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The COVID pandemic has touched many aspects of everyone’s life. Education is one of the fields greatly affected by it, as students and teachers were forced to move online and quickly adapt to the online environment. Assessment is a crucial part of education, especially in STEM fields. A gap analysis was performed by expert groups in the frame of an Erasmus+ project looking at the practices of six European countries. Specialists teaching university-grade mathematics in seven European institutions were asked about their perception of gaps in the assessment of students both before (2019) and during (2021) the pandemic. This qualitative study looks at the difference in perception of such gaps after almost one year of online teaching. The analysis of their responses showed that some gaps were present before the pandemic, as well as others that are specific to it. Some gaps, such as the lack of IT infrastructure and the need to adapt materials to an online environment, have been exacerbated by the outbreak.
Vlad Bocanet; Ken Brown; Anne Uukkivi; Filomena Soares; Ana Lopes; Anna Cellmer; Carles Serrat; Cristina Feniser; Florina Serdean; Elena Safiulina; Gerald Kelly; Joanna Cymerman; Igor Kierkosz; Volodymyr Sushch; Marina Latõnina; Oksana Labanova; M. Bruguera; Chara Pantazi; M. Estela. Change in Gap Perception within Current Practices in Assessing Students Learning Mathematics. Sustainability 2021, 13, 4495 .
AMA StyleVlad Bocanet, Ken Brown, Anne Uukkivi, Filomena Soares, Ana Lopes, Anna Cellmer, Carles Serrat, Cristina Feniser, Florina Serdean, Elena Safiulina, Gerald Kelly, Joanna Cymerman, Igor Kierkosz, Volodymyr Sushch, Marina Latõnina, Oksana Labanova, M. Bruguera, Chara Pantazi, M. Estela. Change in Gap Perception within Current Practices in Assessing Students Learning Mathematics. Sustainability. 2021; 13 (8):4495.
Chicago/Turabian StyleVlad Bocanet; Ken Brown; Anne Uukkivi; Filomena Soares; Ana Lopes; Anna Cellmer; Carles Serrat; Cristina Feniser; Florina Serdean; Elena Safiulina; Gerald Kelly; Joanna Cymerman; Igor Kierkosz; Volodymyr Sushch; Marina Latõnina; Oksana Labanova; M. Bruguera; Chara Pantazi; M. Estela. 2021. "Change in Gap Perception within Current Practices in Assessing Students Learning Mathematics." Sustainability 13, no. 8: 4495.
The goal of this paper is to introduce a technique of creating self-tests that has allowed to actively incorporate university students into the learning process. The study was conducted within the framework of the Erasmus+ Project EngiMath. Partners’ peer reviews, the survey results and the students’ comments in forums and test results were used to conduct the research. The students’ overall satisfaction was in a high level. However, opportunities for some technical improvement has been emerged like the formulation of the tasks needs to be very clear and the time required to perform the tests must be limited. The following conclusions can be drawn from the study. The use of self-tests at all stages of training has intensified the assimilation of the material, i.e. increased understanding of theoretical material and developed computational skills. By completing a series of such assignments on each topic of the course, students had mastered the methodology of studying the topic and mastered specific teaching material on this topic. Feedback made, taking into account typical errors, has allowed the students to analyse their knowledge. A large number of variations for such tasks has allowed students to be involved in the process of active independent and individualized self-study.
Oksana Labanova; Elena Safiulina; Marina Latõnina; Anne Uukkivi; Vlad Bocanet; Cristina Feniser; Florina Serdean; Ana Paula Lopes; Filomena Soares; Ken Brown; Gerald Kelly; Errol Martin; Anna Cellmer; Joanna Cymerman; Volodymyr Sushch; Igor Kierkosz; Javier Bilbao; Eugenio Bravo; Olatz Garcia; Concepción Varela; Carolina Rebollar. Poster: Technique of Active Online Training: Lessons Learnt from EngiMath Project. Advances in Intelligent Systems and Computing 2021, 721 -729.
AMA StyleOksana Labanova, Elena Safiulina, Marina Latõnina, Anne Uukkivi, Vlad Bocanet, Cristina Feniser, Florina Serdean, Ana Paula Lopes, Filomena Soares, Ken Brown, Gerald Kelly, Errol Martin, Anna Cellmer, Joanna Cymerman, Volodymyr Sushch, Igor Kierkosz, Javier Bilbao, Eugenio Bravo, Olatz Garcia, Concepción Varela, Carolina Rebollar. Poster: Technique of Active Online Training: Lessons Learnt from EngiMath Project. Advances in Intelligent Systems and Computing. 2021; ():721-729.
