE. Please submit by email to slkuznetsov@hse.ru (scan or high quality photo is fine).

Home Assignment #1

Everything below the double line is outdated and kept for historical reference. In particular, do not use GitHub links below the line.



Previous Year: 2023

Final Exam

Final exam tasks

The solutions should be submitted by e-mail to slkuznetsov@hse.ru; the deadline is Wednesday October 25, 19:00 Moscow time.

The exam will be checked on Wednesday, and the results will be put in the grading sheet. On Thursday (21:00 Moscow time), the grades will be transmitted to the study office, after that no changes will be possible. The final exam is obligatory for all students enrolled in the course, no exceptions.

Home Assignment #3

Formulation of the task. Submission by GitHub (https://classroom.github.com/a/H4Tm6obL); fallback submission: by e-mail slkuznetsov@hse.ru.

Deadline: October 19, AoE (this means: October 20, 15:00 Moscow time).

Home Assignment #2: Theoretical Midterm

Download [.pdf]

This is a written theoretical assignment. Deadline: October 15, 2023, AoE. Please submit by email to slkuznetsov@hse.ru (scan or high quality photo is fine).

Home Assignment #1


2022

Final Exam

Final exam tasks

The solutions should be submitted by e-mail to slkuznetsov@hse.ru; the deadline (strict!) is Wednesday October 26, 19:00 Moscow time.

The exam will be checked on Wednesday, and the results will be put in the grading sheet. On Thursday (evening), the grades will be transmitted to the study office, after that no changes will be possible. The final exam is obligatory for all students enrolled in the course, no exceptions.

Grading Formula

Total = 0.5 · (HW1 + HW2 + HW3) + 0.5 · Exam

Maximal grades for home assignments: HW1 — 4, HW2 — 4, HW3 — 2 (giving 4+4+2=10).

The final exam is obligatory for all students enrolled in the course, no exceptions.

Home Assignment #3

Formulation of the task. Submission by GitHub: invite link (https://classroom.github.com/a/sVDoBJZz); fallback submission: by e-mail slkuznetsov@hse.ru.

Deadline: October 19, AoE (this means: October 20, 15:00 Moscow time).

Home Assignment #2: Theoretical Midterm

Download [.pdf]

This is a written theoretical assignment. Deadline: Friday, October 14, AoE. Please submit by email to slkuznetsov@hse.ru (scan or high quality photo is fine).

Home Assignment #1

OBSOLETE!

2021

The information here can be used as a reference; the class of 2022 would be similar to that of 2021.
However, concrete links and dates are obsolete, do not rely on them!

Final Exam

Final exam tasks

The solutions should be submitted by e-mail to sk@mi-ras.ru; the deadline is Wednesday October 20, 13:00 Moscow time, and it is strict.

The exam will be checked on Wednesday, and the results will be put in the grading sheet. On Thursday (evening), the grades will be transmitted to the study office, after that no changes will be possible.

The final exam is obligatory for all students enrolled in the course, no exceptions.

Grading Formula

Total = 0.5 · (HW1 + HW2 + HW3) + 0.5 · Exam

Maximal grades for home assignments: HW1 — 4, HW2 — 4, HW3 — 2 (giving 4+4+2=10).

The final exam is obligatory for all students enrolled in the course, no exceptions.

Home Assignment #3: NetworkX and Social Network Analysis

Formulation of the task. Submission by GitHub: invite link (https://classroom.github.com/a/KVxFeqh1); fallback submission: by e-mail sk@mi-ras.ru.

Deadline: October 11, AoE (this means: October 12, 15:00 Moscow time).

Home Assignment #2: Theoretical Midterm

Download [.pdf]

This is a written theoretical assignment. Deadline: October 6, AoE. You may either bring your answers in written form to the lecture on Wednesday, October 6, or send them to sk@mi-ras.ru (scan or high quality photo is fine).

