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This article examines the concept of propositions in mathematics, which are statements referred to as (closed sentences, false, values, and true values). The discussion covers negation, or what is known as negation, as operations that have truth values and truth tables. In addition, this article examines conjunction, or compound propositions that are true. (the combination of two questions), which involves two propositions with either true or false values. Furthermore, this article also examines disjunction, which involves statements containing conjunctionand also has truth tables. The primary objective is to provide a concise yet comprehensive understanding of propositions as logical and mathematical concepts. In addition, this article examines conjunction, or compound propositions that are true. A conjunction involves two propositions that are combined using the logical operator "and," symbolized by ∧. The conjunction of two propositions is true only when both individual propositions are true. For example, if P is true and Q is true, then the conjunction P ∧ Q is also true. However, if either P or Q is false, the conjunction P ∧ Q becomes false. The truth table for conjunction helps to clarify these conditions. Conjunction is often used in mathematical proofs, where multiple conditions must be satisfied simultaneously for a statement to hold true. Furthermore, this article also examines disjunction, which involves statements containing conjunction and also has truth tables. Disjunction, represented by the symbol ∨, involves two propositions and is true if at least one of the propositions is true. If both propositions are false, the disjunction is false. For instance, if P is false and Q is true, then P ∨ Q is true. The truth table for disjunction provides clarity on how this operation works. Disjunction is frequently used in mathematics and logic to express situations where at least one condition must be satisfied.

The lack of interest of young children in learning numbers is a common challenge in kindergarten learning activities. Children tend to be passive during the mathematics learning process because the approach used is not appropriate to their age developmental characteristics, which prefer play, movement, and direct interaction with concrete media. To address this problem, the Community Service Program (KKN) at At-Tien Kindergarten, Sumber Gayam, focused on learning innovation by designing a simple media called the Mathematics Ferris Wheel. This media was designed by combining elements of play and motor activity, making it more engaging for children. The research in this community service activity used a Participatory Action Research (PAR) approach, which actively involved teachers and students in the planning, implementation, and evaluation stages. The media was implemented by children turning the Ferris wheel in turns, then calling out the number indicated along with the numbers before and after. Through this activity, children not only learned to recognize number sequences but also practiced concentration, courage, and communication skills. The implementation results showed that the use of the Mathematics Ferris Wheel was able to significantly improve the understanding of number concepts in early childhood. Furthermore, children's active involvement in learning also increased, demonstrated by their enthusiasm in participating in the game from start to finish. Teachers found this media to be highly beneficial because it is easy to use, flexible, and adaptable to teach other topics such as colors, shapes, and letters. Thus, this KKN activity demonstrates that innovative, participatory learning media can create a fun, contextual, and effective learning environment. Such efforts are a practical solution to improving the quality of learning in early childhood education

This study aims to examine the potential of the Baduy traditional house as a realistic context in mathematics learning, particularly in the material of spatial geometry. The traditional houses of the Baduy people not only function as residences, but also hold cultural values, philosophies, and architectural structures rich in geometric elements. Using a systematic literature review (SLR) approach, this study explores various scientific sources, including journal articles, proceedings, and reference books, that discuss the relationship between spatial elements and the structure of traditional Baduy buildings. This approach was chosen so that the study obtained is comprehensive, directed, and able to illustrate the real contribution of ethnomathematics in learning. The results of the review indicate that the Baduy traditional house contains various forms of spatial geometry that can be clearly recognized, including cuboids, triangular prisms, pyramids, cubes, and cylinders. These elements are reflected in building components such as roofs, walls, floors, support pillars, and traditional household furniture. The visual and functional representation of these spatial geometry has the potential to be a contextual resource that can be utilized by teachers in the mathematics learning process, particularly through the Realistic Mathematics Education (RME) approach. By linking abstract mathematical concepts to local cultural phenomena, students not only gain a better conceptual understanding but also increase their active engagement, motivation to learn, and awareness of their own cultural identity. These findings emphasize the importance of utilizing local wisdom as an ethnomathematics approach that can provide meaningful, contextual learning rooted in the realities of students' daily lives. Through the integration of culture and education, mathematics learning can be more relevant, engaging, and support the preservation of national culture.