Chicago/Turabian StyleOksana Labanova; Elena Safiulina; Marina Latõnina; Anne Uukkivi; Vlad Bocanet; Cristina Feniser; Florina Serdean; Ana Paula Lopes; Filomena Soares; Ken Brown; Gerald Kelly; Errol Martin; Anna Cellmer; Joanna Cymerman; Volodymyr Sushch; Igor Kierkosz; Javier Bilbao; Eugenio Bravo; Olatz Garcia; Concepción Varela; Carolina Rebollar. 2021. "Poster: Technique of Active Online Training: Lessons Learnt from EngiMath Project." Advances in Intelligent Systems and Computing , no. : 721-729.
This paper concerns the question of how chirality is realized for discrete counterparts of the Dirac-Kähler equation in the Hestenes and Joyce forms. It is shown that left and right chiral states for these discrete equations can be described with the aid of some projectors on a space of discrete forms. The proposed discrete model admits a chiral symmetry. We construct discrete analogues of spin operators, describe spin eigenstates for a discrete Joyce equation, and also discuss chirality (A preprint version of the article is available as ArXiv preprint: http://arxiv.org/pdf/1912.01296).
Volodymyr Sushch. Chiral Properties of Discrete Joyce and Hestenes Equations. Springer Texts in Business and Economics 2020, 765 -778.
AMA StyleVolodymyr Sushch. Chiral Properties of Discrete Joyce and Hestenes Equations. Springer Texts in Business and Economics. 2020; ():765-778.
Chicago/Turabian StyleVolodymyr Sushch. 2020. "Chiral Properties of Discrete Joyce and Hestenes Equations." Springer Texts in Business and Economics , no. : 765-778.
We construct a discrete version of the plane wave solution to a discrete Dirac-Kähler equation in the Joyce form. A geometric discretisation scheme based on both forward and backward difference operators is used. The conditions under which a discrete plane wave solution satisfies a discrete Joyce equation are discussed.
Volodymyr Sushch. A Discrete Version of Plane Wave Solutions of the Dirac Equation in the Joyce Form. Advances in Applied Clifford Algebras 2020, 30, 1 -20.
AMA StyleVolodymyr Sushch. A Discrete Version of Plane Wave Solutions of the Dirac Equation in the Joyce Form. Advances in Applied Clifford Algebras. 2020; 30 (3):1-20.
Chicago/Turabian StyleVolodymyr Sushch. 2020. "A Discrete Version of Plane Wave Solutions of the Dirac Equation in the Joyce Form." Advances in Applied Clifford Algebras 30, no. 3: 1-20.
We construct a discrete version of the plane wave solution to a discrete Dirac-K\"{a}hler equation in the Joyce form. A geometric discretisation scheme based on both forward and backward difference operators is used. The conditions under which a discrete plane wave solution satisfies a discrete Joyce equation are discussed.
Volodymyr Sushch. A discrete version of plane wave solutions of the Dirac equation in the Joyce form. 2019, 1 .
AMA StyleVolodymyr Sushch. A discrete version of plane wave solutions of the Dirac equation in the Joyce form. . 2019; ():1.
Chicago/Turabian StyleVolodymyr Sushch. 2019. "A discrete version of plane wave solutions of the Dirac equation in the Joyce form." , no. : 1.
Discrete models of the Dirac–Kähler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the Hestenes equation is established.
Volodymyr Sushch. A Discrete Dirac–Kähler Equation Using a Geometric Discretisation Scheme. Advances in Applied Clifford Algebras 2018, 28, 72 .
AMA StyleVolodymyr Sushch. A Discrete Dirac–Kähler Equation Using a Geometric Discretisation Scheme. Advances in Applied Clifford Algebras. 2018; 28 (4):72.
Chicago/Turabian StyleVolodymyr Sushch. 2018. "A Discrete Dirac–Kähler Equation Using a Geometric Discretisation Scheme." Advances in Applied Clifford Algebras 28, no. 4: 72.
A discrete version of the plane wave solution to some discrete Dirac type equations in the spacetime algebra is established. The conditions under which a discrete analogue of the plane wave solution satisfies the discrete Hestenes equation are briefly discussed.
Volodymyr Sushch. Discrete Versions of Some Dirac Type Equations and Plane Wave Solutions. Springer Texts in Business and Economics 2018, 463 -475.
AMA StyleVolodymyr Sushch. Discrete Versions of Some Dirac Type Equations and Plane Wave Solutions. Springer Texts in Business and Economics. 2018; ():463-475.
Chicago/Turabian StyleVolodymyr Sushch. 2018. "Discrete Versions of Some Dirac Type Equations and Plane Wave Solutions." Springer Texts in Business and Economics , no. : 463-475.
