Discrete Mathematics DSBA 2022/2023 — различия между версиями

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(не показано 87 промежуточных версии 6 участников)
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= Exam =
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== Instructors ==
  
−
= Colloquium =
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=== The lecturer ===
 +
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].
  
−
The rules and the question list are available [https://drive.google.com/file/d/1yP8z3_OJWfWQNA5pdlrXvJoZhTR0ttNO/view?usp=sharing here].
+
=== Seminar instructors ===
 +
{| class="wikitable" style="text-align:center"
 +
|-
 +
! Group !! 221 !! 222 !! 223 !! 224
 +
|-
 +
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov [https://t.me/brdann Telegram]|| Trofimova Anastasia [https://t.me/AnastasiiaTrofimova Telegram]
 +
|-
 +
|| Teaching Assistants || Arseny Bolotnikov [https://t.me/l0i4b Telegram] ||Daria Ivanova [https://t.me/ivanovskayaaaaa Telegram]|| Egor Kornelyuk  [https://t.me/feddes5 Telegram] || Marianna Kouis [https://t.me/mariannakouis Telegram]
 +
|-
 +
|| Lecturer’s Assistant || colspan="4"| Alena Chislova [https://t.me/Alyona_Chislova Telegram]
 +
|}
  
−
[https://docs.google.com/spreadsheets/d/1N2sys3MYTtQiYNfZZ_c3t4oF8xOqoMbvWZDLHppQkMs/edit?usp=sharing Here] you can find your '''Question Card Number''' (the number '''will not''' change, while the Cards themselves are to be updated daily), primary and final marks for the Colloquium.
+
== Current performance ==
  
−
The Cards will be posted to our [https://t.me/+T_YTN4IG1vAJNWT9 TG group].
+
[https://docs.google.com/spreadsheets/d/1KoXyABY4alQu-Gw3HsYy3Vco9rfvHdYQZuUjE_ERJB8/edit?usp=sharing The Table]
 +
 
 +
== Homework ==
 +
The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:
 +
 
 +
HW = (the sum of points given for ordinary problems) / #(ordinary problems);
 +
 
 +
HW* = (the sum of points given for bonus problems) / #(bonus problems).
 +
 
 +
The value HW1 is similar to HW but restricted to the problem sets given in Module 1.
 +
 
 +
A student may be required to explain  orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.
 +
 
 +
== Exam 1 ==
 +
A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:
 +
 
 +
Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);
 +
 
 +
Exam1* = (the sum of points given for bonus problems) / #(bonus problems)
 +
 
 +
== Colloquium ==
 +
An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 10 integer points for his answer; the value Colloq is just this score.
 +
 
 +
Please find the question list and rules [https://drive.google.com/file/d/13gNFBATQ6V3lieUj8vym8OXC2RXmbdt4/view?usp=share_link here].
 +
 
 +
== Exam 2 ==
 +
A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:
 +
 
 +
Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);
 +
 
 +
Exam2* = (the sum of points given for bonus problems) / #(bonus problems).
 +
 
 +
== Bonus activities ==
 +
The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.
 +
 
 +
== Exam retaking ==
 +
Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.
  
−
== Current performance ==
 
  
 
== Course materials ==
 
== Course materials ==
 +
 +
[https://t.me/joinchat/T_YTN4IG1vAJNWT9 Course chat].
  
 
=== Lecture notes ===
 
=== Lecture notes ===
  
 
https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing
 
https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing
 +
 +
=== Classes recordings ===
 +
 +
https://disk.yandex.ru/d/enYKJ6O8NN_3lQ
  
 
=== Lecture video archive ===
 
=== Lecture video archive ===
Строка 21: Строка 73:
 
https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8
 
https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8
  
−
=== Other resources ===
+
=== Compensatory lecture video ===
  
 +
https://youtu.be/SBH4lou-awE
 +
 +
=== Other resources ===
 
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]
 
* [https://tinyurl.com/rwky5vmk The Course's Google Directory]
  
 
* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]
 
* [https://www.youtube.com/playlist?list=PL1Uob8iPTHGTidrmrqEHTJ96Pt3-PmML4 Past years' videos]
 +
 +
* We have a [https://meet.edashkov.net.ru dedicated server] to hold an online meeting if we need one.
  