Traffic congestion in Jakarta has become a serious problem, affecting various aspects of life, such as time efficiency, environmental quality, and economic productivity. As one solution to overcome this problem, the Jakarta government is developing a mass public transportation system, including the Light Rail Transit (LRT). The LRT is expected to reduce congestion by providing a more efficient and environmentally friendly transportation alternative. In the process of planning and optimizing the LRT system, discrete mathematics, particularly graph theory, plays a very important role. Graph theory is used to model the LRT station network and track, with vertices representing stations and edges representing connecting lines between stations. With this model, various analyses can be performed to optimize the LRT line, such as finding the shortest path between two stations or evaluating the connectivity between existing stations. The use of graph theory allows the identification of more efficient routes, resulting in faster travel and reduced passenger waiting times. In addition, graph theory also plays a role in optimizing the LRT route by minimizing the number of transfers between stations or avoiding passenger congestion at certain stations. With proper route and network optimization, the LRT can make a significant contribution to reducing traffic congestion in Jakarta. Furthermore, the development of an efficient public transportation system also supports improved air quality and reduces reliance on private vehicles. Overall, the application of graph theory in LRT system planning is a strategic step towards creating more efficient and sustainable transportation in large cities like Jakarta. Beyond route optimization, graph theory is also very useful in analyzing route capacity and passenger distribution along the LRT system.

The objectives of this Community Service Program are: (1) To introduce the concept of ethnomathematics to students and classroom teachers at UPT SDN 1 Rantepao as a contextual learning approach rooted in local culture, particularly the traditions of the Toraja ethnic group; (2) To enhance students’ understanding and interest in mathematics through the integration of mathematical elements found in Torajan cultural motifs, artifacts, and symbols, such as symmetry, geometric shapes, patterns, and measurement; and (3) To support teachers in developing innovative and meaningful mathematics instruction by connecting mathematical content to real-life contexts that are relevant to students' daily experiences. The program was implemented in five stages: preliminary observation and survey, preparation, implementation, group discussion and reflection, and the final stage—evaluation. Based on the results of the program, the introduction of ethnomathematics based on Torajan local culture successfully contributed to improving students’ mathematical understanding and reinforcing the relevance of mathematics instruction within the local cultural context. The three-day implementation of the program was met with highly positive responses from all school stakeholders, including strong student enthusiasm, active teacher participation, and noticeable changes in instructional practices. Evaluation outcomes demonstrated a significant improvement in student understanding, as reflected by an increase in the average quiz score from 55 to 83. Moreover, the program contributed to social transformation within the school environment, including the formation of culturally based student learning groups, positive shifts in student learning behaviors, the emergence of local student leadership, and increased awareness among both students and teachers of the importance of integrating local cultural values into the learning process.

This study aims to analyze the influence of derivative skills and literacy in economic mathematics on investment decisions of students in the Management Study Program. The study was conducted using a quantitative approach using primary data collected through questionnaires distributed to students. The collected data were then analyzed using multiple regression tests to determine the extent to which the studied variables influence investment decisions. The results of the multiple regression test indicate that derivative skills and economic mathematics literacy simultaneously have a significant influence on students' investment decisions. The coefficient of determination (R²) value is 0.551, which means that 55.1% of the variability in investment decisions can be explained by these two independent variables, while the remaining 44.9% is explained by other factors not examined in this study. This figure indicates that students' ability to understand and use economic mathematics concepts, especially in terms of derivatives, as well as their financial literacy, play an important role in forming rational and informed investment decisions. The results of this study indicate that mastery of economic mathematics concepts, especially derivative skills, has a direct impact on students' ability to make better and more logical investment decisions. On the other hand, financial literacy also influences how students assess and manage investments, resulting in wiser decisions. Therefore, it is important for educational institutions to integrate mathematical economics and financial literacy into their curricula to help students make more rational investment decisions and reduce potential future financial risks. Furthermore, this study also suggests the need to improve students' understanding of basic concepts in mathematical economics and financial literacy. Management study programs can strengthen their curricula by providing more in-depth training in the applications of mathematical economics, such as the use of derivatives in investment analysis.