A discrete analogue of the Dirac equation in the Hestenes form is constructed by introduction of the Clifford product on the space of discrete forms. We discuss the relation between the discrete Dirac-Kähler equation and the discrete Hestenes equation.
Volodymyr Sushch. Discrete Dirac-Kähler and Hestenes Equations. Springer Texts in Business and Economics 2016, 433 -442.
AMA StyleVolodymyr Sushch. Discrete Dirac-Kähler and Hestenes Equations. Springer Texts in Business and Economics. 2016; ():433-442.
Chicago/Turabian StyleVolodymyr Sushch. 2016. "Discrete Dirac-Kähler and Hestenes Equations." Springer Texts in Business and Economics , no. : 433-442.
We discuss a discrete analogue of the Dirac–Kähler equation in which chiral properties of the continuum counterpart are captured. We pay special attention to a discrete Hodge star operator. To build such an operator combinatorial construction of a double complex is used. We describe discrete exterior calculus operations on a double complex and obtain the discrete Dirac–Kähler equation using these tools. Self-dual and anti-self-dual discrete inhomogeneous forms are presented. The chiral invariance of the massless discrete Dirac–Kähler equation is shown. Moreover, in the massive case we prove that a discrete Dirac–Kähler operator flips the chirality.
Volodymyr Sushch. On the Chirality of a Discrete Dirac–Kähler Equation. Reports on Mathematical Physics 2015, 76, 179 -196.
AMA StyleVolodymyr Sushch. On the Chirality of a Discrete Dirac–Kähler Equation. Reports on Mathematical Physics. 2015; 76 (2):179-196.
Chicago/Turabian StyleVolodymyr Sushch. 2015. "On the Chirality of a Discrete Dirac–Kähler Equation." Reports on Mathematical Physics 76, no. 2: 179-196.
We construct a new discrete analog of the Dirac-K\"{a}hler equation in which some key geometric aspects of the continuum counterpart are captured. We describe a discrete Dirac-K\"{a}hler equation in the intrinsic notation as a set of difference equations and prove several statements about its decomposition into difference equations of Duffin type. We study an analog of gauge transformations for the massless discrete Dirac-K\"{a}hler equations.Comment: 19 pages; added references; to appear in Rept. Math. Phy
Volodymyr Sushch. A discrete model of the Dirac-Kähler equation. Reports on Mathematical Physics 2014, 73, 109 -125.
AMA StyleVolodymyr Sushch. A discrete model of the Dirac-Kähler equation. Reports on Mathematical Physics. 2014; 73 (1):109-125.
Chicago/Turabian StyleVolodymyr Sushch. 2014. "A discrete model of the Dirac-Kähler equation." Reports on Mathematical Physics 73, no. 1: 109-125.
We study discrete models which are generated by the self-dual Yang–Mills equations. Using a double complex construction, we construct a new discrete analog of the Bogomolny equations. Discrete Bogomolny equations, a system of matrix-valued difference equations, are obtained from discrete self-dual equations. The gauge invariance of the discrete model is established.
Volodymyr Sushch. A Double Complex Construction and Discrete Bogomolny Equations. Springer Texts in Business and Economics 2013, 47, 615 -624.
AMA StyleVolodymyr Sushch. A Double Complex Construction and Discrete Bogomolny Equations. Springer Texts in Business and Economics. 2013; 47 ():615-624.
Chicago/Turabian StyleVolodymyr Sushch. 2013. "A Double Complex Construction and Discrete Bogomolny Equations." Springer Texts in Business and Economics 47, no. : 615-624.
A discrete model of Bogomolny equations based on the combinatorial structure of a double complex is constructed. It is shown that the difference analogs of the Bogomolny equations can be obtained from the discrete self-dual Yang–Mills equations and preserve the geometric properties of the corresponding equations of continual theory.
Volodymyr Sushch. A discrete analog of the Bogomolny equations. Journal of Mathematical Sciences 2012, 187, 574 -582.
AMA StyleVolodymyr Sushch. A discrete analog of the Bogomolny equations. Journal of Mathematical Sciences. 2012; 187 (5):574-582.
Chicago/Turabian StyleVolodymyr Sushch. 2012. "A discrete analog of the Bogomolny equations." Journal of Mathematical Sciences 187, no. 5: 574-582.
We study a discrete model of the $SU(2)$ Yang-Mills equations on a combinatorial analog of $\mathbb {R}^4$. Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both the techniques of a double complex and the quaternionic approach.
Volodymyr Sushch. Instanton-anti-instanton solutions of discrete Yang-Mills equations. Mathematica Bohemica 2012, 137, 219 -228.
