Grad School, Tips

4.5 Ways to “Keep Calm And __[incert anything]”

How to manage grad school, a part-time job (or jobS), a relationship (or a family) and not to go crazy? If you’ve been to grad school for over 6 month you have probably figured out that it’s a rhetorical question. However, we c

an always brainstorm strategies to “Keep calm and ______”.

The next question is HOW do we keep calm?

1. Put it in perspective

We might be constantly broke, criticized for our life choices or academic performance, etc., etc., etc BUT most of us have a roof above our head, we are not starving, not terminally ill… Hence, we can’t complain TOO much.

Of course there are tons of things that we can complain about such as problems within academia, complicated family dynamics, other less-than-perfect living arrangements, and we continue this list forever. However, it’s OUR choice which list we’ll focus on: the list of complaints, or the list of blessings.

2. Focus on the list of blessings instead on the list of complaints

Of course, a good complaint session might be therapeutic once in a while, however, it’s in our best interest to focus on the list of our blessings and make it as lengthy as possible.

Think your life sucks? Watch The Theory of Everything (, or Leviath ( )

 still think your life sucks as much as the main characters’?

3. Life is more than just grad school

That’s the hardest one to keep in mind at times. We get so immersed in our research or just everyday motions and routines of reading, going to seminars, keeping up with employment, etc, that it is difficult to forget that our personalities are not confined within our theses.  Have you ever had a hobby? Who did you want to become as a kid? What did you friend and relatives think you’ll become? Where is your favorite spot in the city? When was the last time you tasted your favorite ice cream?  Our personalities are somplex and we have so many roles (students, children of our parents, partners, parents, etc).  It is true that we might have chosen the role of a ‘graduate student’ to be the main one at this time, but it is TEMPORARY.

Grad school is not a permanent state of being (although most of the time it feels like one), and if things become unbearable, it’s a great point to keep in mind.

4. Grad school is TEMPORARY, but this fact should not be a panic-trigger

Most of us are worried about employment after obtaining our degree, and we should definitely work towards obtaining experience and keeping our ears and eyes open for relevant possibilities. However, even if you are not 100% sure what kind of employment you wish to take up after graduation, it should not trigger a panic-attack while you are still working on your thesis.

Imagine that you went for a hike up a mountain. The higher you are getting, the more you can see.  Similarly, with your graduate studies: the more you know and the more experience you get, the better is your ‘view’ of other possibilities. You are NOT a horse. You don’t have to wear blinkers or follow a stricter-than-necessary route.

4.5 But really, what all of us need at times to keep calm is a nice friendly hug, so walk over to the nearest human and exchange hugs (if socially acceptable, of course 😉 )

Grad School, Research, Uncategorized

Canadian Mathematical Society Winter Meeting 2016 – Niagara!

This weekend was really mathematical for me!

I went to Canadian Mathematical Society Annual Winter Meeting! This year it was held in Niagara falls. We didn’t get to see the falls and the fire alarm nearly chased us out of the conference halls, but overall the trip was incredibly productive and fun. I also met up with friends who I haven’t seen in such a long time!

Continue reading “Canadian Mathematical Society Winter Meeting 2016 – Niagara!”

Math, Outreach

How not to have a ‘teenage debate’

I work with teens and most of them love arguments and debates [i love debates as well!] But debating is a form of art.  Some of my students have not mastered it yet, so they often end up having a ‘teenage debate’. A ‘teenage debate’ is a discussion where participants criticize each other instead of each others’ ideas, blame each other for not understanding their points of view, and  – most importantly – everyone is very poorly informed about the topic of discussion. Another characteristic of a ‘teenage debate’ is that it gets started to procrastinate on some real tasks that the students have to do at a given moment.

Continue reading “How not to have a ‘teenage debate’”

Art, Drawings, Math, Outreach

Essentials for a freelancing math teacher

I’m a math teacher and a graduate student. I don’t teach at a public school. Instead I teach at special programs for gifted children, or work with children individually. I guess that makes me a freelancing math teacher. Continue reading “Essentials for a freelancing math teacher”

Math, Outreach

Fields Medal Symposium 2016

There’s no Nobel Prize in math but there’s a Fields Medal which is given to mathematicians under the age of 40 for their outstanding achievements. Every year Toronto’s Fields Institute hosts an annual Fields Medal Symposium to honor one of the medalists. This time we have Prof. Manjul Bhargava  – a number theorist born in Hamilton – is the honored guest.