This study aims to describe students' critical thinking skills in solving social arithmetic problems based on the Polya stages and FRISCO indicators. The research subjects consisted of three students in grade VIII R-5 MTs Nurul Jadid who were purposively selected to represent the high, medium, and low ability categories out of a total of 21 students. The research method used was a descriptive qualitative approach with instruments in the form of two social arithmetic description questions and semi-structured interview guidelines. Data analysis was carried out by referring to the four stages of problem solving according to Polya (understanding the problem, planning the solution, executing the plan, and re-examination) as well as the six FRISCO critical thinking indicators (Focus, Reason, Inference, Situation, Clarity, Overview). The results of the study showed that students with high abilities were able to solve problems systematically through all stages of Polya and met almost all FRISCO indicators, especially in the aspects of Focus, Reason, and Clarity. Students with moderate ability show sufficient understanding but are inconsistent in planning and implementing solutions, and experience difficulties in the Reason, Situation, and Overview indicators. Students with low abilities experience obstacles from the early stages of understanding problems and do not show significant indicators of critical thinking. These findings indicate that the Polya stage and the FRISCO indicator can be used in a complementary manner to identify and analyze students' critical thinking skills in solving contextual math problems. The implication of this study is the need for a learning strategy that emphasizes strengthening the stages of problem solving and developing explicit critical thinking indicators in the mathematics learning process. This research also opens up opportunities for the development of more structured diagnostic instruments in measuring students' individual critical thinking skills.

This study aims to determine the effect of using educational gim-based learning media on students' math learning outcomes on the material of Linear Equation One Variable (PLSV). The background of this research is the low student learning outcomes in conventional math learning which is considered less interesting, especially in PLSV material which is abstract. This study used a quantitative approach with a quasi-experimental design and a nonequivalent control group design. The sample consisted of two classes, namely the experimental class (using educational gim media) and the control class (using conventional methods), which were taken from VII grade students of MTs Ra’iyatul Husnan, Wringin Bondowoso. The research instrument was in the form of pretest and posttest tests that had gone through validity and reliability tests. The pretest results showed that both classes had relatively balanced initial abilities. However, in the posttest, the learning outcomes of experimental class students showed a more significant increase than the control class. The data were analyzed using normality, homogeneity, and Mann-Whitney U Test hypothesis tests because the posttest data were not normally distributed. The analysis results showed a significance value of Asymp. Sig. (2-tailed) significance value of 0.000 <0.05, which means there is a significant effect of using educational gim media on student learning outcomes. This finding shows that interesting and interactive learning media such as educational gims can improve students' motivation, understanding and learning outcomes in mathematics. Therefore, the use of educational gims is recommended as an innovative alternative in learning mathematics, especially on material that is abstract and difficult for students to understand.

The study aims to analyze the relationship between learning discipline and students' critical thinking abilities in math learning. A quantitative approach with correlational survey methods is used in this study. Sample of 44 junior high school students selected through simple random sampling technique. Instruments used as lamps to measure learning discipline and tests to measure critical thinking ability. Data analysis was performed through Liliefors normality testing, Pearson correlation testing, and simple linear regression. The normality test results show that discipline learning data is normally distributed (Lo = 0.0995 < Ltable = 0.133), whereas critical thinking data is not normally distributed (Lo = 0.2266 > Ltable = 0.133). The correlation test results show the value of r = 0.211 and thitung = 1.423 < ttable = 1.683, meaning there is no significant relationship between learning discipline and critical thinking ability. The regression results also show the value of Fhitung = 2.15 < Ftabel = 4.08, which means there is no significant influence between learning discipline on critical thinking ability. Thus, that learning discipline does not affect significantly on students' critical thinking ability in math learning. This results in a more comprehensive learning approach to develop critical thinking skills.

