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 model-based 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:
  1. 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.
  2. 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 inner-semester test works, which can be considered as some written parts of a semester-distributed exam.
  3. 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 pre-designed 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 large-size classes. While on the subject of FCA, I bear in mind the following: By "frontal," I mean all-inclusive 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 non-standard 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 project-based 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 student-centered system rather than a teacher-centered one. Specifically, PBL enables students to:
  • learn to work independently and in a team environment
  • acquire project planning and leadership skills
  • acquire problem-solving 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 small-team project work within a large class encourages students' sound competition, their desire for creative solutions and leads to better performance indices.