Gotowa bibliografia na temat „Analytical Mathematics”

Graphic statics is undergoing a renaissance, with computerized visual representation becoming both easier and more spectacular as time passes. While methods of the past are revived, little emphasis has been placed on studying the mathematics behind these methods. Due to the considerable advances of our mathematical understanding since the birth of graphic statics, we can learn a lot by examining these old methods from a more modern viewpoint. As such, this work shows the mathematical fabric joining different aspects of graphic statics, like dualities, reciprocal diagrams, and discontinuous stress functions. This is done by introducing a new, three dimensional force diagram (containing the old two dimensional force diagram) depicting the three dimensional equilibrium of planar force systems. A corresponding three dimensional “form diagram” (dual diagram) is introduced, in which forces are treated as linear functionals (dual vectors). It is shown that the polyhedral stress function introduced by Maxwell is in fact a linear combination of these functionals; and the projective dualities connecting these three dimensional diagrams are also explained.

The importance ability of mathematical representation and connection to owned by the student really help students in understanding the mathematical concepts in the form of pictures, symbols, and the written word. The use of mathematical representation and the correct connection by students will help students make mathematical ideas more concrete and can connect a concept to another concept, so that students can develop a view of mathematics as a whole integration. This research aims to describe and analyze the ability of representation and mathematical connection on the topics of analytical geometry. The research method was descriptive with the subject as much as 22 mathematics students. Data collected through tests and interviews. The results show that the average ability of representation is 46.00; the average mathematical connection ability is 36.77. This means both the abilities still belongs to low, particularly for the ability of mathematical connection.

The importance ability of mathematical representation and connection to owned by the student really help students in understanding the mathematical concepts in the form of pictures, symbols, and the written word. The use of mathematical representation and the correct connection by students will help students make mathematical ideas more concrete and can connect a concept to another concept, so that students can develop a view of mathematics as a whole integration. This research aims to describe and analyze the ability of representation and mathematical connection on the topics of analytical geometry. The research method was descriptive with the subject as much as 22 mathematics students. Data collected through tests and interviews. The results show that the average ability of representation is 46.00; the average mathematical connection ability is 36.77. This means both the abilities still belongs to low, particularly for the ability of mathematical connection.

Mathematical proficiency is the ability to use conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition in problem-solving. This study aims to determine the effect of mathematics anxiety level and cognitive independence level on mathematical proficiency. This research combined quantitative and qualitative methods to determine the effect of mathematics anxiety and cognitive independence on mathematical proficiency. It used the multiple linear regression test for the quantitative approach. Moreover, the qualitative approach was used to see the effect of anxiety level and cognitive independence on mathematical proficiency. One hundred fifty-five high school students participated in this study, and it was found that mathematics anxiety affects mathematical proficiency negatively while cognitive independence affects mathematical proficiency positively. Students who have high mathematics anxiety use trial and error strategies, while their counterparts, having low mathematics anxiety, use analytical strategies. Students with high cognitive independence can process the information and tend to be independent, while those with low cognitive independence do so illogically and tend to need help from others. The results of this study are hoped to be beneficial for teachers in choosing learning methods. Keywords: analytical strategy; cognitive independence; mathematical proficiency; mathematics anxiety; trial-error strategy;