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Journal articles on the topic 'Visual algebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

Iurato, Giuseppe. "Eye Movement Pre-Algebra and Visual Semantic Algebra." International Journal of Cognitive Informatics and Natural Intelligence 13, no. 1 (January 2019): 62–72. http://dx.doi.org/10.4018/ijcini.2019010105.

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This article proposes a new denotational mathematics entity, i.e., the eye movement pre-algebra (EMpA), which may be considered as a pre-algebraic structure in a certain sense generating, according to universal algebra, Husserlian phenomenological theory and structuralism, another basic algebraic structure of denotational mathematics, said to be visual semantic algebra (VSA).

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Wang, Yingxu. "On Visual Semantic Algebra (VSA)." International Journal of Software Science and Computational Intelligence 1, no. 4 (October 2009): 1–16. http://dx.doi.org/10.4018/jssci.2009062501.

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A new form of denotational mathematics known as Visual Semantic Algebra (VSA) is presented for abstract visual object and architecture manipulations. A set of cognitive theories for pattern recognition is explored such as cognitive principles of visual perception and basic mechanisms of object and pattern recognition. The cognitive process of pattern recognition is rigorously modeled using VSA and Real-Time Process Algebra (RTPA), which reveals the fundamental mechanisms of natural pattern recognition by the brain. Case studies on VSA in pattern recognition are presented to demonstrate VAS’ expressive power for algebraic manipulations of visual objects. VSA can be applied not only in machinable visual and spatial reasoning, but also in computational intelligence as a powerful man-machine language for representing and manipulating visual objects and patterns. On the basis of VSA, computational intelligent systems such as robots and cognitive computers may process and inference visual and image objects rigorously and efficiently.

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Kirshner, David. "The Visual Syntax of Algebra." Journal for Research in Mathematics Education 20, no. 3 (May 1989): 274–87. http://dx.doi.org/10.5951/jresematheduc.20.3.0274.

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A structured system of visual features can be seen to parallel the propositional hierarchy of operations usually associated with the parsing of algebraic expressions. Some students (proportionately more women than men) were found to depend on these visual cues in their syntactic decision making. Others were found to have access to sound propositional rules. Possible causes and consequences of these different syntactic representation styles are discussed.

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Kirshner, David. "The Visual Syntax of Algebra." Journal for Research in Mathematics Education 20, no. 3 (May 1989): 274. http://dx.doi.org/10.2307/749516.

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5

Huen, Y. K. "Visual algebra and its applications." International Journal of Mathematical Education in Science and Technology 28, no. 3 (May 1997): 333–44. http://dx.doi.org/10.1080/0020739970280303.

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6

Jackson, Tess, and Ron Goolsby. "VISUAL JUSTIFICATION OF ALGEBRA CONCEPTS." PRIMUS 6, no. 3 (January 1996): 209–20. http://dx.doi.org/10.1080/10511979608965824.

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7

Morelli, Lynn. "A Visual Approach to Algebra Concepts." Mathematics Teacher 85, no. 6 (September 1992): 434–37. http://dx.doi.org/10.5951/mt.85.6.0434.

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8

Shaverdian, Anna A., Hao Zhou, George Michailidis, and Hosagrahar V. Jagadish. "A Graph Algebra for Scalable Visual Analytics." IEEE Computer Graphics and Applications 32, no. 4 (July 2012): 26–33. http://dx.doi.org/10.1109/mcg.2012.62.

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9

Liao, Liang, and Stephen John Maybank. "Generalized Visual Information Analysis Via Tensorial Algebra." Journal of Mathematical Imaging and Vision 62, no. 4 (February 12, 2020): 560–84. http://dx.doi.org/10.1007/s10851-020-00946-9.

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MIRAH MARIATI, NI PUTU AYU, NI LUH PUTU SUCIPTAWATI, and KARTIKA SARI. "ANALISIS PERCOBAAN FAKTORIAL UNTUK MELIHAT PENGARUH PENGGUNAAN ALAT PERAGA BLOK ALJABAR TERHADAP PRESTASI BELAJAR ALJABAR SISWA." E-Jurnal Matematika 2, no. 2 (May 31, 2013): 1. http://dx.doi.org/10.24843/mtk.2013.v02.i02.p030.

