Adaptation DM 20-21 — различия между версиями
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== Schedule == | == Schedule == | ||
| − | The classes are organised online on Fridays at | + | The classes are organised online on Fridays at 18:00. |
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== Course materials == | == Course materials == | ||
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|| 20.11.20 || Logics, induction and number theory || [https://drive.google.com/file/d/1huwfDBQkGTujwaypXbhVN_Vkh1X4YaGD/view?usp=sharing PS 9] || [https://drive.google.com/file/d/1kuCepRg7h1a6HuctJvo5rVwhxf-EXSJO/view?usp=sharing Notes 9]|| [https://youtu.be/dmh1x1GqHzY Video 9] | || 20.11.20 || Logics, induction and number theory || [https://drive.google.com/file/d/1huwfDBQkGTujwaypXbhVN_Vkh1X4YaGD/view?usp=sharing PS 9] || [https://drive.google.com/file/d/1kuCepRg7h1a6HuctJvo5rVwhxf-EXSJO/view?usp=sharing Notes 9]|| [https://youtu.be/dmh1x1GqHzY Video 9] | ||
| + | |- | ||
| + | || 27.11.20 || Revisiting inverse elements and Sets. Cartesian product|| [https://drive.google.com/file/d/1D4HksgUeGiXiBmCOqBzmTyNwro0DvIYy/view?usp=sharing PS 10] || [https://drive.google.com/file/d/17W2c4QPOYIEC_drbGJoHKyx4JLOUbNol/view?usp=sharing Notes 10]|| [Video 10] | ||
| + | |- | ||
| + | || 4.12.20 || Sets. Proofs of equalities. Relations. Compositions|| [https://drive.google.com/file/d/1g6vODUsKGdXiZx9GRmTr5mnXVtfzgJ7_/view?usp=sharing PS 11] || [https://drive.google.com/file/d/14LoJ8L7ReqGKFLEDpqrqiJ5teaqQ_Z7b/view?usp=sharing Notes 11]|| [Video 11] | ||
| + | |- | ||
| + | || 11.12.20 || Relations, image and preimage. Construction of counterexamples|| [https://drive.google.com/file/d/1swRrmDwcGO_l3u_4bAovEj1UzeqCxb3F/view?usp=sharing PS 12] || [https://drive.google.com/file/d/13pWh3dAPycRglkyRW3Zb8BTOAxbd7-9G/view?usp=sharing Notes 12] || [https://youtu.be/iAhUM2vPFIY Video 12] | ||
| + | |- | ||
| + | || 18.12.20 || Functions, their properties.|| [https://drive.google.com/file/d/1QYc3pKNOZYeMYPfMDZqBYjTz45eaUqF7/view?usp=sharing PS 13] || [https://drive.google.com/file/d/1oKFonsNa-8PDpju2NQZVNyjUHz2TrIrM/view?usp=sharing Notes 13] || [https://youtu.be/zoO8QmYnNMg Video 13] | ||
| + | |- | ||
| + | || 15.01.21 || Equivalent sets, bijections, cardinalities.|| [https://drive.google.com/file/d/1mX7FgjLPn4UXm5cHW0_ynFTX8ri3Naxd/view?usp=sharing PS 14] || [https://drive.google.com/file/d/1tCY8ycroREV5H54O30Jf3za15xiyMSLz/view?usp=sharing Notes 14]|| [https://youtu.be/ouKQP6O5DmI Video 14] | ||
| + | |- | ||
| + | || 22.01.21 || More about cardinalities.|| [https://drive.google.com/file/d/1dCNzWpw3ixdJ86BClS688aAmL68_aD_b/view?usp=sharing PS 15] || [https://drive.google.com/file/d/1dCNzWpw3ixdJ86BClS688aAmL68_aD_b/view?usp=sharing Notes 15] || [https://youtu.be/FMKiWO3M11E Video 15] | ||
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| + | |- | ||
| + | || 29.01.21 || Definition of functions and consruction of proofs|| [https://drive.google.com/file/d/1udH4_owTUxT1dm4IJ1rDiv4cH-jKRjuF/view?usp=sharing PS 16] || [https://drive.google.com/file/d/1oUhc1fLFJIbOSoIkChyeLlDLEYBIiONI/view?usp=sharing Notes 16]|| [https://youtu.be/WqLju4f4zDI Video 16] | ||
| + | |- | ||
| + | || 5.02.21 || Countable sets. || [https://drive.google.com/file/d/1KI8wBW2a8OP7M7HNWwVHtV53H5j0judd/view?usp=sharing PS 17] ||[https://drive.google.com/file/d/1elq3s9dzr2E6rPQm9DdhQY6JSmtZSOZ_/view?usp=sharing Notes 17] || [ Video 17] | ||
| + | |- | ||
| + | || 12.02.21 || Combinatirics: binomial coefficients. || [https://drive.google.com/file/d/1KI8wBW2a8OP7M7HNWwVHtV53H5j0judd/view?usp=sharing PS 18] ||[https://drive.google.com/file/d/1KI8wBW2a8OP7M7HNWwVHtV53H5j0judd/view?usp=sharing Notes 18] || [https://youtu.be/E3p2y0pVBkE Video 18] | ||
| + | |- | ||
| + | || 19.02.21 || Pigeonhole principle and Pascal's triangular.|| [https://drive.google.com/file/d/1-Kokd9S8o8Y7MNmiwR_a3fOexK7K7oCw/view?usp=sharing PS 19] ||[https://drive.google.com/file/d/1Go1phKLndhGvNm24RkweVg24ymxe4oix/view?usp=sharing Notes 19] || [ Video 19] | ||
| + | |- | ||
| + | || 26.02.21 || Proof of equalities with binomial coefficients. Generalized binomial coefficients.|| [https://drive.google.com/file/d/1xThgUDKToQR_-emdAIB1-VGcCzyFM9my/view?usp=sharing PS 20] || [https://drive.google.com/file/d/1Bae2NLMPo2I5N-fEG3X1t-DD9eN0fV-F/view?usp=sharing Notes 20]|| [https://youtu.be/KRy6AIcyYVg Video 20] | ||