 
== Problem sets ==
 
== Problem sets ==
Строка 31: Строка 88:
 
=== Class problems ===
 
=== Class problems ===
  
−
* [https://drive.google.com/file/d/14Jmrughp40-h37qT_oL4yDlXlXSyOeS3/view?usp=sharing Set 1]
+
* [https://drive.google.com/file/d/1EP-diSuOTn9f0ryg18Z2w0xjEp8j0bnl/view?usp=sharing Problem set 1]
  
−
* [https://drive.google.com/file/d/1qPzimBBfAqPhvZEKdfTh4dAejQ0q-gKI/view?usp=sharing Set 2]
+
* [https://drive.google.com/file/d/12ct99-ORd7A94Gh5g4Nf9riv7UqNMSRc/view?usp=sharing Problem set 2]
  
−
* [https://drive.google.com/file/d/1oltd62McrXcTju0NKc5S2-Fu6YosZlMl/view?usp=sharing Set 3]
+
* [https://drive.google.com/file/d/1yKKqLsS99V4AhCYqbjafuav2CMCdQTOQ/view?usp=sharing Problem set 3]
  
−
* [https://drive.google.com/file/d/1sgeGsF1FvvCgs8rJ1AQS4JYoOLVEEB6x/view?usp=sharing Set 4]
+
* [https://drive.google.com/file/d/1YgH_AdCk4GcKC0KH7xBA4-sUnOYkUvUK/view?usp=share_link Problem set 4]
  
−
* [https://drive.google.com/file/d/14DGm3mknq2D2FOjxmUdBIhGqqB_OD54K/view?usp=sharing Set 5]
+
* [https://drive.google.com/file/d/1M556PSgTJOo5W-AxYEXjFu94VfledpF5/view?usp=share_link Problem set 5]
  
−
* [https://drive.google.com/file/d/17D8G1Eow2ihUOBmPKTLKP7xw4Rdt28RB/view?usp=sharing Set 6]
+
* [https://drive.google.com/file/d/1-ylVViaBgzxEM-M7Rvrz2iggtK6UiJTY/view?usp=share_link Problem set 6]
  
−
* [https://drive.google.com/file/d/1Qs0znCPJde14-jx2B2uyENTEZMBZMM7b/view?usp=sharing Set 7]
+
* [https://drive.google.com/file/d/15tcTNLW-uFqT2xPJn1imOnEzaGwlaZAq/view?usp=share_link Problem set 7]
  
−
* [https://drive.google.com/file/d/1NCtRSZ4cV8ROCZtS6Jhkfwy0OqJrz8lU/view?usp=sharing Set 8]
+
* [https://drive.google.com/file/d/1N1EuCCe7NIiEa69nXHwncfQG2IOTyzLi/view?usp=share_link Problem set 8]
  
−
* [https://drive.google.com/file/d/1f1ldODYudA4hH9ur9sKzDNOUTVDifKCk/view?usp=sharing Set 9]
+
* [https://drive.google.com/file/d/1PmlR2bysnKSZrJle9Dwa4KiB23G5ORdZ/view?usp=share_link Problem set 9]
−
 
+
−
* [https://drive.google.com/file/d/17q8OE4HxVJMjXry3513HUWxO0ATnB7PC/view?usp=sharing Set 10]
+
  
 
=== Homework problems ===
 
=== Homework problems ===
  
−
* [https://drive.google.com/file/d/1gXT0jRmXUMr5EMIkV5IdoZPHZ9d8_Og8/view?usp=sharing Homework 1]
+
* [https://drive.google.com/file/d/1A8lFPdI3ZvC1vOgz2KEpYcuWOFlsQvb1/view?usp=sharing Homework 1]
  
