biased) sample of student comments [png]
- Applied Linear Algebra
Spring 2016, Fall 2016
- Introduction to Probability
- Introduction to Statistical
- Introduction to Matlab
- Uncertainty, Reliability
of Southern California
A (very biased) sample of student comments
- Mathematical Statistics
Spring 2012, Spring 2013.
- Mathematics of Physics
- Fundamental Principles
Fall 2011, Fall 2012.
Hong Kong University
of Science & Technology
- Mechanics of Materials
Spring 2007, Spring 2008.
- Statics and Dynamics
Fall 2006, Fall 2007.
Moscow State University
- Classical Differential
Notes in Russian [pdf]
of mathematics [jpg]
for Continuous Mathematical Education
Summer 2000, Summer 2002.
Children, write down the proposition:
“The fish was sitting in a tree.”
Pupil: But is it true that fish sit in trees?
Teacher: Well . . . it was a crazy fish.
and Boris Strugatsky, "Monday Begins on Saturday"
- Emir Kusturica and Goran Bregovic,
"Arizona Dream" What are my
general goals as a Teacher?
I believe that the most effective way of education is self-study.
This is especially true in mathematics: the only way to learn mathematics
is to do mathematics. It takes time and effort to deeply understand
the main oncepts of a mathematical theory by constructing examples
and ounterexamples, solving exercises, and finding analogies with
other already learned subjects.
How do I motivate and inspire
Study without desire just ruins the memory. So, I always try
to explain to my Students why I teach what I do, why the topic is important
and interesting, and what kind of problems we are able to solve using
the mathematical theory under study. I hope that eventually my inspiration
will be transmitted to the majority of my Students and that they will
become intrinsically motivated.
What do I mean by good lectures?
First of all, a good course of lectures must reflect the current
state of the subject. I form a time-limited course in such a way that
it contains all the main concepts, important theorems, and illustrative
examples. Although my ambition is to cover as much important content
as possible, the quality of knowledge is definitely more important.
How do I know that my Students
I like questions: I like
to ask, and I like to be asked. So, I always let my Students ask questions
during the lecture. It gives me immediate feedback on how students are
thinking, what they understand, and what is difficult for them. In addition,
asking questions helps students feel more omfortable during the lecture.
I consider the absence of questions as a first sign of a lack of understanding.
How can I improve my teaching?
Feedback from both students
and colleagues plays an important role in teaching improvement. In the
middle of the term I ask Students to complete a short questionnaire
on how to make my lectures and assignments better, which aspects of
my teaching are strong and which need improvement. From time-to-time
I invite my mentors to my lectures and ask them for a feedback on how
to improve my teaching.
When we teach mathematics we
teach just mathematics, don't we?
I always keep in mind
that by no means will all of my Students be professional mathematicians.
This leads to a natural question: what benefits from my course can
my Students get for their future life?