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The experimental design was applied in research in many different fields of science, such as in education, as used in this study. Block algebra visual aids is a visual aids in the form of the geometry model used to concretize understanding the variables and constants in the algebra which is an abstract concept. This visual aids are used as a basis for factoring algebraic forms. In connection with this, the aims of this research is to determine the effect of the application of algebra block in student academic achievement in class VII in the field of algebra in schools categorized as private, SSN (Sekolah Standar Nasional) and the previously categorized RSBI (Rintisan Sekolah Bertaraf Internasional). The method of analysis used in this study was two-factor experimental design in a randomized block design. The results showed that the academic achievement of students in the field of algebra after learning with block algebra visual aids obtained better than the academic achievement of students who received learning without using block algebra visual aids. Moreover, it also shows that the categories of schools have a significant effect on student achievement.

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Peng Chen, Liang Zhou, Yingxue Yao, and Shengdong Gao. "A Visual Glove Based on Conformal Geometric Algebra." International Journal of Advancements in Computing Technology 4, no. 23 (December 31, 2012): 499–506. http://dx.doi.org/10.4156/ijact.vol4.issue23.59.

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12

Honrales, Cynthia C. "Audio-Visual Approach to Remedial Instruction in Algebra." Journal of Social Sciences (COES&RJ-JSS) 6, no. 2S (April 1, 2017): 1–7. http://dx.doi.org/10.25255/jss.2017.6.2s.1.7.

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13

Shen, Gang, Feng Liu, Zhengxin Fu, and Bin Yu. "Visual cryptograms of random grids via linear algebra." Multimedia Tools and Applications 77, no. 10 (June 14, 2017): 12871–99. http://dx.doi.org/10.1007/s11042-017-4921-5.

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14

Velleman, Daniel J. "The Fundamental Theorem of Algebra: A Visual Approach." Mathematical Intelligencer 37, no. 4 (November 5, 2015): 12–21. http://dx.doi.org/10.1007/s00283-015-9572-7.

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15

Darley, Joy W. "Traveling from Arithmetic to Algebra." Mathematics Teaching in the Middle School 14, no. 8 (April 2009): 458–64. http://dx.doi.org/10.5951/mtms.14.8.0458.

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16

Wu, Keqin, Liang Sun, Carl Schmidt, and Jian Chen. "Graph query algebra and visual proximity rules for biological pathway exploration." Information Visualization 16, no. 3 (September 12, 2016): 217–31. http://dx.doi.org/10.1177/1473871616666394.

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We present the design and validation of an example-based pathway graph query algebra and visual proximity rules to address challenging large biological pathway exploration tasks. Our pathway graph query algebra interprets relationship queries given by selected examples to find a match for, extract identical parts between, or trace a path from any pathway components. To support the relationship query, users can composite pathway visualizations through visual proximity rules that use proximity to infer users’ intentions in the exploration process. By allowing selection of one or more objects from multiple on-screen grouped graphs as query inputs and using the query outputs as next-query inputs, pathway graph query algebra and visual proximity rules achieve intuitiveness, concurrence, and dynamics for pathway exploration.

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17

Landy, David, David Brookes, and Ryan Smout. "Abstract numeric relations and the visual structure of algebra." Journal of Experimental Psychology: Learning, Memory, and Cognition 40, no. 5 (2014): 1404–18. http://dx.doi.org/10.1037/a0036823.

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18

López-Franco, Carlos, Nancy Arana-Daniel, and Alma Y. Alanis. "Visual Servoing on the Sphere Using Conformal Geometric Algebra." Advances in Applied Clifford Algebras 23, no. 1 (June 7, 2012): 125–41. http://dx.doi.org/10.1007/s00006-012-0342-8.

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19

David, Maria Manuela, Vanessa Sena Tomaz, and Maria Cristina Costa Ferreira. "How visual representations participate in algebra classes’ mathematical activity." ZDM 46, no. 1 (October 17, 2013): 95–107. http://dx.doi.org/10.1007/s11858-013-0550-2.

