Ushbu maqolada men boshlang‘ich ta’limda kollaborativ yondashuv asosida darslarni tashkil etish metodikasi, uning samarali usullari hamda ta’lim jarayonidagi ahamiyati haqida fikr yuritdim. Shuningdek, kollaborativ ta’limning o‘quvchilarning mustaqil fikrlashi, jamoada ishlashi va kommunikativ kompetensiyalarini rivojlantirishdagi o‘rni yoritildi.

This article highlights the role and importance of mathematics in preparing academic lyceum students for higher education. It also analyzes the pedagogical potential of mathematics in developing students’ logical thinking, analytical reasoning, problem-solving abilities, and professional competencies. The article discusses the effectiveness of teaching mathematics through modern pedagogical technologies, organizing independent learning, and applying innovative methods during the preparation process for higher education. Furthermore, scientific and methodological recommendations are provided to enhance the theoretical and practical significance of mathematics education in academic lyceums.

Maqolada mulk huquqining vujudga kelishi, o‘zgarishi va bekor bo‘lishining huquqiy asoslari tahlil qilinadi. O‘zbekiston Respublikasi Fuqarolik kodeksi normalari hamda ilmiy-huquqiy qarashlar asosida mulk huquqining yuzaga kelishiga sabab bo‘luvchi yuridik faktlar, uning o‘zgarishiga olib keluvchi huquqiy munosabatlar va bekor bo‘lish asoslari o‘rganiladi. Shuningdek, mulk huquqini amalga oshirish va himoya qilish bilan bog‘liq ayrim masalalar yoritiladi.

The rapid development of digital educational technologies has created new demands for the automation and intelligent analysis of educational content. Across the world, and especially in countries undergoing rapid digitalization such as Uzbekistan, educational institutions are increasingly deploying e-learning platforms, digital textbook repositories, and automated assessment systems. These platforms generate and manage enormous volumes of exercises, questions, and instructional tasks that must be organized, classified, and evaluated in a principled manner. Without a rigorous approach to understanding the semantic content of exercises, such platforms cannot effectively adapt to the needs of individual learners, align with curriculum standards, or provide meaningful feedback to educators and policymakers. This article proposes a mathematical model for the semantic analysis of exercises used in automated learning systems. The model is built on three complementary components: vector-space representation of textual content, probabilistic dependency graphs that capture the grammatical and relational structure of exercise statements, and ontological mapping of domain-specific concepts drawn from official curriculum taxonomies. Together, these components allow the model to classify exercises by cognitive complexity, assess their semantic relevance to defined learning objectives, and evaluate their internal structural coherence. Experimental results obtained from a corpus of over four thousand Uzbek-language educational exercises demonstrate the effectiveness of the approach, yielding an average classification accuracy of 91.4% across STEM subject domains. The study makes a foundational contribution to the theoretical basis of intelligent tutoring systems and adaptive learning platforms in Uzbekistan.

Mazkur maqolada yurak-tomir sistemasi kasalliklarining kelib chiqish sabablari, asosiy turlari, diagnostikasi, davolash va profilaktika choralari yoritilgan. Shuningdek, ushbu kasalliklarning inson salomatligiga ta’siri hamda ularni oldini olishda sog‘lom turmush tarzining ahamiyati tahlil qilingan.