Mathematical methods in geology

Description: This discipline considers geological objects and their properties, the principles of mathematical modeling. Analyzed one-, two-and three-dimensional statistical models, including the method of principal components, cluster analysis, pattern recognition, the application of these models to solve geological problems.

Amount of credits: 5

Пререквизиты:

• Mathematics 2

Course Workload:

Component: Component by selection

Cycle: Base disciplines

Goal

• The purpose of the course is to acquaint the student with the content of these tasks and the methodology of their solution based on modern computer technology.

Objective

• The objective of the course is to teach students to evaluate the results of geological exploration; calculation of reserves, assessment of the quality of minerals, mining conditions of the deposit, etc. using mathematical methods.

Learning outcome: knowledge and understanding

• Обладать базовыми знаниями и пониманиями в области математической статистики, основными принципами применения математических методов в геологии.

Learning outcome: applying knowledge and understanding

• Students must have the following skills: - solutions of typical and individual geological problems; - calculation of statistical characteristics; - work with computer graphics.

Learning outcome: formation of judgments

• Performing statistical research, solving geological problems based on the acquired knowledge, independent mathematical modeling of geological objects and phenomena. the use of the latest technologies in geology

Learning outcome: communicative abilities

• Work effectively as a member or team leader, demonstrate responsibility for the result of work. Master the basic methods of obtaining, processing and storing information for solving professional problems of geology.

Learning outcome: learning skills or learning abilities

• Improve existing and introduce advanced methods of conducting research and conducting geological exploration Be mobile and receptive to the improvement of technology and technology, to the use of scientific and technological progress in the field of geology

Teaching methods

project-based learning technologies - the organization of the educational process in accordance with the algorithm of step-by-step solution of a problem problem or performance of an educational task. Problem-based learning technologies - the organization of the educational process, which involves the formulation of problematic issues, the creation of educational problem situations to stimulate the active cognitive activity of students. Interactive technologies – the organization of the educational process, which involves active and nonlinear interaction of all participants, achieving on this basis a personally significant educational result for them.

Topics of lectures

• BRIEF HISTORICAL INFORMATION ABOUT APPLICATION OF MATHEMATICAL METHODS IN GEOLOGY
• THE CONCEPT OF GEOLOGICAL AND MATHEMATICAL MODELING OF OBJECTS AND PHENOMENA
• FUNDAMENTALS OF PROBABILITY THEORY Basic definitions and concepts
• STATISTICS OF RANDOM VARIABLES Statistical estimates of unknown parameters
• BUILDING STATISTICAL SOLUTIONS
• EXPLORING THE DIFFERENCES BETWEEN GEOLOGICAL OBJECTS
• CORRELATION DEPENDENCE BETWEEN PROPERTIES OF GEOLOGICAL OBJECTS
• MULTIDIMENSIONAL STATISTICAL MODELS
• SPATIAL VARIABILITY OF GEOLOGICAL PROPERTIES OBJECTS
• RANDOM FUNCTIONS The main characteristics of random functions

Key reading

• 1.Бахтин, А. И. Статистические методы в геологии : учебное пособие / А. И. Бахтин, Е. М. Нуриева. - Казань : Казанский федеральный университет, 2013. 2. 2. Ядзинская М.Р. Математические методы в геологии. - Перьм, 2022 г.- 902 с.

Further reading