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20

Lee, Sang-Gu, Ji-Eun Jang, and Kyung-Won Kim. "Visualization of Linear Algebra concepts with Sage and GeoGebra." Communications of Mathematical Education 27, no. 1 (February 28, 2013): 1–17. http://dx.doi.org/10.7468/jksmee.2013.27.1.001.

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21

Lin, Xiaoyu, and Yingxu Wang. "Simulation and Visualization of Concept Algebra in MATLAB." International Journal of Software Science and Computational Intelligence 6, no. 1 (January 2014): 30–55. http://dx.doi.org/10.4018/ijssci.2014010103.

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Concept algebra (CA) is a denotational mathematics for formal knowledge manipulation and natural language processing. In order to explicitly demonstrate the mathematical models of formal concepts and their algebraic operations in CA, a simulation and visualization software is developed in the MATLAB environment known as the Visual Simulator of Concept Algebra (VSCA). This paper presents the design and implementation of VSCA and the theories underpinning its development. Visual simulations for the sets of reproductive and compositional operations of CA are demonstrated by real-world examples throughout the elaborations of CA and VSCA.

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22

López-Franco, C., and E. Bayro-Corrochano. "Omnidirectional vision and conformal geometric algebra for visual landmark identification." Robotica 26, no. 5 (September 2008): 559–69. http://dx.doi.org/10.1017/s0263574707003967.

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SUMMARYThe automatic landmark identification is very important in autonomous robot navigation tasks. In this paper, we use a monocular omnidirectional vision system to extract the image features and the conformal geometric algebra to compute the projective invariants from such features. We show how these features can be used to compute projective and permutationp2-invariantsfrom any kind of omnidirectional vision system. Thep2-invariantsrepresent scene sublandmarks, and a set of them characterize a landmark. The advantage of this representation is that the landmarks are more robust than the single cross-ratio.

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23

Bouck, Emily C., and Pei-Lin Weng. "Hearing Math: Algebra Supported eText for Students With Visual Impairments." Assistive Technology 26, no. 3 (June 26, 2014): 131–39. http://dx.doi.org/10.1080/10400435.2013.870939.

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24

Shen, Gang, Feng Liu, Zhengxin Fu, and Bin Yu. "Perfect contrast XOR-based visual cryptography schemes via linear algebra." Designs, Codes and Cryptography 85, no. 1 (October 4, 2016): 15–37. http://dx.doi.org/10.1007/s10623-016-0285-5.

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25

Apsari, Ratih Ayu, Sariyasa, R. I. I. Putri, S. Rejeki, and U. Lu’luilmaknun. "Same pattern, different visualization: visual support does matter in pre-algebra." Journal of Physics: Conference Series 1776, no. 1 (February 1, 2021): 012026. http://dx.doi.org/10.1088/1742-6596/1776/1/012026.

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26

Abdelmajead, Ahmed S. "The Effect of Using Mathematical Correlations and Some Visual Teaching Strategies on the Levels of Information Processing and Self Evaluation of the Written Mathematical Knowledge Patterns of the First year Preparatory Students." Journal of Educational and Psychological Studies [JEPS] 7, no. 2 (March 1, 2013): 167. http://dx.doi.org/10.24200/jeps.vol7iss2pp167-185.

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This research aimed at identifying the effect of using mathematical correlations and some visual teaching strategies on the levels of information processing and self-evaluation of the written mathematical knowledge patterns of the first year preparatory students. To achieve this aim, three groups were selected: two of them were experimental, and the third was a control one. An Algebra unit was taught to the experimental group (39 students) according to the mathematical correlations; and the second experimental group (38 students) studied the same content, according to some visual teaching strategies, and the third group (the control group) (40 students) studied the same content in the same time period according to the usual method used in teaching. The Algebra unit was prepared using the mathematical correlations strategy and some visual teaching strategies. A teacher's manual based on the aformentioned strategies was also prepared. A test for measuring mathematical information processing and a scale for evaluating the written mathematical knowledge patterns was administered to the three groups. The results showed that using mathematical correlations and some visual teaching strategies in teaching the Algebra unit contributed to raising the level of information processing as well as the written mathematical knowledge patterns of the first preparatory students.The results also indicated equal use of the mathematical correlations and some visual teaching strategies on the level of information processing and self evaluation of the written mathematical knowledge patterns of the first year preparatory students.