Home Assignment #1



2020

The information below is outdated and may be used only for historical reference.
Final Exam

Timeline Autumn 2020

September 9, 2020
Lecture: Boolean functions and formulae, DNF and CNF, resolution. Video record
Practice: tasks in Boolean logic.
September 16, 2020
Lecture: soundness and completeness of resolution method; polynomial algorithms for 2-SAT and DNF-SAT. Video record
Practice: video record; new tasks: first-order predicate logic
September 23, 2020
Lecture: parsing with Lex&Yacc (slides); Turing machines. Video record
Practice: video record; new tasks: Turing machines & Graphs.
September 30, 2020
Lecture: NP-completeness, Cook — Levin theorem (slides). Video record
Practice: video record; new tasks: Polynomial Computations
October 7, 2020
Lecture: NetworkX (slides; sample code); NP-completeness of Hamiltonian path (slides). Video record
Practice: video record; new tasks: P and NP
October 14, 2020
Lecture: couting problems, #P (slides); course overview. Video record
Practice: video record; new tasks: Graph Colorings (NP-completeness of 3-COLOR)

Grading Formula

Final grade = 0.5·(Home assignments) + 0.5·(Exam).

Home assignments are graded out of 10: HW #1 out of 4, HW #2 out of 4, HW #3 out of 2.

Grading principles for home assignments are as follows. HW #1 and #3 are graded on a pass/fail basis: maximal grade, if the program works, and zero, if it does not. A half of the maximal grade can be assigned if the assignment was submitted significantly after the deadline, or a correct solution was reached only after significant feedback from the teacher (that is, the original submission was incorrect). HW #2 is graded on a proportional basis: multiply the number of correctly solved tasks by 4/6 and round to the closest integer.

If a student gets 8, 9, or 10 as the mark for home assignments, and all assignments are submitted before or on October 14, then the student is not obliged to pass the exam. In this case, the mark for home assignments is considered as the final one.

Home Assignments

Grading table

HW #3: NetworkX and Social Network Analysis

This is a programming task.

The SNAP dataset called facebook_combined.txt includes a union of 10 ego networks from Facebook. An ego network is a subgraph of the full friendship graph which includes a central node (ego) together with the vertices to which the ego is connected directly, and edges among them. Thus, each vertex in our dataset is either one of the 10 ego network centers, or is directly connected to (at least) one of them.

The task is as follows. Consider the following set of 11 vertices: 0, 107, 348, 414, 612, 686, 698, 1684, 1912, 3437, 3980. It is guaranteed that this set includes all 10 ego network centers, plus one extra vertex. The program should distinguish the added 11th vertex from the 10 ego network centers. As the answer, please provide the number of this additional vertex.

Notice: for testing, the nodes in the dataset can be renamed, in order to aviod hard-coding of the correct answer.

Deadline: Oct 14, 2020, 16:00 MSK.

HW #2: Theoretical Assignment

PDF
Deadline: Oct 16, 2020. (The students are encouraged to bring the solutions to the class of Oct 14, but submitting by email till Oct 16 is also fine.)
Erratum: there was a typo spotted and fixed in Problem 1. One should consider not the formula itself but rather its negation.

HW #1: Practice in Boolean Logic

This is a programming task. Choose one of the following two tasks and write a program which solves it.

  1. Given a Boolean formula, constructed from variables using /\ (conjunction), \/ (disjunction), -> (implication), and ~ (negation), translate it into Conjunctive Normal Form and into Disjunctive Normal Form.
  2. Given a Boolean formula in 2-CNF, use the resolution method to determine whether it is satisfiable. Clauses of the 2-CNF can be of one of the three forms: α \/ β, or α -> β, or just α. Here α and β are literals (p or ~p, where p is a variable). The CNF is presented in the usual notation, for example: (p -> q) /\ (~r \/ s) /\ (~q -> p)
Deadline: October 11, 2020 (23:59 MSK). Submissions by e-mail welcome.
Students are encouraged to use Python and PLY, but solutions in other programming languages are also OK.

Materials for HW #1

Tentative Outline

Course Materials

Previous Years

2016; 2017; 2018; 2019.