|} | |} | ||
== Homeworks == | == Homeworks == | ||
| + | ==Semester 1 == | ||
[https://drive.google.com/file/d/1gyB_XMLqrHgeFadu09k2WB3nXdbFc4AF/view?usp=sharing Homework 1 (Logics and Induction)], Deadline 7th November extended to 26th November | [https://drive.google.com/file/d/1gyB_XMLqrHgeFadu09k2WB3nXdbFc4AF/view?usp=sharing Homework 1 (Logics and Induction)], Deadline 7th November extended to 26th November | ||
| Строка 42: | Строка 65: | ||
[https://drive.google.com/file/d/1TZ6dJxpSLZ48IlMmjth8McyPNbdgZf3Q/view?usp=sharing Homework 2 (Number Theory)], Deadline 7th December | [https://drive.google.com/file/d/1TZ6dJxpSLZ48IlMmjth8McyPNbdgZf3Q/view?usp=sharing Homework 2 (Number Theory)], Deadline 7th December | ||
| − | [ Homework 3 (Set Theory)], Deadline 20th December | + | [https://drive.google.com/file/d/1dRlAAKXxaBIE7hcPlqR8csPJVVpy7lN-/view?usp=sharing Homework 3 (Set Theory and Relations)], Deadline 20th December |
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| + | ==Semester 2== | ||
| + | |||
| + | [https://drive.google.com/file/d/1qKL0Q3tu0CPlBBZr1O7fWkkr0wS0GUfP/view?usp=sharing Homework 1 (Combinatorics)], Deadline 1st March | ||
== References == | == References == | ||
Текущая версия на 20:18, 26 февраля 2021
Содержание
General Information
The main goal of the Discrete Mathematics Adaptation Course is to help students keep up with the course curriculum by discussing the most important and challenging topics in detail. The second very important goal of the course is to teach students to work competently with mathematical definitions and proofs, correctly logically build solutions to problems and prove statements. The topics of the course are coordinated with the "basic" course of the DSBA and SE program, but its study will also be useful for the direction of AMI. The approximate order of topics is sets and logic, combinatorics, functions and relations, graphs, the beginning of number theory, the foundations of probability theory, generating functions.
Schedule
The classes are organised online on Fridays at 18:00.
Course materials
First semester
| Date | Topic | Problem Set | Class note | Video |
|---|---|---|---|---|
| 25.09.20 | Statements, connectives, quantifiers | PS 1 | ||
| 2.10.20 | Logics and inductive definitions | The same PS | ||
| 9.10.20 | Mathematical Induction. Formal Proofs. | PS 3 | ||
| 16.10.20 | Divisibity. | PS 4 | Notes 4 | Video 4 |
| 23.10.20 | Divisibility. Great common dividers. | PS 5 | [ Notes 5] | Video 5 |
| 30.10.20 | The Euclidean algorithm. Bezout equations. | PS 6 | Notes 6 | Video 6 |
| 6.11.20 | Euler's and Fermat's Little Theorems | PS 7 | Notes 7 | Video 7 |
| 13.11.20 | Bezout equalities and sotition of congruences | PS 8 | Notes 8 | Video 8 |
| 20.11.20 | Logics, induction and number theory | PS 9 | Notes 9 | Video 9 |
| 27.11.20 | Revisiting inverse elements and Sets. Cartesian product | PS 10 | Notes 10 | [Video 10] |
| 4.12.20 | Sets. Proofs of equalities. Relations. Compositions | PS 11 | Notes 11 | [Video 11] |
| 11.12.20 | Relations, image and preimage. Construction of counterexamples | PS 12 | Notes 12 | Video 12 |
| 18.12.20 | Functions, their properties. | PS 13 | Notes 13 | Video 13 |
| 15.01.21 | Equivalent sets, bijections, cardinalities. | PS 14 | Notes 14 | Video 14 |
| 22.01.21 | More about cardinalities. | PS 15 | Notes 15 | Video 15 |
| 29.01.21 | Definition of functions and consruction of proofs | PS 16 | Notes 16 | Video 16 |
| 5.02.21 | Countable sets. | PS 17 | Notes 17 | [ Video 17] |
| 12.02.21 | Combinatirics: binomial coefficients. | PS 18 | Notes 18 | Video 18 |
| 19.02.21 | Pigeonhole principle and Pascal's triangular. | PS 19 | Notes 19 | [ Video 19] |
| 26.02.21 | Proof of equalities with binomial coefficients. Generalized binomial coefficients. | PS 20 | Notes 20 | Video 20 |
Homeworks
Semester 1
Homework 1 (Logics and Induction), Deadline 7th November extended to 26th November
Homework 2 (Number Theory), Deadline 7th December
Homework 3 (Set Theory and Relations), Deadline 20th December
Semester 2
Homework 1 (Combinatorics), Deadline 1st March
References
Grading and Results
Final grade = 1/2*Homework 1 + 1/2*Homework 2 + Bonus points
Bonus point number is between 0 to 20. Such points may be given for a variety of auxiliary activities.
