Advanced Mathematics Research Articles

The Role of Higher Mathematics in Public Security Political Work Specialty Based on the New Liberal Arts

The construction of new liberal arts is a systematic education reform project, which is of great significance to improve the quality of college liberal arts talents training in the new era. Under the background of new liberal arts construction, higher mathematics plays an indispensable role in the political work of public security. In fact, statistics, linear algebra and probability theory are widely used and play an important role in the public security cause. In addition, based on the follow-up study of advanced mathematics in liberal arts, students who graduate from the police offi cer will make a great role in crime analysis and prediction case analysis and case analysis of public safety management. Finally, based on the concept of OBE, the paper puts forward the refl ection of designing the teaching content of higher mathematics in public security political work specialty.

Joining the Math Circus: exploring advanced mathematics through collaborative hands-on activities and performative storytelling

This paper details a qualitative study examining the experience and motivation of participants, facilitators, and organizers of the Math Circus, an event hosted by the University of Arkansas Honors College in Fayetteville, Arkansas, as part of the university’s 150th anniversary celebrations. The aim of the Math Circus was to entice participants to explore advanced mathematical concepts through collective mathematical art creations and dramatic storytelling of comic tales around the history behind mathematics. The study was carried out in two phases; an autoethnographic case study during the event; and a series of deep, semi-structured interviews with participants, facilitators, and organizers. The study examined pedagogical motivations behind the event’s activities and their mathematical content, as well as the experiences of the interviewees. Findings indicate that an interactive and festive event like the Math Circus is likely to encourage confidence to explore mathematical concepts further.

Using Advanced Mathematical Method to find Normal Curvature of the Curve on Regular Surfaces

Curvature, being a crucial geometric parameter in many applications of surface analysis, is the amount of deviation of curve from a straight line or plane. This study's objective is to use Matlab to objectively calculate Normal Curvature on Smooth Surfaces. The following article concerns curvature and normal curvature with the focus on two uses: first for the manufacturing of automobile tire’s inner tubes, and second one to identify the ideal choice degree of normal curvature. The aim of the study is finding the normal curvature numerically and using Matlab, which can carry out complex computational tasks with general commands and is relatively more precise and swifter than the standard numerical calculations.

Design and Construction of Ideological and Political Micro-platform for Higher Mathematics Courses

This article focuses on the design and construction of an ideological and political micro-platform for higher mathematics courses. It actively builds a micro-platform for ideological and political teaching in higher education courses through two aspects: platform design and construction and the design of ideological and political elements of advanced mathematics. The project team will improve the "Basic Mathematics Knowledge of Economics and Management" Library" WeChat public platform to explore the establishment of a learning platform with the construction of course network resources and interactive integration of mathematics courses as its main modules. The goal is to truly understand students' learning status through communication between students and teachers at different stages, establish a new method system for the organic integration of advanced mathematics courses and professional courses, and form a new situation of teacher-student and teacher-teacher interaction. To serve the construction of application oriented high-level universities.

Analogical structure sense: A case study of students’ analogical reasoning between groups and rings

Analogical reasoning is an important mathematical process for undergraduate students. However, it is unclear how students understand analogies that are presented to them, and more importantly, how students understand and create their own analogies. In this paper, we present a case study of four students as they reason analogically about several structures in abstract algebra. In particular, we expand on the notion of structure sense to include a wider range of structures in advanced mathematics and attend to each students’ analogical structure sense associated with each structure. Findings suggest that although students may possess a strong structure sense for group-theoretic structures, it is not necessarily the case that they possess a comparatively strong analogical sense of structure for ring-theoretic structures. In addition, those students with weaker senses of structure for group-theoretic structures are still able express productive reasoning about ring-theoretic analogies. Implications for future research and instructional practice are discussed.

Analysing the quality of real analysis lectures using a structured observation tool

This paper reports a study investigating the quality of advanced mathematics lectures following three goals. First, we present our conceptualisation and operationalisation concerning the quality of mathematics lectures. Second, we test the reliability of a structured observation tool that is based on the aforementioned conceptualisation. Third, we describe the quality of mathematics lectures based on data collected with the observation tool and illustrate its use. The results show that our observation tool is suitable for collecting data about characteristics of mathematics lectures observed on-site and from video recordings. The analysis of the data shows that our findings are in line with previous research: formal aspects of mathematical statements are presented in verbal and written forms mostly correctly; informal aspects of mathematical statements (such as examples, visual or mental representations) are, if they are presented, usually presented only verbally. Furthermore, students have the opportunity to participate during lectures, but there are seldom presentations of alternative solutions, examples or proofs and only a few opportunities for formative assessment. Finally, we discuss implications for future research.