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27

Beigie, Darin. "Solving Optimization Problems with Spreadsheets." Mathematics Teacher 111, no. 1 (September 2017): 26–33. http://dx.doi.org/10.5951/mathteacher.111.1.0026.

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28

Sholihah, Ummu, and Maryono Maryono. "Students’ visual thinking ability in solving the integral problem." JRAMathEdu (Journal of Research and Advances in Mathematics Education) 5, no. 2 (June 27, 2020): 175–86. http://dx.doi.org/10.23917/jramathedu.v5i2.10286.

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Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with technological tools, describing and communicating information and ideas, developing ideas, and understanding improvement. This research describes students’ visual thinking ability to solve integral problems. The approach used in this study was descriptive qualitative. The subjects in this study were three students from the Department of Mathematics Education at the State Islamic Institute of Tulungagung. The data were collected by using tests and interviews. The steps to analyze the data were categorization, reduction, exposure, interpretation, and conclusion. Based on the analysis of students’ visual thinking skills in solving integral problems, there were three levels of visual thinking: semi-local visual, local visual, and global visual. At the semi-local visual level, students could only understand algebraically, and they have not shown it graphically at all. Meanwhile, at the local visual level, they have already understood geometry as an alternative language and been able graphically represented problems or concepts, even though it was not perfectly done yet. While on a global visual level, they could perfectly visualize visual thinking indicators, understand algebra and geometry as alternative languages for problem-solving, extract specific information from diagrams, graph problems, and use them to solve problems perfectly.

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29

S., L. L., Andrew Blake, and Andrew Zisserman. "Visual Reconstruction." Mathematics of Computation 53, no. 188 (October 1989): 772. http://dx.doi.org/10.2307/2008745.

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Bennett, Albert B., and Eugene Maier. "A Visual Approach to Solving Mixture Problems." Mathematics Teacher 89, no. 2 (February 1996): 108–11. http://dx.doi.org/10.5951/mt.89.2.0108.

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In the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), the 9–12 standards call for a shift from a curriculum dominated by memorization of isolated facts and procedures to one that emphasizes conceptual understandings, multiple representations and connections, mathematical modeling, and mathematical problem solving. One approach that affords opportunities for achieving these objectives is the use of diagrams and drawings. The familiar saying “A picture is worth a thousand words” could well be modified for mathematics to “A picture is worth a thousand numbers.” As an example of visual approaches in algebra, this article uses diagrams to solve mixture problems.

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Burkhardt, Paula, Alice Zhuo-Yu Chan, Gabriel Currier, Stephan Ramon Garcia, Florian Luca, and Hong Suh. "Visual properties of generalized Kloosterman sums." Journal of Number Theory 160 (March 2016): 237–53. http://dx.doi.org/10.1016/j.jnt.2015.08.019.

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32

McGlaughlin, Sean M., Andrew J. Knoop, and Gregory A. Holliday. "Differentiating Students with Mathematics Difficulty in College: Mathematics Disabilities vs. No Diagnosis." Learning Disability Quarterly 28, no. 3 (August 2005): 223–32. http://dx.doi.org/10.2307/1593660.

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Difficulties with college algebra can be the gatekeeper for earning a degree. Students struggle with algebra for many reasons. The focus of study was to examine students struggling with entry-level algebra courses and differentiate between those who were identified as having a mathematics disability and those who were not. Variables related to working memory, math fluency, nonverbal/visual reasoning, attention, and reading were analyzed using a MANOVA and separate ANOVAs. Significant differences were found on all but attention, supporting the findings of research on students in elementary and secondary education. Implications include a focus on techniques that help to remediate these specific deficits.

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GONZÁLEZ-JIMÉNEZ, LUIS ENRIQUE, ALEXANDER G. LOUKIANOV, and EDUARDO JOSE BAYRO-CORROCHANO. "DISCRETE INTEGRAL SLIDING MODE CONTROL IN VISUAL OBJECT TRACKING." International Journal of Humanoid Robotics 07, no. 03 (September 2010): 491–509. http://dx.doi.org/10.1142/s0219843610002167.