−
* [https://drive.google.com/file/d/1ewp12RK_sCvi46oFz6CIXf9h02U98a25/view?usp=sharing Homework 2]
+
* [https://drive.google.com/file/d/1LOPPwGjyVleR_mclxTKUJ_bxFrxt44sW/view?usp=sharing Homework 2a]
  
−
* [https://drive.google.com/file/d/1jdmRefkbNZ3-K9elU9T9FcJ9mMZ8MRnv/view?usp=sharing Homework 3]
+
* [https://drive.google.com/file/d/1W7k1OTiIMlPOpo-2mwmGegrc4RDHz5_j/view?usp=share_link Homework 2b]
  
−
* [https://drive.google.com/file/d/1k-hWPl1ks1uZ629Noa2JFVSH8le7p2Mc/view?usp=sharing Homework 4]
+
* [https://drive.google.com/file/d/1UvF-3gRwMrnsDAT9H4KDpoUafhrthKPw/view?usp=share_link Homework 3]
  
−
* [https://drive.google.com/file/d/1CPdEKTkMZi_q5wfDOAtViJS4MWt3f162/view?usp=sharing Homework 5]
+
* [https://drive.google.com/file/d/1I25qKW9F_ZJi8akim-X8Op17VTLnZznJ/view?usp=share_link Homework 4]
  
−
* [https://drive.google.com/file/d/1XPYeblYu26642Yhfbv94WgSI0Qp9nyX5/view?usp=sharing Homework 6]
+
* [https://drive.google.com/file/d/1roiMcNs0jYJJYyCRmM2p5Mg3UoLG_26A/view?usp=share_link Homework 5]
  
 
=== Assignment deadlines ===
 
=== Assignment deadlines ===
−
 
−
==== Group 211 ====
 
−
 
−
* HW1 --- September 26.
 
−
 
−
* HW2 --- November 8 for Problems 1--17; November 15 for the others.
 
−
 
−
* HW3 --- December 12 for Problems 1--5; December 31 for the others.
 
−
 
−
* HW4 -- February 12.
 
−
 
−
* HW5 -- March 4 for Problems 1--8, March 15 for the others.
 
−
 
−
* HW6 -- March 27. Every Problem from 4 on is considered 'bonus'.
 
−
 
−
==== Group 214 ====
 
  
 
{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
−
! Задание !! colspan="22" | Срок сдачи в группе 214
+
! Home problem set !! colspan="11" | Deadline
 
|-
 
|-
−
|Problems || 1 || 2 || 3 || 4 || 5  || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16 || 17 || 18 || 19 || 20 || 21 || 22
+
| || 221 || 222 || 223 || 224
 
|-
 
|-
−
| Homework Set 1 || 24.09 || 24.09 || 24.09 || 1.10 || 1.10 || 1.10 || - || - || - || - || - || - || - || - || - || - || - || - || - || - || - || -
+
| HW 1 №1-3 || || 22.IX || 22.IX || 22.IX
 
|-
 
|-
−
| Homework Set 2 || 15.10 || 15.10 || 15.10 || 15.10 || 15.10 || 15.10 || 7.11 || 7.11 || 7.11 || 7.11 || 7.11 || 7.11 || 7.11 || 26.11 || 26.11 || 26.11 || 26.11 || 26.11 || 26.11 || 26.11 || 26.11 || 26.11
+
| HW 1 || October 6 || October 6 || October 6 || October 6
 
|-
 
|-
−
| Homework Set 3 || 10.12 || 10.12 || 10.12 || 10.12 || 10.12 || 24.12 || 24.12 || 24.12 || 24.12 || 24.12 || 24.12 || 24.12 || - || - || - || - || - || - || - || - || -
+
| HW 2a №1-3 || || October 20 || October 20 ||  
 
|-
 
|-
−
| Homework Set 4 || 30.01 || 30.01 || 30.01 || 30.01 || 30.01 || 30.01 || - || - || - || - || - || - || - || - || - || - || - || - || - || - || -
+
| HW 2a || October 24 || October 27 || October 27 || October 27
−
|| -
+
−
|}
+
−
 
