Department of General Mathematics
Our Department is aimed to solve the following problems: First, we
are preparing mathematicians-teachers. After graduating the University,
they can work as teachers and lecturers in higher education
institutions, high schools, colleges, secondary schools, etc.,
with advanced study of mathematical disciplines. Abilities to
teach on both Russian and Tatar (when desired) are previewed as well.
While other Chairs of the Institute dwell in both common and specific
formation of the students in various directions of the
Contemporaneous Mathematics, our Chair supply to them the methodological
principles of formation, supports a future specialist to
refine his/her knowledge in Elementary Mathematics for Secondary School.
This means a possession of new methods for solving problems of
Elementary Mathematics, the knowledge of both classical and modern
pedagogical technique. To this end our staff elaborated a number
of general and special courses concerning the methodology of teaching to
Mathematics; we systematically prepare new manuals and books, which support
the students in acquiring necessary pedagogical experience and knowledge.
The practical training of teaching takes place in the
best high and higher schools of the city under supervision
of our most experienced specialists. Namely in these schools the
knowledge, accumulated during the years of study, is verified
and the practical experience of both curricular and additional
educational work is adhered; the first lessons in their professional
teacher life are given.
Experience of several years shows that the mathematicians -- graduates of
the Kazan University -- possess significantly greater knowledge
than those who graduated from pedagogical institutes. Moreover,
our graduates have an augmented mathematical culture (a fact known at
international level), though their preparation in methodical courses
is lesser in its volume, but not quality. Their accommodation to the
high school requirements seems to continue during the first one or two
years, but afterwards they turn to occupy the leading places among
the teacher staff. Their creative abilities and skills for active
work, their dedication to the Mathematics help them to become
brilliant persons attracting the young school pupils.
The next objective of our Department is formation in Mathematics of the
students at non-mathematical Faculties, including Biological,
Chemical, Geological, Geographical and other faculties.
In last years some new trends started to prevail in Higher Education
-- both the humanization and mathematization. By recent
governmental decisions, mathematical disciplines are introduced
practically in all curricula of university faculties. We are trying to
help to our students to understand the basic elements of both Classical and
Discrete Mathematics, to refine their knowledge in Computer
Science, form their necessary skills for free working at PCs and
Significant forces of our staff are directed to help those
young men and women, who already have some practical experience after
graduating from a secondary school, but wish to continue their
study in our University.
To this end they must restore their knowledge and skills. This objective
is realised at the Preparatory Division of Kazan University (so-called "Rabfak").
So, a significant part of our staff works with the students of "Rabfak",
thus dedicating their efforts to the aim of forming persons possessing a
significant "lacunas" in their Mathematics.
The staff of Department holds almost all mathematical courses at university
faculties related to Natural Sciences, creating thus a foundation for
adequate posterior teaching for the consequent scientific courses and
development of a young specialist.
A significant research work is carried out along the
lines of Methods for Teaching the Mathematics, many various
manuals and tutor books are already published, we permanently prepare new
didactic materials. We are studying the ways to activate
the processes of learners' perception in their studying complex parts of
mathematical courses. A technique for analysis of the complexity of
exercises and problems in Elementary and Higher Mathematics is developed
in order to make more adequate the composition of the corresponding
courses. We prepare specialists - teachers of Mathematics for both
High and Higher education levels with a fundamental theoretic basement
in Mathematics, Pedagogy, and Psychology.
Scientific Research Works
- Psychological-pedagogical Basements for
Development of Formation in Mathematics in Higher and Secondary School
- Conceptual and Algorithmic Aspects of the Intellectualization
of Man-Computer Interface
Courses of Specialization
- Elementary Mathematics (in Russian) on 1st, 2nd, 4th, and 5th years
- Methods for Teaching the Mathematics (in Russian)
- Methodological Problems of Mathematical Pedagogy in
the Modern Situation
- Elliptic Functions
- The Geometry of Images with Basements of The Projective Geometry
- Projective Geometry and Projective Metrics
- Boundary Value Problems in a Rectangle
- Riemannian Geometry and Tensorial Analysis
- Basements of The Theory of Differentiation
- Elementary Mathematics (in Tatar) on 1st and 4th years
- Methods for Teaching Mathematics in Tatar