DSBA Algebra 2024 2025 - История изменений

Dima Trushin: /* Lecture abstracts */

2025-06-24T18:12:16Z

Lecture abstracts

← Предыдущая версия		Версия от 18:12, 24 июня 2025
Строка 60:		Строка 60:

	'''Lecture 8''' (05.06.2025). Polynomials in several variables. Lexicographical orders, stabilization of strictly descending chains of monomials. An elementary reduction, a reduction with respect to a set of polynomials, remainders, Groebner basis. Stabilization of reduction.		'''Lecture 8''' (05.06.2025). Polynomials in several variables. Lexicographical orders, stabilization of strictly descending chains of monomials. An elementary reduction, a reduction with respect to a set of polynomials, remainders, Groebner basis. Stabilization of reduction.

			'''Lecture 9''' (09.06.2025). S-polynomials and the Buchberger criterion. Ideals in a polynomial ring, the Buchberger algorithm to produce a Groebner basis of an ideal. A ring of remainders. Membership problem and variable elimination.

			'''Lecture 10''' (19.06.2025). The Diamond Lemma. A proof of the Buchberger criterion.

	= Problem sheets =		= Problem sheets =

Dima Trushin: /* Results */

2025-06-06T13:54:46Z

Results

← Предыдущая версия		Версия от 13:54, 6 июня 2025
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	{\| class="wikitable" style="text-align:center"		{\| class="wikitable" style="text-align:center"
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	! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246]		! [https://docs.google.com/spreadsheets/d/1YPkyaDATcgg-GtZD0uwXft78pmx-Bw64k2x4as4nh1Y/edit?gid=0#gid=0 241] !! [https://docs.google.com/spreadsheets/d/1YPkyaDATcgg-GtZD0uwXft78pmx-Bw64k2x4as4nh1Y/edit?gid=1135622375#gid=1135622375 242] !! [https://docs.google.com/spreadsheets/d/1YPkyaDATcgg-GtZD0uwXft78pmx-Bw64k2x4as4nh1Y/edit?gid=1298301779#gid=1298301779 243] !! [https://docs.google.com/spreadsheets/d/1YPkyaDATcgg-GtZD0uwXft78pmx-Bw64k2x4as4nh1Y/edit?gid=961128608#gid=961128608 244] !! [https://docs.google.com/spreadsheets/d/1YPkyaDATcgg-GtZD0uwXft78pmx-Bw64k2x4as4nh1Y/edit?gid=1640834821#gid=1640834821 245] !! [https://docs.google.com/spreadsheets/d/1YPkyaDATcgg-GtZD0uwXft78pmx-Bw64k2x4as4nh1Y/edit?gid=1692805811#gid=1692805811 246]
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Dima Trushin: /* Results */

2025-06-06T13:53:57Z

Results

← Предыдущая версия		Версия от 13:53, 6 июня 2025
Строка 98:		Строка 98:
	{\| class="wikitable" style="text-align:center"		{\| class="wikitable" style="text-align:center"
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	! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246]		! [https://docs.google.com/spreadsheets/d/1SWVSQRerqIrnsDEXWzU2fXIonYIxuZ70FhqOmDjRnWQ/edit?gid=0#gid=0 241] !! [https://docs.google.com/spreadsheets/d/1SWVSQRerqIrnsDEXWzU2fXIonYIxuZ70FhqOmDjRnWQ/edit?gid=450771951#gid=450771951 242] !! [https://docs.google.com/spreadsheets/d/1SWVSQRerqIrnsDEXWzU2fXIonYIxuZ70FhqOmDjRnWQ/edit?gid=1614217882#gid=1614217882 243] !! [https://docs.google.com/spreadsheets/d/1SWVSQRerqIrnsDEXWzU2fXIonYIxuZ70FhqOmDjRnWQ/edit?gid=370973814#gid=370973814 244] !! [https://docs.google.com/spreadsheets/d/1SWVSQRerqIrnsDEXWzU2fXIonYIxuZ70FhqOmDjRnWQ/edit?gid=150412147#gid=150412147 245] !! [https://docs.google.com/spreadsheets/d/1SWVSQRerqIrnsDEXWzU2fXIonYIxuZ70FhqOmDjRnWQ/edit?gid=1833172109#gid=1833172109 246]
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Dima Trushin: /* Lecture abstracts */