Mathematics learning, particularly in geometry, is often perceived as abstract and less engaging by students, leading to reduced interest and creativity. One of the geometry topics that demands a more creative and concrete approach is the tessellation of flat shapes, which emphasizes the understanding of patterns, symmetry, and regularity of shapes. The absence of contextual learning media has contributed to students’ low enthusiasm and limited ability to apply concepts in real-life contexts. This community service activity was designed to address these challenges by enhancing students’ creativity and conceptual understanding through the use of ceramic media as an innovative and enjoyable learning tool. The program was conducted at SD Negeri 1 Rowosari, Tembalang District, Semarang City, involving mathematics teachers, elementary school students, and university students. The implementation method included training and mentoring sessions. Activities encompassed the introduction of tessellation concepts, hands-on demonstrations, and the guided creation of tessellation patterns using ceramic media. Participants consisted of teachers and students who actively engaged in both theoretical and practical sessions. Evaluation was conducted through pre-test and post-test questionnaires administered before and after the training. The results revealed a significant improvement in students’ average scores after the activity. Pre-test data showed that approximately half of the students scored above the average, with two students achieving nearly perfect scores. Post-test results indicated that most students demonstrated increased understanding and creativity in applying tessellation concepts. Nevertheless, a small number of students still required further guidance, particularly in translating abstract tessellation concepts into real-life applications. Overall, the findings suggest that integrating ceramic media into mathematics learning is effective in making abstract geometry concepts more tangible, stimulating students’ creativity, and improving learning outcomes, especially in the topic of tessellation of flat shapes.

This study aims to: (1) produce e-LKPD based on problem-based learning oriented to mathematical problem-solving ability and self-confidence of high school students on the material of equations and quadratic functions and (2) describe the feasibility of PBL-based e-LKPD oriented to mathematical problem- solving ability and self-confidence of high school students on the material of equations and quadratic functions seen from the aspects of validity,  practicality, and effectiveness. This type of research is research and development using the ADDIE model (Analysis, Design, Development, Implementation, and Evaluation). The research was conducted at SMA Negeri 1 Malinau with the research subject of class X-3 students totaling 35 students. Data collection was carried out using interview techniques, observation, e-LKPD validation sheets, pretest-posttest, and questionnaires. To determine the validity, the e-LKPD assessment sheet of material and media experts was used, practicality used student and teacher response questionnaires, and effectiveness used mathematics problem solving ability test questions and student self-confidence questionnaires. Data analysis consisted of qualitative data analysis and quantitative data analysis. Qualitative data analysis was conducted by analyzing the results of interviews, observations, and comments or suggestions given to make improvements to the e-LKPD products developed. Quantitative data analysis was conducted by converting quantitative data into qualitative data in the form of certain categories, normality test using shapiro-wilk, t-test with paired samples test, and N-Gain score. The results showed: (1) PBL-based e-LKPDs oriented towards mathematical problem solving skills and self-confidence of high school students on the material of quadratic equations and functions have been produced, (2) PBL-based e-LKPDs developed meet product feasibility, namely valid with excellent categories based on material and media experts; practical with very practical categories based on teacher responses and practical based on student responses; effective on math problem solving skills with classical completeness of 77%, the t-test results obtained a significance value of 0.000 <0.05 which means that there is a difference in the average ability to solve mathematical problems before and after learning using e-LKPD, the N-Gain result is 0.65 with moderate criteria, and effective on student self-confidence with an increase in the average score of each indicator before and after learning,  the N-Gain result is 0.49 with moderate criteria, and the t-test results with a significance value of 0.000 < 0.05.

