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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">infojournal</journal-id><journal-title-group><journal-title xml:lang="ru">Информатика и образование</journal-title><trans-title-group xml:lang="en"><trans-title>Informatics and education</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0234-0453</issn><issn pub-type="epub">2658-7769</issn><publisher><publisher-name>Publishing House Education and Informatics</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.32517/0234-0453-2019-34-1-50-55</article-id><article-id custom-type="elpub" pub-id-type="custom">infojournal-358</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ИКТ В ПРЕДМЕТНОЙ ОБЛАСТИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>ICT IN THE SUBJECT AREA</subject></subj-group></article-categories><title-group><article-title>ВАРИАНТЫ ПРИМЕНЕНИЯ СИСТЕМ КОМПЬЮТЕРНОЙ АЛГЕБРЫ В ОБУЧЕНИИ УГЛУБЛЕННЫМ РАЗДЕЛАМ МАТЕМАТИКИ</article-title><trans-title-group xml:lang="en"><trans-title>WAYS OF USE OF COMPUTER ALGEBRA SYSTEMS IN THE TEACHING OF ADVANCED SECTIONS OF MATHEMATICS</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6580-0653</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Сафуанов</surname><given-names>И. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Safuanov</surname><given-names>I. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Сафуанов Ильдар Суфиянович, доктор пед. наук, профессор, профессор кафедры высшей математики и методики преподавания математики, Институт цифрового образования</p><p>129226, Россия, г. Москва, 2-й Сельскохозяйственный проезд, д. 4, корп. 1</p></bio><bio xml:lang="en"><p>Ildar S. Safuanov, Doctor of Sciences (Education), Professor, Professor at the Department of Higher Mathematics and Methods of Teaching Mathematics, Institute of Digital Education</p><p>129226, Russia, Moscow, 2nd Selskohozoyastvenny proezd, 4/1</p></bio><email xlink:type="simple">SafuanovIS@mgpu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Чугунов</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Chugunov</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чугунов Владимир Аркадьевич, доктор физ.-мат. наук, профессор, заведующий кафедрой высшей математики и методики преподавания математики, Институт цифрового образования</p><p>129226, Россия, г. Москва, 2-й Сельскохозяйственный проезд, д. 4, корп. 1</p></bio><bio xml:lang="en"><p>Vladimir A. Chugunov, Doctor of Sciences (Physics and Mathematics), Professor, Head of the Department of Higher Mathematics and Methods of Teaching Mathematics, Institute of Digital Education</p><p>129226, Russia, Moscow, 2nd Selskohozoyastvenny proezd, 4/1</p></bio><email xlink:type="simple">chug@rambler.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Московский городской педагогический университет<country>Россия</country></aff><aff xml:lang="en">Moscow City University<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>13</day><month>03</month><year>2019</year></pub-date><volume>0</volume><issue>1</issue><fpage>50</fpage><lpage>55</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Сафуанов И.С., Чугунов В.А., 2019</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="ru">Сафуанов И.С., Чугунов В.А.</copyright-holder><copyright-holder xml:lang="en">Safuanov I.S., Chugunov V.A.</copyright-holder><license license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://info.infojournal.ru/jour/article/view/358">https://info.infojournal.ru/jour/article/view/358</self-uri><abstract><p>В статье рассматриваются возможные пути использования компьютеров для обучения сложным разделам математики, традиционно относящимся к программам высшей школы: элементам математического анализа, элементам теории чисел и абстрактной алгебры. Использование компьютерных технологий может помочь также осуществить такие методы, как генетический подход и использование различных способов представления изучаемых объектов в образовании. Согласно культурно-исторической теории Л. С. Выготского, компьютерные технологии можно рассматривать как инструмент для формирования понятий в процессе обучения. Наиболее приспособлены для обучения высшей математике такие системы компьютерной алгебры, как Maple и Mathematica, а также различные системы динамической геометрии. Показаны возможности программы Geogebra для работы с функциями на начальных этапах вузовских курсов математического анализа, в частности, для работы с понятиями пределов и производных функций.</p></abstract><trans-abstract xml:lang="en"><p>In this article, possible ways of use of computers for the teaching of advanced sections of mathematics that traditionally belong to undergraduate curricula, namely elements of calculus, number theory and abstract algebra are considered. Use of computer technologies can help also to implement such approaches as genetic method and the use of various modes of representation in education. According to cultural-historical theory of L. S. Vygotsky, computer technologies can be considered as the tool for the construction of concepts in the process of learning. The most appropriate for teaching advanced mathematics are such computer algebra systems as Maple, Mathematica, and various systems of dynamic geometry. We will consider the possibilities of Geogebra for the work with functions at the initial stages of undergraduate calculus courses, namely for the work with concepts of limits and derivatives of functions.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>информационные технологии</kwd><kwd>системы компьютерной алгебры</kwd><kwd>Geogebra</kwd><kwd>алгебра</kwd><kwd>теория чисел</kwd><kwd>математический анализ</kwd></kwd-group><kwd-group xml:lang="en"><kwd>information technologies</kwd><kwd>computer algebra systems</kwd><kwd>Geogebra</kwd><kwd>algebra</kwd><kwd>number theory</kwd><kwd>calculus</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Safuanov I. S., Polikarpov S. A. “Singapurskaya matematika”: shkol’nye uchebniki [“The Singapore mathematics”: school textbooks]. Nizhegorodskoe obrazovanie — Education in Nizhny Novgorod, 2016, no. 1, p. 32–39. 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