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Object tracking is an important process for many applications in computer vision. This process must be implemented in a discrete manner because the images are available only at certain periods. A discrete integral sliding mode algorithm is proposed to control a stereo vision system and perform the aforementioned second task. The kinematic model of the structure is obtained using geometric algebra. The performance of the controller is compared with proportional-integral-derivative control via simulation. The implementation for a pan tilt unit is presented in real time. The algorithm presents a good and robust performance.

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WANG, YINGXU. "ON FORMAL AND COGNITIVE SEMANTICS FOR SEMANTIC COMPUTING." International Journal of Semantic Computing 04, no. 02 (June 2010): 203–37. http://dx.doi.org/10.1142/s1793351x10000833.

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Semantics is the meaning of symbols, notations, concepts, functions, and behaviors, as well as their relations that can be deduced onto a set of predefined entities and/or known concepts. Semantic computing is an emerging computational methodology that models and implements computational structures and behaviors at semantic or knowledge level beyond that of symbolic data. In semantic computing, formal semantics can be classified into the categories of to be, to have, and to do semantics. This paper presents a comprehensive survey of formal and cognitive semantics for semantic computing in the fields of computational linguistics, software science, computational intelligence, cognitive computing, and denotational mathematics. A set of novel formal semantics, such as deductive semantics, concept-algebra-based semantics, and visual semantics, is introduced that forms a theoretical and cognitive foundation for semantic computing. Applications of formal semantics in semantic computing are presented in case studies on semantic cognition of natural languages, semantic analyses of computing behaviors, behavioral semantics of human cognitive processes, and visual semantic algebra for image and visual object manipulations.

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Marchetti, Elena, and Luisa Rossi Costa. "Reconstruction of Forms by Linear Algebra." Nexus Network Journal 7, no. 1 (April 2005): 58–68. http://dx.doi.org/10.1007/s00004-005-0006-2.

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36

Kreknin, V. A., and M. S. Lvov. "The Usage of Programming Software “The Library of Electronic Visual Aids “Algebra 7-9” During Algebra Learning in 7-9 Forms." Information Technologies in Education, no. 1 (April 12, 2008): 78–87. http://dx.doi.org/10.14308/ite000011.

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37

Flores, Alfinio. "Explorations with 142857: Connecting the Elementary with the Advanced." Mathematics Teacher 101, no. 6 (February 2008): 418–21. http://dx.doi.org/10.5951/mt.101.6.0418.

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Explorations with the cyclic number for students and teachers help connect the mathematics taught in school with algebra and number theory concepts learned in college. Additional ways to manipulate sequential numbers and how they relate create new sequences as well as graphical and visual representations are given.

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38

Booze, David A. "Delving Deeper: Visualizing Pythagorean Triples and Beyond." Mathematics Teacher 104, no. 5 (December 2010): 393–98. http://dx.doi.org/10.5951/mt.104.5.0393.

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Exploring the algebraic properties that form the framework for analytical generation of Pythagorean triples and quadruples is a challenging topic for high school algebra students. I have had considerable success in motivating my students to explore these properties by using a visual method. Students can use this visual method to find Pythagorean triples and quadruples easily and can capably and colorfully supply as many integer solutions as they desire to these well-known equations. Here I will present a visual method for producing integer solutions to the equations a2 + b2 = c2 and a2 + b2 + c2 = d2 and then develop an algebraic representation of this method.

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Booze, David A. "Delving Deeper: Visualizing Pythagorean Triples and Beyond." Mathematics Teacher 104, no. 5 (December 2010): 393–98. http://dx.doi.org/10.5951/mt.104.5.0393.

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Exploring the algebraic properties that form the framework for analytical generation of Pythagorean triples and quadruples is a challenging topic for high school algebra students. I have had considerable success in motivating my students to explore these properties by using a visual method. Students can use this visual method to find Pythagorean triples and quadruples easily and can capably and colorfully supply as many integer solutions as they desire to these well-known equations. Here I will present a visual method for producing integer solutions to the equations a2 + b2 = c2 and a2 + b2 + c2 = d2 and then develop an algebraic representation of this method.