2025-06-06T13:28:24Z

Lecture abstracts

← Предыдущая версия		Версия от 13:28, 6 июня 2025
Строка 54:		Строка 54:

	'''Lecture 5''' (15.05.2025). Rings, commutative rings, fields, subrings. Invertible elements, zero divisors, nilpotent and idempotent elements. Ideals. Description of ideals in Z and Z_n. Homomorphisms and isomorphisms of rings. The Chinese remainder theorem for rings. The kernel and the image of a homomorphism, their properties.		'''Lecture 5''' (15.05.2025). Rings, commutative rings, fields, subrings. Invertible elements, zero divisors, nilpotent and idempotent elements. Ideals. Description of ideals in Z and Z_n. Homomorphisms and isomorphisms of rings. The Chinese remainder theorem for rings. The kernel and the image of a homomorphism, their properties.

			'''Lecture 6''' (22.05.2025). Polynomials in one variable. Euclidean algorithm, greatest common divisor, ideals of F[x]. Irreducible polynomials and unique factorization of polynomials in F[x]. Ring of remainders, the Chinese Remainder Theorem for polynomials.

			'''Lecture 7''' (29.05.2025). Characteristic of a field. Field extensions, an extension by a root. Finite fields: number of elements in a finite field, multiplicative group of a finite field is cyclic, classification of finite fields (without proof). How to produce finite fields. Galois random generator. Stream cipher.

			'''Lecture 8''' (05.06.2025). Polynomials in several variables. Lexicographical orders, stabilization of strictly descending chains of monomials. An elementary reduction, a reduction with respect to a set of polynomials, remainders, Groebner basis. Stabilization of reduction.

	= Problem sheets =		= Problem sheets =

Dima Trushin: /* Problem sheets */

2025-06-06T13:27:47Z

Problem sheets

← Предыдущая версия		Версия от 13:27, 6 июня 2025
Строка 72:		Строка 72:

	'''Seminar 7''' (29.05.2025). [https://disk.yandex.ru/i/jZFQDVf9apa-1Q Problems]		'''Seminar 7''' (29.05.2025). [https://disk.yandex.ru/i/jZFQDVf9apa-1Q Problems]

			'''Seminar 8''' (05.06.2025). [https://disk.yandex.ru/i/qPfdD9lx4L4k1A Problems]

	= Test =		= Test =

Dima Trushin: /* Problem sheets */

2025-05-31T14:02:01Z

Problem sheets

← Предыдущая версия		Версия от 14:02, 31 мая 2025
Строка 69:		Строка 69:
	'''Seminar 5''' (15.05.2025). [https://disk.yandex.ru/i/lzYLUAMfHDBI2Q Problems]		'''Seminar 5''' (15.05.2025). [https://disk.yandex.ru/i/lzYLUAMfHDBI2Q Problems]

	'''Seminar 6''' (12.05.2025). [https://disk.yandex.ru/i/nUvIl-eGV6-clg Problems]		'''Seminar 6''' (22.05.2025). [https://disk.yandex.ru/i/nUvIl-eGV6-clg Problems]

			'''Seminar 7''' (29.05.2025). [https://disk.yandex.ru/i/jZFQDVf9apa-1Q Problems]

	= Test =		= Test =

Dima Trushin в 19:57, 28 мая 2025

2025-05-28T19:57:18Z

← Предыдущая версия		Версия от 19:57, 28 мая 2025
Строка 68:		Строка 68:

	'''Seminar 5''' (15.05.2025). [https://disk.yandex.ru/i/lzYLUAMfHDBI2Q Problems]		'''Seminar 5''' (15.05.2025). [https://disk.yandex.ru/i/lzYLUAMfHDBI2Q Problems]

