
Teaching Philosophy (Prof. I.V. Semushin) 


Why Applied Math, Models, and Computers ?
 We live in a highly technological world in which the computer is becoming more integtal every day. Our society is also dependant on mathematics.
Any problem is solved easier when there has been found an appropriate (or adequate) mathematical model.
You may need varying amounts of mathematical knowledge,
however everyone should have the thinking skills to build mathematical
models and so attack mathematically oriented problems successfully.
Given the problem model, to get the efficient solution for it, you need good
computer literacy because modelbased solutions are now implemented as
computer application programs.
General computer literacy is needed for you to survive in current job market
and function as a literate user.
It would be an educational crime to earn a university degree and not have these skills. To this end you are enrolled in my courses.

My courses are characterized by their interdisciplinary content.
In the first place, they are based on the apparatus and tools of several
mathematics disciplines: algebra and geometry, calculus, differential
equations, probability theory, random processes theory, and mathematical
statistics.
Second, they always include your personal program implementation of those
mathematical methods you are currently studying because, by doing so, a more
sound and actualized knowledge is gained.
 In each of my courses (details for a particular course can be found in Current Courses desciprion), I have three main goals:

The students will develop thinking skills in proving mathematical theory propositions and so  in designing solutions to mathematical and computer oriented problems.
These acquired theoretical knowledge and abilities will be verified by the final examination.

The students will be exposed to how mathematics and computers are applied to
the real world problems, i.e. they will become able to solve practical
problems. These practical skills and abilities will be verified
by the innersemester test works, which can be considered as some written parts of a semesterdistributed exam.

The students will gain actual experience  practically of professional level  using a computer to solve problems through writing, entering, and running programs.
These practical skills and experience will be verified by home work assignments to do laboratory works, which for their complexity and significance are considered academic program projects.




PBE  Project Based Education

I am a great supporter of the following teaching principles:
 Focusing on HOW to teach, rather than WHAT to teach
 Strict adherence to the predesigned syllabi, in combination with a greater
sensitivity to students' needs
 An articulate and mathematically rigorous account of each course's contents
 Considering examples more instructive than rules
 Encouraging students' creativity
In practice, I follow the Frontal Competitive Approach I have formulated based
on my own experience of teaching very largesize classes. While on the subject of FCA,
I bear in mind the following:
 By "frontal," I mean allinclusive approach, involving the entire audience
in pursuit of a common goal
 By "competitive," I mean an opportunity for success owing to every individual's
creative and nonstandard solutions or actions
To implement FCA, we do the following:
 Organize creative environment
 Encourage student's creative potential
 Give start to the spirit of academic competition among students
 Ensure clearness of assessment

 


PBE  Project Based Education
 However what is above is a didactic premise only answering the question WHAT is to be done to develop
students' computational talent and generic skills of a CS/AM
(Computational Science / Applied Mathematics) professional.
As a curricular vehicle to obtain this desired result I suggest the application of the
projectbased learning (PBL), thus answering the question HOW to implement the FCA.
 I define PBL as a teaching paradigm stating that
the student has perfectly understood a computational method not until he or she
becomes able to make the computer to do all the work prescribed by the method.
I express this by a piece of advice I give in jest to some of my students: 'If
you argue that you know the method well, please teach the computer to do the same job.'
 In the other words, PBL states that the true understanding of a numerical method
may be achieved if and only if:
 A student completes assignments related to a challenging programming project
 Each project results in practical use of that particular method assigned for the
student
 The student conducts a set of extensive computational experiments with the
software product he/she developed independently, and
 Frontal rating of the projects is carried out by the teacher together with the students
 In this approach, students are not forbidden to create teams if a project is too
large for one student. Thus, the shift in the teaching and learning process is to a
more studentcentered system rather than a teachercentered one. Specifically,
PBL enables students to:
 learn to work independently and in a team environment
 acquire project planning and leadership skills
 acquire problemsolving and critical thinking skills
 develop collaborative learning skills
 exchange and share information with others
 enhance report writing, oral project defence and communication skills
 Application of FCA and PBL for many years has proved that students have a generally positive
response to it. Individual and smallteam project work within a large class encourages students'
sound competition, their desire for creative solutions and leads to better performance
indices.
 