Spaced example-based learning facilitates advanced mathematics learning in college students

ABSTRACT Numerous studies have delved into the role of spaced learning in factual memory retention. However, there is a limited understanding of the spacing effect in acquiring problem-solving skills, particularly in advanced mathematics. In this study, 68 female collegiate scholars were randomly assigned to either spaced or massed learning groups. Both groups engaged in solving advanced mathematical problems, specifically those related to implicit function derivation, using worked examples. Results indicated comparable performance immediately after a 5-minute interval, but the spaced learning group demonstrated superior outcomes during a prolonged assessment after one week. Importantly, the spacing effect was observed irrespective of participants' prior mathematical performance. These findings underscore the effectiveness of spaced example-based learning in sustaining advanced mathematical knowledge among female collegiate scholars. The study concludes by discussing its limitations and proposing directions for future research.

On using a core idea to foster the transition to advanced mathematics – transferring the idea of average to complex path integrals

The transition from Riemann integrals to other real integrals has been discussed previously in mathematics education literature. In this transition, the interpretation of integrals as averages of the integrated functions generalises smoothly to measure and probability theory. In this paper, I address the transition to complex path integrals. Based on the premise that using core ideas throughout mathematics curricula may facilitate the transition from earlier to more advanced courses, I analyse epistemologically to what extent the idea of averaging may be transferred to complex path integrals. In this case, the transition poses special epistemological challenges. Using an example from an expert interview, in which the expert aims to apply the interpretation of integrals as averages to complex path integrals, I illustrate the aforementioned challenges empirically.

Advanced Mathematical Modelling of Leaching Processes in Porous Media: An Averaging Approach

Advanced Mathematical Modelling of Leaching Processes in Porous Media: An Averaging Approach

Journal Vol – 19 No -1, January 2024 Journal > Journal > Journal Vol – 19 No -1, January 2024 RELIABILITY OPTIMIZATION OF A DEGRADED SYSTEM UNDER PREVENTIVE MAINTENANCE USING GENETIC ALGORITHM Authors: Shakuntla Singla, Diksha Mangla, Poonam Panwar, S Z Taj DOI NO: https://doi.org/10.26782/jmcms.2024.01.00001 admin January 20, 2024 Abstract: The reliability parameters of a Mathematical model are analyzed for

The present paper deals with the lacunary interpolation problem called the mixed values problem or (0, 3; 0, 2) problem for which known data points are function values at all the points, third derivatives at even knots, and second derivatives at odd knots of the unit interval I = [0,1]. For this problem, we obtained an interpolating function. The paper is divided into two parts, where we have shown that the spline function exists and is convergent.

The centennial sustainable assessment of regional construction industry under the multidisciplinary coupling model

Sustainability research in the construction industry is of great strategic significance to the ecological environment of countries worldwide. This paper innovates theoretical models such as “structural response sensitivity weight” through interdisciplinary research on advanced mathematics, engineering science, computer science, environmental management and economic sociology. The model solves the limitations of multi-factor, multi-discrete, multi-constraint and low coupling iteration accuracy. The article shows the robustness of the model through case studies. The research data shows that the construction industry in China will reach its highest life cycle assessment emission peak of 2.73 GT in 2030 and will have harmful emissions of -2.78 GT between 2061 and 2098. The social impact assessment will peak at 4.26 GT in 2048 and harmful emissions of −3.75 GT per year from 2061 to 2098. This research provides a comprehensive research theory system and reference standards for scientific calculation and accurate assessment of the sustainable development of the construction industry in various countries around the world.