			'''Seminar 6''' (12.05.2025). [https://disk.yandex.ru/i/nUvIl-eGV6-clg Problems]

	= Test =		= Test =

Dima Trushin: /* Lecture abstracts */

2025-05-17T17:06:36Z

Lecture abstracts

← Предыдущая версия		Версия от 17:06, 17 мая 2025
Строка 52:		Строка 52:

	'''Lecture 4''' (24.04.2025). Multiplicative version of the Chinese Remainder Theorem. Structure of Z_{p^n}^*. Cryptography. Exponentiation by squaring (fast raising to a power algorithm). The discrete logarithm problem. Diffie-Hellman key exchange.		'''Lecture 4''' (24.04.2025). Multiplicative version of the Chinese Remainder Theorem. Structure of Z_{p^n}^*. Cryptography. Exponentiation by squaring (fast raising to a power algorithm). The discrete logarithm problem. Diffie-Hellman key exchange.

			'''Lecture 5''' (15.05.2025). Rings, commutative rings, fields, subrings. Invertible elements, zero divisors, nilpotent and idempotent elements. Ideals. Description of ideals in Z and Z_n. Homomorphisms and isomorphisms of rings. The Chinese remainder theorem for rings. The kernel and the image of a homomorphism, their properties.

	= Problem sheets =		= Problem sheets =

Dima Trushin: /* Problem sheets */

2025-05-17T17:06:02Z

Problem sheets

← Предыдущая версия		Версия от 17:06, 17 мая 2025
Строка 57:		Строка 57:
	The solutions should be sent to your teaching assistant before the beginning of the next seminar. If you send the solution after the deadline your grade will be multiplied by 0.7<sup>t</sup> where t -- is the time passed after the deadline in days (not rounded). So, it is not an issue to send your work 1 or 2 hours after the deadline.		The solutions should be sent to your teaching assistant before the beginning of the next seminar. If you send the solution after the deadline your grade will be multiplied by 0.7<sup>t</sup> where t -- is the time passed after the deadline in days (not rounded). So, it is not an issue to send your work 1 or 2 hours after the deadline.

	'''Seminar 1''' (03.04.~~2024~~). [https://disk.yandex.ru/d/ikcTBq5kJDP1iw Problems]		'''Seminar 1''' (03.04.2025). [https://disk.yandex.ru/d/ikcTBq5kJDP1iw Problems]

	'''Seminar 2''' (10.04.~~2024~~). [https://disk.yandex.ru/d/0da7rDLB2b2O_w Problems]		'''Seminar 2''' (10.04.2025). [https://disk.yandex.ru/d/0da7rDLB2b2O_w Problems]

	'''Seminar 3''' (17.04.~~2024~~). [https://disk.yandex.ru/i/lsR5vMFIwP9F_Q Problems]		'''Seminar 3''' (17.04.2025). [https://disk.yandex.ru/i/lsR5vMFIwP9F_Q Problems]

	'''Seminar 4''' (24.04.~~2024~~). [https://disk.yandex.ru/i/cFA__aXT662WEA Problems]		'''Seminar 4''' (24.04.2025). [https://disk.yandex.ru/i/cFA__aXT662WEA Problems]

			'''Seminar 5''' (15.05.2025). [https://disk.yandex.ru/i/lzYLUAMfHDBI2Q Problems]

	= Test =		= Test =

Dima Trushin: /* Problem sheets */

2025-05-17T17:00:18Z

Problem sheets

← Предыдущая версия		Версия от 17:00, 17 мая 2025
Строка 62:		Строка 62:

	'''Seminar 3''' (17.04.2024). [https://disk.yandex.ru/i/lsR5vMFIwP9F_Q Problems]		'''Seminar 3''' (17.04.2024). [https://disk.yandex.ru/i/lsR5vMFIwP9F_Q Problems]

			'''Seminar 4''' (24.04.2024). [https://disk.yandex.ru/i/cFA__aXT662WEA Problems]

	= Test =		= Test =