Элементарная математика. Рабочая программа учебной дисциплины

Робоча програма навчальної дисципліни "Елементарна математика" для студентів спеціальності 111 Математика освітнього рівня першого (бакалаврського) освітньої програми 111.00.01 МатематикаWork program of the discipline "Elementary Mathematics" for students specialty 111 Mathematics educational level of the first (bachelor) educational program 111.00.01 MathematicsРабочая программа учебной дисциплины "Элементарная математика" для студентов специальности 111 Математика образовательного уровня первого (бакалаврской) образовательной программы 111.00.01 Математик

On Nonlocal Modified Gravity and Cosmology

Despite many nice properties and numerous achievements, general relativity is not a complete theory. One of actual approaches towards more complete theory of gravity is its nonlocal modification. We present here a brief review of nonlocal gravity with its cosmological solutions. In particular, we pay special attention to two nonlocal models and their nonsingular bounce solutions for the cosmic scale factor.Comment: 11 pages, Published in Springer Proceedings in Mathematics & Statistics 111 (2014) 251-26

Математический практикум по критическому мышлению: рабочая программа

Робоча програма навчальної дисципліни "Математичний практикум з критичного мислення" для студентів спеціальності: 111 Математика освітнього рівня: першого (бакалаврського) спеціалізації: Прикладна математикаThe work program of the discipline "Mathematical Workshop on Critical Thinking" for students specialties: 111 Mathematics educational level: first (bachelor's) Specializations: Applied MathematicsРабочая программа учебной дисциплины "Математический практикум по критическому мышлению" для студентов специальности: 111 Математика образовательного уровня: первый (бакалаврской) специализации: Прикладная математик

Математическое моделирование Основы математического моделирования. Рабочая программа учебной дисциплины

Робоча програма навчальної дисципліни Математичне моделювання: Основи математичного моделювання для студентів спеціальності 111 Математика, освітнього рівня другого (магістерського), освітньої програми 111.00.02 Математичне моделюванняWork program of the discipline Mathematical Modeling: Fundamentals of Mathematical Modeling for students specialty 111 Mathematics, educational level of the second (master's), educational program 111.00.02 Mathematical modelingРабочая программа учебной дисциплины Математическое моделирование Основы математического моделирования для студентов специальности 111 Математика, образовательного уровня второго (магистерского), образовательной программы 111.00.02 Математическое моделировани

Mathematics of the Quantum Zeno Effect

We present an overview of the mathematics underlying the quantum Zeno effect. Classical, functional analytic results are put into perspective and compared with more recent ones. This yields some new insights into mathematical preconditions entailing the Zeno paradox, in particular a simplified proof of Misra's and Sudarshan's theorem. We empahsise the complex-analytic structures associated to the issue of existence of the Zeno dynamics. On grounds of the assembled material, we reason about possible future mathematical developments pertaining to the Zeno paradox and its counterpart, the anti-Zeno paradox, both of which seem to be close to complete characterisations.Comment: 32 pages, 1 figure, AMSLaTeX. In: Mathematical Physics Research at the Leading Edge, Charles V. Benton ed. Nova Science Publishers, Hauppauge NY, pp. 111-141, ISBN 1-59033-905-3, 2003; revision contains corrections from the published corrigenda to Reference [64

Working curriculum on the course "Teaching in high school: teaching method mathematical disciplines"

Робоча навчальна програма з курсу «Викладання у вищій школі: методика викладання математичних дисциплін» є нормативним документом Київського університету імені Бориса Грінченка, який розроблено кафедрою комп’ютерних наук і математики на основі освітньо-професійної програми підготовки здобувачів другого (магістерського) рівня відповідно до навчального плану спеціальності 111 МатематикаРабочая учебная программа по курсу «Преподавание в высшей школе: методика преподавания математических дисциплин »является нормативным документом Киевского университета имени Бориса Гринченко, разработанный кафедрой компьютерных наук и математики на основе образовательно-профессиональной программы подготовки соискателей второго (магистерского) уровня соответствии с учебным планом специальности 111 МатематикаRobocha Navalnaya program from the course “Cycling from Vishchiy Schools: Methodology from Cycling Mathematical disciplines "є normative document of the Kyiv University Іmenі University Boris Grinchenko, a branch of computer science and mathematics based on mastering professional training programs for health workers of a different (magіster) district Understood to the final plan for the specialty 111 Mathematic

Cartesian Products of Family of Real Linear Spaces

In this article we introduced the isomorphism mapping between cartesian products of family of linear spaces [4]. Those products had been formalized by two different ways, i.e., the way using the functor [:X, Y:] and ones using the functor "product". By the same way, the isomorphism mapping was defined between Cartesian products of family of linear normed spaces also.Okazaki Hiroyuki - Shinshu University, Nagano, JapanEndou Noboru - Nagano National College of Technology, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Nicolas Bourbaki. Topological vector spaces: Chapters 1-5. Springer, 1981.Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. The product space of real normed spaces and its properties. Formalized Mathematics, 15(3):81-85, 2007, doi:10.2478/v10037-007-0010-y.Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990

Kecerdasan Visual-Spasial, Kemampuan Numerik, dan Prestasi Belajar Matematika

This research uses survey method aimed to know the influence of visual-spatial intelligence and numerical ability on mathematics learning achievement, in class VIII students of PGRI Junior High School in Tenjolaya Subdistrict. Sampling technique with random sampling to 111 samples. The technique of collecting data 25-point test of visual-spatial intelligence and 30 items about numerical ability in multiple choice, while mathematics learning achievement data is taken from grade repetition value (UKK). Before performing the hypothesis test, the validity test item for visual-spatial intelligence test and numerical ability test were tested using biserial point correlation. The calculation result of normality of data using chi-square means otherwise. Testing of statistical hypothesis with t-test and F-test. The result of the research shows that there is a significant influence on visual-spatial intelligence and numerical ability together to the achievement of learning mathematics

Riemann Integral of Functions from R into Real Normed Space

In this article, we define the Riemann integral on functions from R into real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to a wider range of functions. The proof method follows the [16].Miyajima Keiichi - Faculty of Engineering, Ibaraki University, Hitachi, JapanKato Takahiro - Faculty of Engineering, Graduate School of Ibaraki University, Hitachi, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Darboux's theorem. Formalized Mathematics, 9(1):197-200, 2001.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Formalized Mathematics, 9(1):191-196, 2001.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.Murray R. Spiegel. Theory and Problems of Vector Analysis. McGraw-Hill, 1974.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992