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40

Munifah, Munifah, Annisa Nurhuda Romadhona, Ilma Ridhona, Rahmi Ramadhani, Rofiqul Umam, and Hasan Said Tortop. "How to Manage Numerical Abilities in Algebra Material?" Al-Jabar : Jurnal Pendidikan Matematika 10, no. 2 (December 18, 2019): 223–32. http://dx.doi.org/10.24042/ajpm.v10i2.5325.

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Numerical ability is very help students understand the material, analyze any problems, and apply math concepts in daily life so that numerical abilities of students is a factor that can affect learning outcomes. Determine the effect of learning model Scramble and learning model with SAVI (Somatic, Auditory, Visual, and Intellegence) on the ability of numerical be the purpose of this article. The design of the research used Quasy Experimental Design, with the instrument used for the study in the form of test numerical ability. Data analysis used the T-test. Based on the results of the research concluded that the learning model Scrambler and learning model SAVI has a significant influence on numerical ability. And both of them is a model of learning which is equally effective against numerical abilities in order to improve learning outcomes is more optimal. But model pembelajaran SAVI is more effective than learning models scramble

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Cairó, Osvaldo, and Karen Poblete. "KAMET II Conceptual Modeling Language, a Visual and Consistent Language Proved using Concept Algebra." Procedia Computer Science 60 (2015): 45–54. http://dx.doi.org/10.1016/j.procs.2015.08.103.

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42

Bouck, Emily C., Pei-Lin Weng, and Rajiv Satsangi. "Digital versus Traditional: Secondary Students with Visual Impairments’ Perceptions of a Digital Algebra Textbook." Journal of Visual Impairment & Blindness 110, no. 1 (January 2016): 41–52. http://dx.doi.org/10.1177/0145482x1611000105.

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43

Huo, Xinming, Tao Sun, Yimin Song, Yang Qi, and Panfeng Wang. "An analytical approach to determine motions/constraints of serial kinematic chains based on Clifford algebra." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 7 (August 9, 2016): 1324–38. http://dx.doi.org/10.1177/0954406216643561.

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Determining the motions and constraints of serial kinematic chains in a concise and visual way is an inevitable step in the analysis and design of both serial and parallel mechanisms. The now most used method is the numerical approach which resorts to solving linear equations. By introducing Clifford algebra, this paper intends to propose an analytical approach to determine the unknown 6- n ( n < 6) constraints (motions) from the known n motions (constraints) of serial kinematic chains in different configurations only by drawing some auxiliary points, lines, and planes. The axes and action lines of motions and constraints are characterized by the lines that would be described by Clifford algebra. These lines can be determined analytically according to the relations among points, lines, and planes, which have been expressed by using the operation rules of Clifford algebra Cl(0, 3, 1) such as inner, outer, dual, and shuffle products. Based upon the mechanics principle that the constraint does not work on the motion, the unknown 6- n constraints (motions) of serial kinematic chains from known n motions (constraints) are determined both in an analytical algebraic form and in a visual manner. Finally, four examples are given to demonstrate how to use this approach and test its validity. The merit of this approach is beneficial to the digital analysis and design of both the serial and parallel mechanisms by means of computer and programming languages.

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44

Hutchinson, Nancy L. "Effects of Cognitive Strategy Instruction on Algebra Problem Solving of Adolescents with Learning Disabilities." Learning Disability Quarterly 16, no. 1 (February 1993): 34–63. http://dx.doi.org/10.2307/1511158.

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This study investigated the effects of a two-phase cognitive strategy on algebra problem solving of adolescents with learning disabilities. The strategy was designed to enable students to represent and solve three types of word problems. The study used a modified multiple baseline with 11 replications as well as a two-group design. Conditions of the multiple-baseline design included baseline, instruction to mastery, transfer, and maintenance. Visual analysis of the single-subject data showed the strategy to be an effective intervention for this sample of students with deficits in algebra problem solving, but with criterial knowledge of basic operations and one-step problems. Statistical analyses of the two-group data showed that the instructed students had significantly higher posttest scores than the comparison group. Overall, the instructed students demonstrated improved performance on algebra word problems. Maintenance and transfer of the strategy were evident. This study has implications for teaching complex problem solving to adolescents with learning disabilities in secondary schools.

