Presentation of examples of modern scenarios with digital mediametamath
The document discusses modern teaching and learning methods using digital media. It presents examples of how professors in Saxonian universities are using technologies like digital texts, videos, simulations, and online surveys. Specific examples are given of uses like central distribution of materials, flexibility in timing with video lectures, and demonstrations with digital media. Implications for constructive alignment of learning outcomes, assessments and teaching activities are discussed. The use of social learning technologies like wikis, blogs, and video conferencing are also examined. Throughout, implications for integrating these methods into teaching projects are highlighted.
Intelligent Adaptive Services for Workplace-Integrated Learning on Shop Floorsmetamath
The document discusses intelligent adaptive services to support workplace-integrated learning on the shop floor. It provides context on Industry 4.0 and the transformation of manufacturing workplaces through digitalization and cyber-physical systems. The APPsist project aims to develop assistance and knowledge acquisition services for smart production environments. Services select appropriate work processes, learning content, and assistance based on the user and machine context to guide operators and support flexible on-the-job learning. The services were implemented and tested in pilot scenarios at industry partners.
Introduction to the e-Learning networ in mathematics in Saxony - E-Assessment...metamath
This document introduces an e-learning network in mathematics across universities in Saxony, Germany. The network shares electronic assessments created using ONYX and MAXIMA. Over 50 authors have created more than 1000 questions across various topics in mathematics. The assessments provide interactive practice and feedback for students and inform instructors. OPAL is the central learning platform used by 80,000 members across 11 universities. ONYX allows for different question types and MAXIMA can analyze student responses with random parameters and expressions as answers. The speaker's university courses use 4 online tests throughout a semester to provide practice for approximately 200 students.
Quality Assurance in Large Scale E-Assessmentsmetamath
The document discusses quality assurance in large scale e-assessments. It outlines a quality assurance process that involves (1) planning assessments according to constructive alignment principles by defining learning outcomes and designing an assessment blueprint, (2) developing assessments by creating test items and compiling tests, and (3) analyzing and evaluating assessments by analyzing item-level metrics like difficulty and discrimination and test-level reliability. The process aims to ensure assessments are valid, objective, and reliable. Quality assurance is about more than just technical issues - it also requires communication and buy-in from students and faculty.
The document describes a project to develop self-directed e-learning mathematics courses on an online platform to help students from diverse educational backgrounds succeed in their university studies, with features like entry tests, short instructional videos, interactive examples, and online exercises with personalized feedback to support learning both individually and collaboratively before classroom lessons.
Erasmus+: Capacity Building in Higher Educationmetamath
This document provides an overview of the Erasmus+ Capacity Building in Higher Education programme. It discusses the types of projects that can be funded, including joint projects focusing on curriculum development and structural projects aimed at modernizing higher education systems. Eligible applicants and partners are described. National and regional priorities for different countries/regions are outlined. Budget information is presented, including funding amounts for previous calls and budget categories. The application and selection process are also summarized.
This document outlines an evaluation methodology for reformed math courses. It proposes conducting a longitudinal study comparing student outcomes between a controlled group taught with old courses and an experimental group taught with new reformed courses. Student outcomes would be assessed using pre-and post-tests, pre-and post-questionnaires, and measures of grades, knowledge gain, drop-out rates, motivation, and student evaluations. Challenges include accounting for differences between groups and ensuring high response rates to electronic questionnaires.
This document provides instructions for translating the user interface of a math training program called Math-Bridge. It explains that interface phrases are saved in Java properties files labeled Phrases_LANG.properties using UTF-8 encoding, and that translators should open the file, translate the phrases, save it, and run an 'ant i18n' target to restart the system with the new translations.
This document provides guidance for authoring advanced math exercises in Math-Bridge, an education solution. It explains that exercise steps should include different interaction types and that the order of transition conditions is important, with the first matching the final correct answer and the default transition last. It also recommends using syntactic comparison for the exact correct answer and semantic comparison for other conditions like correct but simplified answers or typical errors. Partial credit can be given based on syntactic and semantic analysis of responses.
