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I. The content of science

The purpose of teaching the subject - Algorithm Design is to form the skills and competencies necessary for students to solve any programming problem, such as algorithmic thinking, designing and analyzing effective algorithms. The theoretical concepts of the subject are mainly studied through the completion of exercises and problems that gradually become more complex in order to achieve all the concepts being studied.

The task of the discipline is to analyze the principles of algorithm design, ensure sufficient mastery of algorithm design methods and develop skills in their application in practice, apply algorithm design methods to solve practical problems, improve the quality of algorithms, and reveal the role and importance of compaction methods and techniques.

II. Main theoretical part (lectures)

II.I. The subject includes the following topics:

Topic 1. Introduction to algorithm design.

Evaluating algorithms by time and size . Polynomials values in calculation Horner scheme .

Topic 2. Linear algorithms.

Cycles . Integrals approximate calculation methods , efficiency . Matrices multiplication . Determinant​ calculation

Topic 3. Networking algorithms .

Algebraic and transcendental equations approximate solution methods . Efficiency evaluation . Iterative cycles

Topic 4 . Vatars , Newton .

Simple iteration algorithms , programs

Topic 5. Game Theory .

Topic 6. Statistics in modeling the most small squares method .

Speaker programming

III. Instructions and recommendations for practical training

The following topics are recommended for practical training:

1. Designing algorithms. Evaluating the correctness and efficiency of the algorithm.

2 Dividing the interval into equal halves, iteration methods in solving algebraic and transcendental equations.

3. Linear programming problem. Mathematical model of the problem , economic analysis.

4. Expand the table function into a Fourier series. Calculate the Fourier coefficients.

5. Routes in connected graphs, evaluating them by cost (distance).

I V. Independent learning and independent work

Recommended topics for independent study:

1. Static and dynamic measures of algorithm complexity. Time and memory constraints.

2. Evaluate algorithms in worst-case and average cases.

3. Flat and logarithmic comparison criteria for evaluating the time and volume complexity of algorithms.

4. Sequences , sets , trees , graphs​ expression methods .

5. Comparison of approximate integration methods in terms of accuracy and computational complexity .

6. Evaluation of methods for approximate solution of algebraic and transcendental equations by the speed of convergence .

7. Methods for approximate solution of systems of linear algebraic equations. Approximation conditions .

8. Linear programming issues canonical appearance . Simplex​ method​

9. Digital information again at work Fur method . Spectral analysis .

10. Dynamic programming methods in statistical information processing and forecasting problems.

11. Transforming graphs into width and height (verification).

12. Graphs the most cheap support tree in construction Kruskal stingy algorithm .

13. Prima - Dijkstra's algorithm. Its time evaluation.

14. Algorithms in the language of "divide and conquer".

15. P and NP classes , NP - complete issues concept .

16. Criteria for evaluating algorithms. Examples of evaluation by time and volume.

17. Newton-Cotes formulas in the approximate calculation of integrals. Idea and error order.

18. Gaussian formulas in the approximation of integrals. Idea and error order. Efficiency .

19. Abbreviation expressions in collections . Examples of them and practical applications.

20. Algebraic and transcendent equations approximate in solution the interval equal for two to be and fathers methods efficiency according to comparison .

21. Comparison of the efficiency of the Watters and Newton methods in the approximate solution of algebraic and transcendental equations .

22. Recommendations for developing a simple iteration method and its effective variants for approximate solution of algebraic and transcendental equations.

23. Matrix norm and methods for its determination.

24. Linear algebraic equations system in solution simple iteration and Seidel methods , their approach conditions .

25. Linear programming issues for support solution concept , them determination methods .

V. Results of science teaching (developed competencies)

As a result of mastering the subject, the student will:

• Have an understanding of working in different development environments and creating complex software ;
• Must know and apply types of algorithms, data retrieval, sorting, and hashing algorithms and methods, and be able to design and implement algorithms and use them in software;
• have the skills to design, develop, and implement new algorithms in the learning and production process, depending on the problem being addressed .

VI. Educational technologies and methods:

• lectures ;
• practical work to perform and to conclude ;
• interactive case studies ;
• blist- survey ;​
• in groups work ;
• presentations preparation ;
• team with work and protection to do for design .

VII. Requirements for obtaining loans:

Fully master the theoretical and methodological concepts of the subject, be able to correctly reflect the results of the analysis, conduct independent observations of the processes being studied, and complete the tasks assigned in the current and intermediate control forms, and submit the final control work.

Main literature

1. Томас Кормен, Чарльс Лейзерсон, Рональд Ривес, Клиффорд Штайн. Алгоритмы: построение и анализ. Москва-Санк-Петербург-Киев. 2013.
2. Levetan Anany. Introduction to the design & analisis of  algorithms. 3rd ed. Villanova university. New Jersey. 2012. 693 page.
3. Ding-Zhu Du, Ker-I Ko. Design and Analysis of Approximation Algorithms. Springer New York Dordrecht Heidelberg London. 2012, 453 page.
4. M.H.Alsuwaiyel. Algorithms Design Techniques and Analysis, New Jersey. World Scientific, 2016. 571 page.

Additional literature

5. O’zbekiston Respublikasi Konstitutsiyasi. Yangi tahrirdagi O’zbekiston Respublikasi Konstitutsiyasi. 2023-yil 30-aprel. 31 bet. (Qonunchilik ma’lumotlari milliy bazasi, 01.05.2023-y., 03/23/837/0241-son)
6. Horton I.-Beginning Visual C++ 2012/ I. Horton. Published imultaneously in Canada.-2016.-P.988.
7. Mirzayev A.N., Asadov Q.U. “Sonli usullar va dasturlash, modellashtirish” fanidan laboratoriya topshiriqlarini bajarish bo’yicha uslubiy ko’rsatmalar. 2019.
8. “Mirzayev A.N., Abduraxmanova Yu.M. “Sonli usullar va dasturlash” fanidan ma’ruzalar matni. “Aloqachi”, 2015.
9. Хайдарова М.Ю., Маллаев О.У., Абдуллаева З.Ш., Сатаров А.Б. Методическое пособие для выполнения лабораторных работ по предмету «Программирование на C++» (1 часть) ТУИТ, Ташкент 2017 г. 145 стр.
10. M.O‘.Ashurov, Sh.A.Sattarova, Sh.U.Usmonqulov. Algoritmlar. -T.: «Fan va texnologiya», 2018, 244 bet.

Internet resources​​

1. www.ziyonet.uz
2. http//www.intencia.ru
3. http//www.ido.rudn.ru.
4. http//www.filam.ru/sait.phg
5. http//www.phenomen.ru