AMA StyleVolodymyr Sushch. Instanton-anti-instanton solutions of discrete Yang-Mills equations. Mathematica Bohemica. 2012; 137 (2):219-228.
Chicago/Turabian StyleVolodymyr Sushch. 2012. "Instanton-anti-instanton solutions of discrete Yang-Mills equations." Mathematica Bohemica 137, no. 2: 219-228.
We study a discrete model of the SU(2) Yang-Mills equations on a combinatorial analog of $Bbb{R}^4$. Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both techniques of a double complex and the quaternionic approach. Interesting analogies between instanton, anti-instanton solutions of discrete and continual self-dual, anti-self-dual equations are also discussed.
Volodymyr Sushch. Self-Dual and Anti-Self-Dual Solutions of Discrete Yang-Mills Equations on a Double Complex. Cubo (Temuco) 2010, 12, 99 -120.
AMA StyleVolodymyr Sushch. Self-Dual and Anti-Self-Dual Solutions of Discrete Yang-Mills Equations on a Double Complex. Cubo (Temuco). 2010; 12 (3):99-120.
Chicago/Turabian StyleVolodymyr Sushch. 2010. "Self-Dual and Anti-Self-Dual Solutions of Discrete Yang-Mills Equations on a Double Complex." Cubo (Temuco) 12, no. 3: 99-120.
We prove essential self-adjointness for a semibounded from below discrete magnetic Schrödinger operator in a space that represents a combinatorial model of the two-dimensional Euclidean space. The Dezin discretization scheme is used for constructing a discrete model.
V. N. Sushch. Essential self-adjointness of a discrete magnetic Schrödinger operator. Journal of Mathematical Sciences 2009, 160, 368 -378.
AMA StyleV. N. Sushch. Essential self-adjointness of a discrete magnetic Schrödinger operator. Journal of Mathematical Sciences. 2009; 160 (3):368-378.
Chicago/Turabian StyleV. N. Sushch. 2009. "Essential self-adjointness of a discrete magnetic Schrödinger operator." Journal of Mathematical Sciences 160, no. 3: 368-378.
Some method of constructing intrinsically defined discrete models for differential operators on the space with the Lorentz metric is described. The difference wave equation and a discrete model of the mixed problem are constructed.
Volodymyr Sushch. On discrete models of the wave equation. Equadiff 99 2000, 354 -356.
AMA StyleVolodymyr Sushch. On discrete models of the wave equation. Equadiff 99. 2000; ():354-356.
Chicago/Turabian StyleVolodymyr Sushch. 2000. "On discrete models of the wave equation." Equadiff 99 , no. : 354-356.
We study optimal control problems with a quadratic optimization criterion. The state of the system is described by the solution of an operator-differential equation under nonlocal boundary conditions; the control is on the righth- and side of the equation. We prove existence and uniqueness theorems for the optimal control.
V. N. Sushch. Distributed control in a class of nonlocal boundary-value problems. Journal of Mathematical Sciences 1999, 96, 2838 -2842.
AMA StyleV. N. Sushch. Distributed control in a class of nonlocal boundary-value problems. Journal of Mathematical Sciences. 1999; 96 (1):2838-2842.
Chicago/Turabian StyleV. N. Sushch. 1999. "Distributed control in a class of nonlocal boundary-value problems." Journal of Mathematical Sciences 96, no. 1: 2838-2842.
Two discrete models of Yang-Mill equations are constructed in the space ℝn for some matrix-valued Lie group. A gauge-invariant discrete model is examined.
V. N. Sushch. Gauge-invariant discrete models of Yang-Mills equations. Mathematical Notes of the Academy of Sciences of the USSR 1997, 61, 621 -631.
AMA StyleV. N. Sushch. Gauge-invariant discrete models of Yang-Mills equations. Mathematical Notes of the Academy of Sciences of the USSR. 1997; 61 (5):621-631.
Chicago/Turabian StyleV. N. Sushch. 1997. "Gauge-invariant discrete models of Yang-Mills equations." Mathematical Notes of the Academy of Sciences of the USSR 61, no. 5: 621-631.
We study the problem of optimal control with a quadratic optimization criterion. The state of the system is described by operator-differential equations with nonlocal boundary conditions. We prove an existence and uniqueness theorem for an optimal control.
Volodymyr Sushch. Nonlocal problems with boundary controls. Journal of Mathematical Sciences 1993, 66, 2595 -2600.
AMA StyleVolodymyr Sushch. Nonlocal problems with boundary controls. Journal of Mathematical Sciences. 1993; 66 (6):2595-2600.
Chicago/Turabian StyleVolodymyr Sushch. 1993. "Nonlocal problems with boundary controls." Journal of Mathematical Sciences 66, no. 6: 2595-2600.