+
−
{| class="wikitable"
+
 
|-
 
|-
−
!  !! colspan="10" | Видеозаписи
+
| HW 2b №1-7 || November 30 || November 20 || November 20 || November 20
 
|-
 
|-
−
| Дата семинара || [https://youtu.be/zy932Zi1BFs 29.10] || [https://youtu.be/IzdhhQDEfMk 5.11] || [https://youtu.be/vx9Xgdg6Cmk 12.11] || [https://youtu.be/dVmxSNXzDKo 19.11] || [https://youtu.be/9kfWZ9_awnU 23.11] || [see notes 26.11] || [https://youtu.be/kMtymhW2Ozk 3.12] || [https://youtu.be/bBb7yQNhWmo 10.12] || [https://youtu.be/cGyAQdtCHo0 17.12]|| [https://youtu.be/5h7aa-RlTQQ 21.01] || [https://youtu.be/862xSo9VOf0 28.01]
+
| HW 2b №8-14 || December 14 || December 4 || December 4 || December 4
 
|-
 
|-
−
| Записки || [https://drive.google.com/file/d/15MHS-OxiWuKX-qusfwzMcQEmF_5aa0aL/view?usp=sharing 29.10] || [https://drive.google.com/file/d/15MHS-OxiWuKX-qusfwzMcQEmF_5aa0aL/view?usp=sharing 5.11] || [https://drive.google.com/file/d/1uomvWKepeQffpdu0ECd90r2O4ABEvn4t/view?usp=sharing 12.11] || [https://drive.google.com/file/d/1CiYmAN5IpegYhlbck4QuRFAw3GGP2mbW/view?usp=sharing 19.11] || [https://drive.google.com/file/d/1PcHWlM_31r7-b2Il3-5Q_uQQ48cC6Yvl/view?usp=sharing 23.11] || [https://drive.google.com/file/d/1-UI7gOhl7REOpsR73IYUX8PIJjGJuunC/view?usp=sharing 26.11] || [https://youtu.be/kMtymhW2Ozk 3.12] || [https://drive.google.com/file/d/1SIWAW5dT9ILL4yDw9RVzxZeVXHEyJN_y/view?usp=sharing 10.12] || [https://drive.google.com/file/d/10W8HU654hoA9_4uN8SNhju9xE99TG7f4/view?usp=sharing 17.12] || [https://drive.google.com/file/d/1HhR0bc6wmmcu7PrCSmL4gwwza8489SzI/view?usp=sharing 21.01] || [https://drive.google.com/file/d/1JqlN09GYk6jHRQ-MsT3RMDCd9ewthOFU/view?usp=sharing 28.01]
+
| HW 3 №1-3 || December 22  || December 22 || December 22 || December 24
−
 
+
−
|}
+
−
 
+
−
= Other resources =
+
−
* It is HIGHLY recommended to join our [https://t.me/joinchat/T_YTN4IG1vAJNWT9 Telegram chat].
+
−
 
+
−
* We have a [https://meet.edashkov.net dedicated server] to hold an online meeting if we need one.
+
−
 
+
−
= Professors and assistants =
+
−
 
+
−
== The lecturer ==
+
−
My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, [https://t.me/edashkov Telegram], or [https://vk.com/evgeny.v.dashkov VK].
+
−
 
+
−
== Seminar instructors ==
+
−
{| class="wikitable" style="text-align:center"
+
 
|-
 
|-
−
! Group !! 211 !! 212 !! 213 !! 214
+
| HW 3 №4-12 || February 11 || February 11 || February 11 || February 11
−
|-  
+
−
|| Teachers || Evgeny Dashkov ||colspan="2"| Boris Danilov|| Trofimova Anastasia
+
 
|-
 
|-
−
|| Assistants ||Arseny Kazankov || Jan Maksimov || Archipov Nikolay || Marianna Kouis
+
| HW 4 || March 16 || March 18 || March 18 || March 19
 
|-
 
|-
−
|| Lecturer’s assistant || colspan="4"| Daria Ivanova
+
| HW 5 || March 26 || March 26 || March 26 || March 26
 
|}
 
|}
  
−
= Grading system =
+
'''Each deadline is set by the respective group's instructor.'''
 +
 
