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.

Ushbu maqolada yangi Konstitutsiyaning Ikkinchi bo'limi (V–XI boblar, 19–64-moddalar)da mustahkamlangan inson huquqlari kafolatlarining mazmuni, tarkibiy tuzilishi va huquqiy tabiati kompleks tarzda tahlil etiladi. Tadqiqot qiyosiy-huquqiy va matn tahlili metodlaridan foydalanib, inson huquqlarning bevosita amal qilishi tamoyili, aybsizlik prezumpsiyasi va ekologik huquq singari konstitutsiyaviy yangiliklardagi kontseptual siljishlarni aniqlaydi. Natijalar shuni ko'rsatadiki, 2023 yilgi yangi Konstitutsiya inson huquqlari himoyasida davlatning ijobiy majburiyatlarini sezilarli darajada kengaytirdi va "insonning qadr-qimmati oliy qadriyat" paradigmasini butun huquqiy tizim uchun markaziy asos sifatida belgiladi. Shu bilan birga, bir qator huquqlarning amaliy tatbiqini ta'minlash uchun qo'shimcha tarmoq qonunchiligi zarurligining qolib turishi muammo sifatida aniqlanadi.

Mazkur maqolada o‘smirlarda kasb tanlash jarayoniga ta’sir etuvchi psixologik omillar tahlil qilinadi. Jumladan, qiziqish, qobiliyat, motivatsiya, oilaviy muhit, tengdoshlar ta’siri hamda shaxsning o‘zini anglash darajasi kasbiy yo‘nalishni belgilashdagi muhim omillar sifatida yoritilgan. Shuningdek, o‘smirlik davrining psixologik xususiyatlari va ularning kasb tanlashdagi ahamiyati ilmiy manbalar asosida bayon etilgan. Maqolada o‘quvchilarning ongli ravishda kasb tanlashiga yordam beruvchi tavsiyalar ham keltiriladi.

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.