This document provides instructions for using the jEdit text editor with the OQMath plugin to author and transform content using Math-Bridge. It describes how to configure jEdit and OQMath, enter mathematical formulas, browse available symbols, transform content to omdoc format, and common errors that may occur. Examples of different types of exercises that can be authored using this process are also provided, including fill in the blank, single choice, and multiple choice exercises.
Probability Theory and Mathematical Statistics in Tver State Universitymetamath
Project MetaMath outlines a probability theory and mathematical statistics course offered at Tver State University. The course is offered over two semesters for a total of 9 credits. It includes lectures, laboratory work, seminars, course projects each semester, and exams. The goal of the course is to present basic information about probability models that account for random factors. Upon completing the course, students should have mastered key probability and statistics concepts and techniques. The course also discusses modernizing elements like pre-testing students and incorporating online homework assignments.
This document compares the Discrete Mathematics curricula and courses between OMSU (National Research Ogarev Mordovia State University) in Russia and TUT (Tampere University of Technology) in Finland. It analyzes the competencies, topics, and learning outcomes covered in the Discrete Mathematics courses based on three levels of difficulty. Overall, the OMSU course covers more topics like set theory, combinatorics, algebraic structures, and coding theory over a longer duration, while the TUT course focuses more on number theory over a shorter period. The document proposes increasing engineering applications and using an online learning system to help modernize the Discrete Mathematics courses.
This document outlines a course of calculus for IT students at Lobachevsky State University of Nizhni Novgorod. The course is divided into 3 terms covering sequences, differential calculus, integral calculus, and series. Tests and exams are given throughout each term to assess student competency in mathematical thinking and problem solving. The course aims to develop skills in applying modern mathematical tools. Plans are discussed to modernize the course by adding an introductory section to address low student preparation, using online tools like METAMATH to support independent work, and testing key concepts to address educational problems.
The document discusses the discrete mathematics curriculum at Saint-Petersburg Electrotechnical University. It provides an overview of which discrete math topics are covered in each year of study for different degree programs. It also compares course parameters like credits and hours between the university and TUT. Key modules covered in the second year Math Logic and Algorithm Theory course are outlined. Competencies addressed in the curriculum are mapped to SEFI levels, with additional competencies covered uniquely at the university. Suggested modifications to improve the curriculum structure are presented.
Probability Theory and Mathematical Statisticsmetamath
This document provides information about a Probability Theory and Mathematical Statistics course taught at KNITU, Russia. It includes details about the course such as the number of students, preliminary courses required, distribution of working time, topics covered in lectures and workshops/laboratories. It also compares the methodology and topics studied in this course to a similar course taught at TUT, Finland. Key differences highlighted include the use of Matlab at TUT and more emphasis on practical work/tutorials versus lectures. Overall competencies covered are also summarized and compared between the two courses based on the SEFI framework.
This document compares the optimization methods courses between KNITU (Russia) and TUT (Finland).
The KNITU course is mandatory, has fewer credits (3 vs 5), and less time spent (108 student hours vs 138). Key topics are similar but KNITU spends less time on lectures (10 vs 28) and nonlinear optimization.
The main difference is KNITU has fewer lectures, almost half that of TUT. This could be addressed by using an online math platform like Math-Bridge to provide additional lecture material and practice problems. Mid-term tests on Math-Bridge could help evaluate knowledge gained from the extra online content.
This document summarizes the course content and structure for Discrete Mathematics at the National Research Ogarev Mordovia State University. The course is divided into 4 modules covering set theory, graph theory, algebraic structures, and coding theory. Students take exams and write 3 essays throughout the semester to assess their understanding of each module. Pedagogical methods include lectures, practice problems, subgroup work, computer programming assignments, and a final exam to evaluate students on a 100 point scale.
SEFI comparative study: Course - Algebra and Geometrymetamath
The document describes a course in Algebra and Geometry for Informatics and Computer Science (ICS) and Programming Engineering (PE) majors. It analyzes the course content based on the SEFI framework and finds that the course covers most competencies in linear algebra and geometry at the core and level 1 levels. Some level 2 and 3 competencies are also covered. However, not all competencies are addressed as some assume knowledge from secondary school, others are covered in other courses, and some are not necessary for the ICS and PE profiles.