Mathematics is a universal science that underlies the development of modern science and technology, and has an important role in the development of human thinking. Mathematics is a subject that is based on logical, rational, critical, and systematic thinking patterns. Religion and rationality are two perspectives that have a strong influence. Humans view religious values ​​and rational values ​​as different entities, causing a dichotomy paradigm, especially in the realm of education. In the perspective of the epistemology of science in Islam, Islam and science are complementary and interdependent entities. The mathematical approach used here does not mean that Islamic values ​​are low, but only to increase the belief of Muslims that all knowledge is valuable and can lead to true goodness and increase faith and closeness to Allah SWT.To examine how Islamic values ​​are applied in mathematics learning, To identify and develop effective strategies or methods in integrating Islamic values ​​in mathematics learning materials, To measure the extent of the application of Islamic values ​​in mathematics learning.This study uses a qualitative approach, while the type of research used by the researcher is descriptive research.Mathematics as a logical and systematic science, has a meeting point with Islamic teachings that emphasize truth, justice, and balance. For example, the concept of monotheism can be associated with the order of the universe expressed through mathematical formulas, fostering a sense of gratitude and obedience. The implementation of Islamic values ​​that are rahmatan lil 'alamin (blessing for all nature) in mathematics learning, especially to form honest and fair characters in students.

This study aims to analyze the influence of learning interest, learning discipline, and critical thinking skills on student learning outcomes in the Simple Financial Processing subject for class XI MPLB at SMK PGRI 2 Sidoarjo. Learning outcomes are understood as skills or abilities acquired by students after participating in the learning process, the success of which is measured through scores in the form of numbers, symbols, or letters. Three factors selected in this study as independent variables are learning interest, learning discipline, and critical thinking skills. This type of research is quantitative research with an explanatory approach, which aims to explain the cause-and-effect relationship between these variables. The population in this study were all 102 class XI MPLB students. The sampling technique used non-probability sampling with a total sampling type, so that the entire population was sampled. Data collection was carried out by distributing questionnaires to students. The data obtained were then analyzed using SPSS version 27 software. Before conducting multiple linear regression analysis, validity and reliability tests were first conducted to ensure that the instruments used were appropriate and consistent in measuring the variables studied. The analysis results show that the three independent variables—learning interest, learning discipline, and critical thinking skills—have a significant influence on student learning outcomes. Therefore, it can be concluded that improvements in these three aspects will positively impact student learning outcomes in the subjects studied.

This study aims to develop a contextual learning-based mathematics test instrument focused on Statistics and intended for eighth-grade junior high school (SMP) students. The instrument developed consists of essay questions designed by integrating real-life situations to make them more relevant and meaningful for students. This contextual approach is expected to help students understand statistical concepts more deeply and improve their ability to solve mathematical problems related to everyday life. In the instrument development process, a series of analyses were conducted to test the quality of the test items, including validity, reliability, discriminating power, and difficulty level. The validity of the test items was tested using the correlation between item scores and total scores, with the results showing that all test items had a correlation coefficient greater than the r value of the table, thus being declared valid. Meanwhile, the reliability coefficient obtained was 0.84, indicating that this instrument has a high level of consistency and is suitable for use in measurement. Analysis of the discriminating power showed that each test item had excellent ability to differentiate students with high and low abilities. The analysis of the difficulty level showed balanced variations, namely from easy, medium, to difficult categories. This variation is important to accommodate differences in student ability levels and reflect the diversity in the context of the problems presented. Overall, the results of this study indicate that the developed test instrument is of excellent quality and can be used as an evaluation tool to measure students' mathematical problem-solving abilities. Furthermore, this instrument supports more contextual, interactive, and meaningful statistics learning.