Study on the status and problems of teaching system of “medical advanced mathematics”: data based on a research of 11 universities in China

Background and aimDriven by Innovation 2.0 (the information age, the innovation form of the knowledge society), the form evolved by the Internet development, giving rise to economic and social development (“Internet +”). With this background, a novel approach is presented for fostering excellence in physicians, aligning with the contemporary demands of our era.MethodsSelf-administered questionnaire was used to facilitate the collection of data on medical advanced mathematics course offerings, distribution of teaching hours of each major and the perception of the course teaching system in 11 medical universities in China. The distribution of course offerings in each major was analyzed, and one-sample t-test was conducted on the perspectives of course offerings, content settings (theoretical & practical), educational objectives, teaching reforms, and Synthetical Sensation (SS) of the curriculum system and educational model.ResultsThe study included various specialties such as clinical medicine, pharmacy, public health, health management, and life sciences, all of which offered advanced mathematics course. The content of medical mathematics textbooks was designed to meet the practical needs of relevant professions, and encompass online laboratory classes and social practice. However, a noticeable misalignment was observed between the content of medical mathematics courses and the realistic requirements of professions (t = -3.614~-3.018, P < 0.05). The perceived difference in the completeness of curriculum systems was not significantly apparent. There was a difference in the perception of the effectiveness of teaching reforms (t = -4.485, P < 0.05), and there was a difference in the perception of the synthesis of the educational model in all cases (t = -5.067, P < 0.05).ConclusionThere are localized differences in curricula, and the number of course hours is basically reasonable; course content needs to be updated; the implementation of course objectives is not in place; the curriculum system can meet the needs of talent training; the innovation of the education model needs to be put into practice; and there are obvious differences in the comprehensive cognition of the teaching system and the education model. Based on the analysis of the problems, we build a new STC teaching mode with smart classroom based on “professional needs, practical needs and requirements for cultivating excellent physician talents”.

The Exploration of Curriculum Ideology and Politics in Advanced Mathematics from the Perspective of the Three-Wide Education

For advanced mathematics courses for science and engineering students, the course guided by three-wide education (TWE) explores the ideological and political teaching in the curriculum, analyzes the relationship between TWE and curriculum ideology and politics (CIP), and determines the course objectives. The course is related to the ideological and political elements of the curriculum, establishes the feelings of home and country, integrates into educational activities, creates a collaborative education classroom, and formulate assessment and evaluation standards. Finally, through the questionnaire survey and feedback on the implementation effect, it is concluded that integrating ideology and politics into advanced mathematics can stimulate learning motivation, realizes all-round education throughout the process, and well implement the task of building morality and cultivating people.

Special tutorials to support pre-service mathematics teachers learning differential equations and mathematical modelling

Special tutorials both online and off-line were experimented in order to provide extra support for the senior pre-service mathematics teachers at an Australian regional university to improve their learning experience and achieve the best possible learning outcomes in an advanced mathematics course focusing on solving ordinary differential equations and applying mathematical modelling. Two types of special tutorials were offered to the students, the progressive tutorials on solving the same problem with different methods according to the learning progression and student’s instant requests, and the targeted tutorials to address the common problems shared by many students in attempting questions in the formal assessments. The experiments on these special tutorials indicated that the targeted tutorials were immensely useful for the students to either expand the scientific knowledge related to a real-world scenario described by words so as to begin problem solving with correct setting-ups or streamline multiple mathematical processes together to solve a complicated real-world problem described in words. This approach motivated most students to achieve their best possible learning outcomes. The progressive tutorials were effective in addressing student’s curiosity of solving the same problem by multiple techniques and hence improving student’s mathematical thinking and problem-solving skills in general. This exploratory study also found that there were common problems with a lack of general science knowledge and retention of the previously learnt mathematical techniques among most students. There also existed a portion of students who showed no interest in engaging with learning regardless of how much extra learning support provided to them.

Thoughts on Education and Teaching of “Curriculum Ideological and Political Education” in Advanced Mathematics

Thoughts on Education and Teaching of “Curriculum Ideological and Political Education” in Advanced Mathematics

The Exploration and Practice of the Teaching Mode of Cross-School Credits in Advanced Mathematics

The Exploration and Practice of the Teaching Mode of Cross-School Credits in Advanced Mathematics

Application of Multiple Integrals in Advanced Mathematics

Application of Multiple Integrals in Advanced Mathematics

“高等数学”全过程多元化考核模式的探索与实践

“高等数学”全过程多元化考核模式的探索与实践

高等数学之知识点探究——以空间直角坐标系、函数的连续性及柯西审敛原理为例

高等数学之知识点探究——以空间直角坐标系、函数的连续性及柯西审敛原理为例

Exploration of the Path for the Four-Dimensional Construction of Ideological and Political Education in “Advanced Mathematics” Curriculum

Exploration of the Path for the Four-Dimensional Construction of Ideological and Political Education in “Advanced Mathematics” Curriculum