This document discusses the mathematical foundations of fuzzy systems, including:
- The curriculum covers theory of fuzzy sets, theory of possibility, crisp vs. fuzzy values, model tasks, and possibilistic optimization tasks over two semesters for a total of 324 hours.
- The theory of possibility introduced in 1978 uses axiomatic approach and possibility measures to define possibilistic space and possibilistic (fuzzy) variables characterized by possibility distributions.
- Model tasks and possibilistic optimization tasks are presented, where the coefficients can be crisp or possibilistic variables.
Calculus - St. Petersburg Electrotechnical University "LETI"metamath
This document provides an overview of the calculus concepts covered in school and in various university courses at the Electrotechnical University “LETI” in Saint Petersburg, Russia. It outlines the key competencies developed in functions, sequences, series, logarithmic/exponential functions, rates of change, differentiation, integration, and other topics. The levels of mastery increase across the core courses in Calculus, Computing Mathematics, and some additional advanced topics covered in only two specialized groups.
1. The document outlines discrete mathematics competencies covered at different levels in the undergraduate curriculum at Saint-Petersburg Electrotechnical University.
2. Many competencies are covered in the discrete mathematics course in the first year, while others are covered in courses like mathematical logic and algorithm theory in later years.
3. LETI aims to develop additional competencies beyond the SEFI levels, such as skills in mathematical logic, graphs, algorithms, and finite state machines.
Probability Theory and Mathematical Statisticsmetamath
This document discusses a computer tutorial on probability theory and mathematical statistics that was developed for a bachelor's degree program in computer science and engineering. It provides details on the course, including the typical number and gender of students, prerequisite courses, and time allocation. It also outlines the history of the degree program and standards from 1990 to 2014. The document describes the contents, structure, and development of the computer tutorial, and shows some screenshots of different learning management systems used to deliver the tutorial over time, including Lotus Learning Space, IBM Workplace Collaborative Learning, and Blackboard.
This document provides an overview of optimization methods. It discusses both single-variable and multi-variable optimization techniques, including necessary and sufficient conditions for local minima. Specific optimization methods covered include golden section search, dichotomous search, gradient descent, Newton's method, the simplex method for linear programming problems, and the method of Lagrange multipliers for constrained optimization problems. The document is intended to provide information about an optimization methods course, including preliminary courses, time distribution, and types of optimization techniques taught.
Math Education for STEM disciplines in the EUmetamath
The document discusses math education reforms in the EU. It notes declining math skills among students and describes efforts across Europe to shift from a content-focused approach to developing mathematical competencies. Recommendations include changing curricula to emphasize real-world problem solving, improving teacher training, and leveraging technology as a teaching tool while maintaining the important role of educators. Overall, the document outlines the need for pedagogical reforms to address shortcomings identified by assessments like PISA and better prepare students for STEM careers.
International Activities of the University in academic fieldmetamath
The document summarizes the international activities of Kazan National Research Technical University (KNRTU-KAI) in academic fields. It outlines several milestones in the university's international relations starting from the 1950s when it first hosted foreign students. It then discusses KNRTU-KAI's participation in international projects, associations, and TEMPUS programs. The document also provides details on international accreditation of academic programs, the new German-Russian Institute of Advanced Technologies, and KNRTU-KAI's approach to developing new curricula/modules based on the qualifications framework of the European Higher Education Area.
2. СТРУКТУРА ДИСЦИПЛИНЫ
1. 3-й курс, 6-й семестр (весенний)
2. 144 часа (68 – аудиторная нагрузка, 76 – самостоятельная работа)
3. Входные требования: теория вероятностей, методы оптимизации
4. Базовые требуемые навыки:
1. Работа с простейшими функциями, заданными в аналитической и графической формах.
2. Работа с инструментарием теории множеств.
3. Работа с уравнениями, неравенствами и их системами.
3. ПРОБЛЕМЫ
Уже с базовыми требуемыми навыками есть проблемы (не только на первом
курсе):
1. Не могут по графику записать функцию и наоборот.
2. Не владеют теоретико-множественной символикой (∀, ∃, ∈,∪,∩, … ).
3. Не могут производить тривиальные манипуляции с элементарными
функциями.