 +
== Grading system ==
 +
For the final grading, we compute the following values:
 +
 
 +
Module 1 grade = round ((50*HW1 + 50*Exam1)/100);
  
−
Intermediate grade-2 = (1/3) test-1 + (1/3) colloquium-2 + (1/3) homework-2.
+
basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;
  
−
Cumulative grade-3 = (3/10) test-1 + (3/10) colloquium-2 + (4/10) homework-3.
+
adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;
  
−
Final grade-3 = min(10, (7/10) cumulative grade-3 + (3/10) final exam + (1/10) bonus points).
+
Final grade = round(min(10, 8 * basic + 2 * adv)).
  
−
The number in a grade’s name is the number of the module when grading takes place. The grade homework-n is the normalized average grade for the homework in Modules from 1 to n. The Intermediate and Final grades are subject to rounding half up to an integer. All the other grades are reported with the greatest precision available.
+
The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.  
  
−
Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.
 
  
−
= Recommended reading =
+
== Recommended reading ==
 
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''
 
''Please notice that '''The Book''' for our Course does not exist. The latter is based on many sources.''
  

Текущая версия на 22:08, 16 января 2024

Instructors

The lecturer

My name is Evgeny Dashkov. Feel free to contact me via email: edashkov@gmail.com, Telegram, or VK.

Seminar instructors

Group 221 222 223 224
Teachers Evgeny Dashkov Boris Danilov Telegram Trofimova Anastasia Telegram
Teaching Assistants Arseny Bolotnikov Telegram Daria Ivanova Telegram Egor Kornelyuk Telegram Marianna Kouis Telegram
Lecturer’s Assistant Alena Chislova Telegram

Current performance

The Table

Homework

The homework includes a few problem sets, one in a fortnight or so (the deadlines are announced on giving each set). Every problem set consists of about 10 – 15 problems, some of which are labeled as ‘bonus’ while all the remaining are considered ‘ordinary’. One can get either 0, ½, or 1 point for each problem. For the entire homework, two values are computed:

HW = (the sum of points given for ordinary problems) / #(ordinary problems);

HW* = (the sum of points given for bonus problems) / #(bonus problems).

The value HW1 is similar to HW but restricted to the problem sets given in Module 1.

A student may be required to explain orally his written solution to any problem. His grade for the problem may be decreased if he fails to do so properly.

Exam 1

A written examination is held past Module 1. Students may not consult any sources during the exam. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point, and the entire exam with two values:

Exam1 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam1* = (the sum of points given for bonus problems) / #(bonus problems)

Colloquium

An oral colloquium is held at the beginning of Module 3. Each student is given two questions concerning statements and definitions as well as one question requiring a proof. After no less than 45 minutes of preparation (when using any literature is allowed), the student is required to answer ‘from scratch’, that is, with no recourse to any materials. The examiner may pose additional questions as he sees fit. The student may get from 0 to 10 integer points for his answer; the value Colloq is just this score.

Please find the question list and rules here.

Exam 2

A written examination is held at the end of the Course. Students may not consult any sources during the exam. The examination takes about 120 minutes. Some problems of the exam are labeled as ‘bonus’; the others are ‘ordinary’. Each problem solution is graded with either 0, ¼, ½, ¾, or 1 point; finally, two values are computed:

Exam2 = (the sum of points given for ordinary problems) / #(ordinary problems);

Exam2* = (the sum of points given for bonus problems) / #(bonus problems).

Bonus activities

The students may be graded for a variety of ‘bonus activities’ (like quizzes, etc.) with an overall integer value Bonus from 0 to 25.

Exam retaking

Examinations 1 and 2 are subject to be retaken if Module 1 grade or Final grade (see below), respectively, is unsatisfactory. Retaking the exam is similar to the regular examination. The resulting grade is substituted for that of the latter. The last try Commission retaking is held for those whose final grade is still unsatisfactory after the retaking. A designated Commission carefully examines the student’s performance and gives him a final mark not better than ‘satisfactory’; at that the Commission is not bound by the grading formulas herein.