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Abdulhamid, Mohanad, and Lwanga Wanjira. "Image Processing Techniques Based Crowd Size Estimation." Radioelectronics. Nanosystems. Information Technologies 12, no. 3 (October 30, 2020): 407–14. http://dx.doi.org/10.17725/rensit.2020.12.407.

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Image processing algorithms are the basis for image computer analysis and machine Vision. Employing a theoretical foundation, image algebra, and powerful development tools, Visual C++, Visual Fortran, Visual Basic, and Visual Java, high-level and efficient computer vision techniques have been developed. This paper analyzes different image processing algorithms by classifying them in logical groups. In addition, specific methods are presented illustrating the application of such techniques to the real world images. In most cases more than one method is used. This allows a basis for comparison of different methods as advantageous features as well as negative characteristics of each technique is delineated. The main objective of this paper is to use image processing techniques to estimate the size of a crowd from a still photograph. The simulation results show that the different images have different efficiencies.

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46

On, Jin-Ho, Jung-Rhan Choi, and Moon-Kun Lee. "Visual Representation of Temporal Properties in Formal Specification and Analysis using a Spatial Process Algebra." KIPS Transactions:PartD 16D, no. 3 (June 30, 2009): 339–52. http://dx.doi.org/10.3745/kipstd.2009.16-d.3.339.

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47

Bouck, Emily C., Nancy K. Meyer, Gauri S. Joshi, and Dave Schleppenbach. "Accessing Algebra via MathSpeak™: Understanding the Potential and Pitfalls for Students with Visual Impairments." Journal of Special Education Technology 28, no. 1 (March 2013): 49–63. http://dx.doi.org/10.1177/016264341302800105.

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Flores, Alfinio. "Delving Deeper: The Babylonian Method for Approximating Square Roots: Why Is It So Efficient?" Mathematics Teacher 108, no. 3 (October 2014): 230–35. http://dx.doi.org/10.5951/mathteacher.108.3.0230.

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Mathematicians from the Old Babylonian period (2000–1600 BC) knew a method for using a first approximation to the square root of a number to obtain a second, much better approximation. This article will show that their method is remarkably efficient. We use geometric algebra, much like the Babylonians might have done, to give a visual rationale for the method and its efficiency.

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Effendi, Leo Adhar, and Sindi Amelia. "Students’ Achievement Levels, Gender, and Learning Styles on Abstract Algebra: A Profile of Evidence Developing Ability." Mathematics Research and Education Journal 4, no. 1 (August 24, 2020): 7–16. http://dx.doi.org/10.25299/mrej.2020.vol4(1).2776.

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Mathematics education students’ ability on developing evidence needs to be reviewed by lecturers. 50% of the subjects in the mathematics education departement require students' accuracy in analyzing mathematical statements. This is increasingly important because the Indonesian National Qualifications Framework (KKNI) for the Bachelor level requires graduates to become technicians / analysts. The diversity of levels of students’ ability, gender, and learning styles are assumsed to be the discrepancy abilities to develop evidence. This study aims to describe the evidence developing ability based on the levels of achievement, gender, and student learning styles. The subjects of this study were abstact algebra students in the mathematics education department. Type of this research was descriptive qualitative with data collection techniques using test and non-test techniques. Students were given five questions about abstact algebra that demanded the evidence developing ability. The achivement levels and gender were obtained from students’ academic achievement data. The learning styles were attained from questionnaires. The results of the study is higher the students’ academic achievement, better the evidence developing ability on Abstract Algebra. The gender does not affect the evidence developing ability on Abstact Algebra. Students with visual learning styles have the ability to develop evidence better than students with other learning styles.

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Praveen, Kanakkath, Madathil Sethumadhavan, and Ramakrishnan Krishnan. "Visual cryptographic schemes using combined Boolean operations." Journal of Discrete Mathematical Sciences and Cryptography 20, no. 2 (February 17, 2017): 413–37. http://dx.doi.org/10.1080/09720529.2015.1086067.

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