Indonesia is a country rich in culture, one of which is batik, recognized by UNESCO as an intangible cultural heritage of Indonesia. Batik is not only a visual art form but also holds significant potential as a context for teaching mathematics. Unfortunately, the integration of local culture into mathematics education has not been widely implemented. Therefore, this community service activity aims to train teachers and assist students in applying Realistic Mathematics Education (RME) based on batik culture at MTs Nurul Ummah Kotagede, Yogyakarta. The activity was carried out in three stages: preparation, implementation, and evaluation. In the preparation stage, teachers were provided with training on the theory and practice of RME, which was then applied in the classroom. The lesson focused on geometric transformations, using batik patterns as a real-world context. By linking mathematical concepts to the familiar cultural context of batik, it was hoped that students would more easily understand abstract mathematical ideas and find them more meaningful. The results of the activity showed high enthusiasm from the students and positive appreciation from the teachers toward the RME model based on culture. Students demonstrated a better understanding of mathematical concepts, as the learning process connected theoretical knowledge to real-world contexts they recognized. Additionally, teachers acknowledged that using batik culture in mathematics education made the learning experience more enjoyable and meaningful. This activity proves that integrating local culture, such as batik, into RME can increase students' interest in mathematics and help them understand abstract concepts by relating them to real-life experiences.

This study aims to describe students' critical thinking skills in solving numeracy literacy problems by considering their mathematical dispositions. Critical thinking skills are an important competency in 21st-century learning because they play a significant role in understanding concepts, analyzing information, and solving problems with a logical and systematic approach. Numeracy literacy, as part of basic mathematical competencies, requires students not only to be able to calculate but also to understand the context and apply mathematical concepts in real life. In this context, mathematical disposition—which includes self-confidence in mathematics, persistence in solving problems, and curiosity—is seen as a factor that influences students' critical thinking skills. This study used a descriptive qualitative approach with student subjects selected based on high, medium, and low mathematical disposition categories. The instruments used consisted of a numeracy literacy test and a semi-structured interview guide. Data were collected through completing a mathematical disposition questionnaire, working on numeracy literacy problems, and in-depth interviews with selected subjects. Data analysis techniques included data reduction, data presentation, and inductive conclusion drawing. The results of the study indicate that students with a high mathematical disposition tend to have more developed critical thinking skills. They are able to analyze problems in depth, evaluate relevant information, and draw logical and structured conclusions. Conversely, students with medium and low dispositions tend to have limited critical thinking skills, particularly in the aspects of evaluation and conclusion drawing. This finding emphasizes the importance of strengthening mathematical dispositions as an integral part of learning strategies to improve students' critical thinking skills in the context of numeracy literacy.

This research aims to develop a mathematics teaching module based on differentiated learning integrated with the Project-Based Learning (PjBL) method, specifically for the topic of spatial structures ("get up room") for students at Nanasi 1 Elementary School. The development process follows the 4D model, which includes the stages of Define, Design, Develop, and Disseminate. In the Define stage, analysis revealed the absence of instructional modules that align with students' learning styles and needs. Consequently, learning objectives were formulated based on geometric elements and problem-solving criteria. During the Design stage, a prototype module and validation instruments were produced. Validation was conducted by two experts, yielding high scores for both content and visual presentation—each achieving 90% validity. Practicality assessments also showed strong results, with content rated at 90.8% and visual aspects at 90%, categorizing the module as “very valid” and “very practical.” The integration of the PjBL method was implemented to enhance active student participation, encouraging collaborative exploration and real-world application of mathematical concepts. The developed module is considered suitable for supporting differentiated mathematics instruction in elementary schools. It accommodates diverse learning styles and promotes student engagement through project-based tasks. The findings suggest that combining differentiated learning with PjBL fosters a more inclusive and effective learning environment, particularly in geometry-related topics. This module not only meets pedagogical standards but also contributes to the advancement of innovative teaching practices in primary education.

