Caltech
Courses
- Statistical Inference
Winters 2016, 2017, 2020, Springs
2018, 2019, 2021-2024
[IDS/ACM/CS 157]
- Introduction to Probability
Models
Falls 2016-2023
[ACM/EE/IDS 116]
- Introductory Methods of
Applied Mathematics
Winters 2018, 2019, 2021-2023
[ACM 95a/100a]
- Fundamentals of Statistical
Learning
Spring 2020, Winter
2024
[IDS/ACM/CS 158]
- Introduction to Matlab
and Mathematica
Springs 2016, 2017
[ACM 11]
Honors & Awards
- Associated Students of Caltech Teaching
Award, 2023
Photo: [jpg1,
jpg2]
- Graduate Student Council Teaching
Award, 2023
- Invited Faculty Speaker, Senior Graduation
Banquet 2022
Text of speech: [www].
Photo: [jpg]
- A biased sample of student comments
[pdf],
2016-present
- In action: [jpg1,
jpg2, jpg3].
Send me more funny photos! :)
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Teaching Philosophy
Teacher:
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.
— Arkady
and Boris Strugatsky, Monday Begins on Saturday
“I would urge every
teacher to become an actor. His classroom technique must be enlivened
by every device used in theatre. He can be and should be dramatic
where appropriate. He must not only have facts but fire. He can utilize
even eccentricities of
behavior to stir up human interest. He should not be afraid of humor
and should use it freely. Even an irrelevant joke or story perks up
the class enormously.”
— Morris
Kline, Mathematics Teacher 49:171
What are my general goals
as a teacher?
I believe that the most effective
way of education is self-study. As Ray Bradbury wrote, “teachers
are to inspire; librarians are to fulfill.” This is especially
true in mathematical sciences: the only way to learn is through
the independent self-study. It takes time and effort to understand
a new subject by constructing examples, exploring special cases,
solving exercises, and finding analogies and connections with other
already learned subjects.
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However, the importance of the teacher's
role in the process of student's self-education cannot be overstated.
Obviously, self-study is extremely effort-consuming and, therefore,
requires strong motivation. So, my first objective is to inspire my
students, to show them why the subject I teach is interesting, beautiful,
and useful, and so motivate them.
Imagine a classroom of bright-eyed
freshmen. Having just entered university, they are highly-motivated
and eager to learn. How many of them will still be motivated and inspired
after the end of the course? Frankly, not all of them. There are several
reasons for that, and clearly the quality and style of lectures plays
a crucial role. So, my next very important aspiration is to design
my lectures in such a way that it allows me to keep the interest of
students and the integrity of the knowledge simultaneously.
Finally, whenever someone learns a
new subject plenty of questions appear. Undoubtedly, I consider it
my responsibility to help students to tackle their difficulties arising
during the course. To put it in a nutshell, my main goals as a teacher
are to motivate and inspire my students, to provide them with well-designed
and high-quality lectures and to be open for questions, discussions,
and collaboration.
How do I motivate and inspire
my students?
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, what kind of problems we are able to solve using the
corresponding concepts and notions, what we can learn about the world.
I hope that eventually my inspiration will be transmitted to the majority
of my students and that they will become intrinsically motivated.
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However, I fully realize that there
is no way to motivate all students in the classroom. There are always
students without intrinsic motivation. I try to help them by extrinsic
motivators in the form of rewards. People like to repeat behavior
that is rewarded and students are no exception. A joint coffee break
and simple verbal encouragement are external rewards that can, after
a short period of time, produce intrinsic motivation.
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, at least to some extent, all main definitions, theorems,
proofs, algorithms, illustrative examples, and applications. Although
my ambition is to cover as much important content as possible, the quality
of knowledge is definitely more important.
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Next, the content is not what a course
is all about. I believe that the quality of knowledge highly depends
on the manner and style of lecturing. In my teaching, I combine two
popular lecture modes: using slides and using a piece of chalk. I
use slides only for demonstration of visual information (e.g., graphs,
figures, and tables). I use blackboard for all computations, proofs,
and explanation of technical details. This allows students to follow
the lecture in real-time and gives them more time to digest new information.
Finally, the lecture style is also
very important. I try to follow Kline's advice cited above. During
my lectures, I never use any notes and always teach from the bottom
of my heart.
How do I know that my students
are learning?
I like questions: I like
to ask, and I like to be asked. So, I always let students ask questions
during my lectures. It gives me immediate feedback on how students are
thinking, what they understand, and what is difficult for them. In addition,
asking questions during a lecture helps students to feel more involved
into the learning process. I consider the absence of questions as a
first sign of a lack of understanding.
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Sometimes I ask students questions
during my lecture. This stimulates active thinking and develops intuition.
Moreover, it is much easier to remember an answer you have to think
about rather than rote knowledge. Also I like to spend time with students
in an informal atmosphere, whether it is a coffeehouse or a hiking
trip. Occasionally, in such unofficial activities some students may
discuss their concerns more freely.
When I teach mathematics, do
I teach just mathematics?
I always keep in mind
that by no means will all of my students be professional mathematicians,
scientists, or engineers. This leads to a natural question: what
benefits from my teaching can my students get for their future life?
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Mathematics adjusts our minds. Learning
mathematics develops logical, creative, critical, and abstract thinking.
There is no lie in mathematics and this teaches us to be honest. Mathematical
beauty nurses our spirit. Mathematical complexity strengthens our
character. I hope that even if many formulas, theorems, and proofs
are forgotten with time, my students will still have very useful skills
and qualities for the rest of their lives.
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