4. …
4. ПРИМЕР 1
Выписать формулу функции, график которой изображен на рисунке:
𝜇 𝐴 𝑥
1
32 4 x
𝑥 − 2 , 4 − 𝑥min{ }
5. ПРИМЕР 1
Выписать формулу функции, график которой изображен на рисунке:
𝜇 𝐴 𝑥
1
32 4 x
𝑥 − 2 , 4 − 𝑥min{ }𝜇 𝐴 𝑥 = max{ , 0}
6. ПРИМЕР 2
Пусть функция представления формы L(t)=R(t) = max{0, 1 – t}, t >= 0. Определим
с ее помощью функцию принадлежности нечеткого множества A:
𝜇 𝐴 𝑥 =
𝐿
𝑎 − 𝑥
𝛼
, 𝑥 < 𝑎,
1, 𝑎 ≤ 𝑥 ≤ 𝑏,
𝑅
𝑥 − 𝑏
𝛽
, 𝑥 > 𝑏.
Пусть α = 2, β = 1, a = 3, b = 6. Постройте графики функции 𝜇 𝐴 𝑥 :
a. при x < a,
b. при x > b,
c. на всей числовой прямой.
7. ПУТИ РЕШЕНИЯ (МОДЕРНИЗАЦИИ)
Два направления:
1. Выравнивающий курс, развивающий требуемые базовые навыки
2. Подкрепление основного курса системой электронного обучения
I курс
II курс
III курс
IV курс
Осенний семестр Весенний семестр
Нечеткая логика
Выравнивающий курс Элементы нечеткой
логики (e-course)
8. ВЫРАВНИВАЮЩИЙ КУРС
1. В основном состоит из базовых определений, свойств и упражнений на тему
Построить график функций:
a. y=3x-10
b. y=|x| + 2
c. y=max{0, 1 – t}, t >= 0
d. y = 5x2 – x – 4
e. 𝑦 = 𝑒−𝑥2
f. y=x3-1
Пусть дано две функции y(x) и g(x). Построить графики
функций min{y(x), g(x)} и max{y(x), g(x)}:
a. y(x) = 2, g(x) = 1-x
b. y(x) = 3x + 2, g(x) = 5 – 6x
Пусть дана следующая задача условной оптимизации:
2𝑥 + 1 → 𝑚𝑎𝑥,
𝑦 − 𝑥 ≥ 0,
𝑦 + 𝑥 ≤ 10,
𝑥 ≥ 0.
Решите данную задачу графически, выполнив следующие шаги:
1. Постройте область решений, определяемую первым ограничением системы.
2. Постройте область решений, определяемую вторым ограничением системы.
3. Укажите (графически) область допустимых решений, определяемую
системой ограничений задачи.
4. Найдите оптимальное решение экстремальной задачи.
9. ЭЛЕМЕНТЫ НЕЧЕТКОЙ ЛОГИКИ (E-COURSE)
1. Определение нечеткого подмножества. Функция принадлежности. Операции над нечеткими подмножествами.
2. Возможностная мера. Нечеткая (возможностная) переменная(величина) и ее функция распределения (по С.Намиасу).
Свойства возможностных распределений.
3. Функции нечетких величин.
4. Классы параметризованных возможностных распределений (функций принадлежности). Распределения L-R типа.
5. t-нормы.
6. Взаимно T–связанные нечеткие величины.
7. Бинарные операции над нечеткими величинами.
8. Исчисление нечетких величин в классах параметризованных возможностных распределений и распределений L-R типа.
9. Отношения между возможностными величинами.
10. Нечеткие отношения. Операции над нечеткими отношениями.
11. Нечеткие и лингвистические переменные (по Л.Заде).
12. Нечеткие алгоритмы и выводы. Формирование базы правил.
13. Нейронные сети. Нечеткие нейронные сети.
14. Генетические алгоритмы.
15. Программное обеспечение нечеткой логики.
По каждой теме в e-course будут
созданы отдельные учебные модули
с определениями, примерами
и упражнениями.
12. РИСКИ И ПУТИ ИХ НЕЙТРАЛИЗАЦИИ
Риски заявленной модернизации обусловлены тем, что студенты будут
игнорировать систему электронного обучения.
Один из вариантов решения: положительный результат освоения электронных
учебных модулей является обязательным условием допуска к экзамену.