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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]
  • Applied Linear Algebra
    Spring 2016, Falls 2016-2023
    [ACM/IDS 104]
  • 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! :)

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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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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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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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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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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