Course materials

Course chat.

Lecture notes

https://drive.google.com/file/d/1mmNLLQ0--EDihGNRKwSyXLOA1KL7A0lD/view?usp=sharing

Classes recordings

https://disk.yandex.ru/d/enYKJ6O8NN_3lQ

Lecture video archive

https://youtube.com/playlist?list=PLEwK9wdS5g0pk-1YWDc3hezRt_rNpQDf8

Compensatory lecture video

https://youtu.be/SBH4lou-awE

Other resources

Problem sets

Class problems

Homework problems

Assignment deadlines

Home problem set Deadline
221 222 223 224
HW 1 №1-3 22.IX 22.IX 22.IX
HW 1 October 6 October 6 October 6 October 6
HW 2a №1-3 October 20 October 20
HW 2a October 24 October 27 October 27 October 27
HW 2b №1-7 November 30 November 20 November 20 November 20
HW 2b №8-14 December 14 December 4 December 4 December 4
HW 3 №1-3 December 22 December 22 December 22 December 24
HW 3 №4-12 February 11 February 11 February 11 February 11
HW 4 March 16 March 18 March 18 March 19
HW 5 March 26 March 26 March 26 March 26

Each deadline is set by the respective group's instructor.

Grading system

For the final grading, we compute the following values:

Module 1 grade = round ((50*HW1 + 50*Exam1)/100);

basic = (21*Exam1 + 21*Colloq + 28*HW + 30*Exam2)/100;

adv = (30*Exam1* + Bonus + 35*HW* + 35*Exam2*)/100;

Final grade = round(min(10, 8 * basic + 2 * adv)).

The final grade is rounded half up to an integer. All the other values are reported with the greatest precision available.


Recommended reading

Please notice that The Book for our Course does not exist. The latter is based on many sources.

  1. Anderson J. A., Discrete Mathematics With Combinatorics. Prentice Hall, 2003.
  2. Biggs N. L., Discrete mathematics. 2nd ed., New York; Oxford: Oxford University Press, 2004.
  3. Gavrilov G. P., Sapozhenko A. A. Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences 14. Springer, 1996.
  4. Lehman E., Thomson Leighton F., Meyer A. R. Mathematics for Computer Science, 2017.
  5. Lovasz L., Vesztergombi K. Discrete Mathematics. Lecture Notes; Yale University, 1999.
  6. Melnikov O., Sarvanov V., Tyshkevich R., Yemelichev V., Zverovich I. Exercises in Graph Theory. Kluwer Texts in the Mathematical Sciences 19. Springer, 1998.
  7. Rosen K. H. Discrete Mathematics and Its Applications. McGraw-Hill, 1999.
  8. Stein C., Drysdale R. L., Bogart K. Discrete mathematics for computer scientists. Addison-Wesley, 2010.
  9. Vinogradov I. M. Elements of number theory. Dover, 1954.

In Russian

If you understand Russian (by any chance), you will probably benefit from reading the following books.

  1. Виноградов И. М. Основы теории чисел. 9-е изд., М.: Наука, 1981.
  2. Вялый М., Подольский В., Рубцов А., Шварц Д., Шень А. Лекции по дискретной математике.
  3. Гаврилов Г. П., Сапоженко А. А. Задачи и упражнения по дискретной математике. 3-е изд., М.: ФИЗМАТЛИТ, 2004.
  4. Дашков Е. В. Введение в математическую логику. Множества и отношения. М.: МФТИ, 2019.
  5. Зубков А. М., Севастьянов Б. А., Чистяков В. П. Сборник задач по теории вероятностей. 2-е изд., М.: Наука, 1989.
  6. Мельников О. И. Теория графов в занимательных задачах. 5-е изд., М.: Книжный дом "ЛИБРОКОМ", 2013.
  7. Шень А., Математическая индукция. 5-е изд, М.: МЦНМО, 2016.
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