This research explores the effectiveness of heuristic techniques for solving combinatorial optimization problems, with a particular focus on the Traveling Salesman Problem (TSP). Combinatorial optimization is a critical area of study, especially in fields like computer science, engineering, and economics, where finding optimal solutions from a finite set of possibilities is crucial. However, the NP-hard nature of many combinatorial problems, such as the TSP, makes traditional exact methods like Branch-and-Bound and Dynamic Programming computationally expensive and inefficient for larger problem sizes. The primary objective of this research is to evaluate the performance of heuristic methods, including Simulated Annealing (SA), Genetic Algorithms (GA), and Iterative Computation techniques, such as Tabu Search (TS) and Particle Swarm Optimization (PSO). These methods are tested for their ability to provide approximate solutions efficiently. The findings reveal that while ACO provided the best solution quality, it had the longest runtime. TS was the fastest, though with slightly lower solution quality. SA and GA demonstrated a balance between solution quality and computational efficiency, but their performance heavily depended on parameter tuning. The hybridization of SA and GA showed potential for improving solution quality but introduced additional complexity. The research concludes that heuristic methods, especially when combined, offer viable solutions for large-scale combinatorial optimization problems, though the trade-off between solution quality and computational time must be considered when selecting an algorithm.

Limited access to learning resources appropriate to the local context presents a challenge in the mathematics learning process in indigenous communities such as the Baduy Tribe. Conventional mathematics learning is often considered too abstract and less relevant to the daily lives of Baduy children, especially in the Outer Baduy region. To address this challenge, this community service activity aims to introduce contextual mathematics learning media based on the surrounding environment and local culture. The media developed is designed to be easily accessible, affordable, and environmentally friendly, while still respecting prevailing traditional values. The method used in this activity is Participatory Action Research (PAR), with a collaborative approach between a team of lecturers and the Outer Baduy community. The activity implementation process includes six stages, namely: identification of local problems and potential, planning, designing learning media, implementation, evaluation, and documentation of activity results. The results of the activity show an increase in interest and understanding of basic mathematics concepts among Outer Baduy children. Children appear more active, enthusiastic, and confident in participating in the learning process through educational games and concrete activities. The media used utilizes natural objects and local cultural elements, such as woodcuts, ancient angklungs, traditional hats, and distinctive Baduy woven motifs. The community responded positively because these media do not conflict with traditional values. This activity has had positive cognitive and social impacts and strengthened awareness of the importance of a contextual and culturally based educational approach as a relevant and inclusive learning strategy.  

Integral equations are essential tools in applied mathematics, with wide-ranging applications in fields such as physics, engineering, and finance. However, solving these equations presents significant challenges, particularly when dealing with complex, high-dimensional, or singular problems. Traditional methods, such as manual analytical techniques or direct numerical approaches, often struggle with computational efficiency, especially for large-scale systems, and may not be suitable for handling ill-conditioned problems. This study aims to develop an efficient numerical method for solving integral equations by combining adaptive quadrature techniques with Python-based iterative solvers. The adaptive quadrature method adjusts the step size dynamically based on error estimates, ensuring high accuracy even in the presence of singularities or near-singularities, which are common in many real-world problems. The iterative solver, based on Krylov subspace methods, enhances computational efficiency by reducing memory usage and improving the convergence speed of the solution. By using these techniques together, the proposed method significantly improves the computational time required to solve large-scale and complex systems of integral equations, while maintaining satisfactory accuracy. The results demonstrate that the adaptive quadrature technique, when combined with the Python-based iterative solver, offers a substantial advantage in both speed and precision compared to traditional methods. The proposed method is especially effective in handling complex, high-dimensional systems and ill-conditioned problems, making it a powerful tool for applied mathematics, physics, and engineering applications. In conclusion, this study presents a robust and efficient approach for solving integral equations, with potential for future research in solving non-linear and multi-dimensional integral equations.