Prof. Bhargava is the first Canadian born mathematician who received the Fields Medal! This makes this year’s symposium even more special. There were no empty seats in the Isabel Bader Theatre where the Public Opening of the Symposium was taking place yesterday evening. The audience was composed of professionals from a variety of fields and students. Prof. Bhargava’s talk was engaging and accessible for everyone in the audience.  Colorful diagrams and interesting facts about nature that he mentioned were especially appreciated.

We brought our Math Circles class from UTM to the public opening. This was their first time attending such a large event.  Luckily, they enjoyed the talk and the festive atmosphere around the Public Opening night.  Moreover, they even had a chance to take a picture with Prof. Bhargava!

Prof. Bhargava will be giving a special lecture for high school students this evening at the Fields Institute, but unfortunately I will not be able to attend it, cause I’ll be teaching my own students.

If you want to find out more information about the Fileds Medal Symposium, click here:


Art, Photography

Hi, October 2016!


The First Impressions of Each Month Photo Series: October edition!

My October started off with a rain, an early rise, and a teaching session.

Afternoon and evening were charged with positive energy and lots of work related to performing and rehearsing for the Little Mermaid Show (refer here: )

The day ended off with pretty flowers, browsing the streets of Toronto filled with Nuit Blanche sights and tasting awesome local food.


Math, Outreach

Math Snippet: Graphs, Instagram, Internet


I’m taking an online course on graph theory now and the lecturer is so good that listening to him is like watching an engaging movie.  His language is simple enough and he does not assume any previous knowledge of higher level math (just high school knowledge). For now, here are some very basic snippets about graphs:

Imagine we have a classroom full of desks that can seat two people.  We could represent people as dots (vertices) and connect these dots with lines (or edges).  We have created a graph that provides us with information about the pairs of students, the ways they are paired up.  More formally, graphs are structures that describe pairwise relationships between objects.

Continue reading “Math Snippet: Graphs, Instagram, Internet”

Grad School, Research

Pedagogy -Balancing on the Border of the ‘Image’ and the ‘Body’ of Knowledge

apple, bag, client

I notice that I work better when I have very concrete goals in mind, or when I hold myself accountable to someone. I am in the process of creating a draft of my thesis and I will be sharing some excerpts with you. Most likely they will not be direct or exact excerpts, but rather adapted snippets.

Here is the first one in which I’ll tell you about the ‘image’ and the ‘body’ of mathematics, and about pedagogy that falls exactly into the intersection of these terms.

In summary, the body of knowledge encompasses the intellectual content that a certain scientific discipline is concerned with and the image of knowledge represents the attitudes, beliefs and concerns of the scientific community about the body of knowledge  Continue reading “Pedagogy -Balancing on the Border of the ‘Image’ and the ‘Body’ of Knowledge”

Grad School, Research

A ‘quirk’ that Dedekind, Mendeleev and Hilbert had in common :)

I always get an extra boost of creativity, motivation and productivity in my graduate research after periods of teaching.  I’ve been working at different math summer camps for the last few weeks, and the experience was tiring and challenging at times.  However, after the camps were finished I noticed that some ideas related to my research have just ‘appeared’ in my head – sounds great, right? …Except that when I share this experience with some of my friends in academia, they usually exclaim: “But teaching is a ‘distraction’ from your ‘real’ work, isn’t it!”

So I convinced myself that I’m just an ‘odd apple’ in academia with this strange quirk of not hating the process of teaching… Then I found out that I’m not the only one.  Apparently many works of Mendeleev, Dedekind and Hilbert were inspired, and driven by their teaching experiences, or dissatisfaction with existing teaching methods.

For instance, Dmitri Mendeleev’s table of elements was first published in [drum roll] a TEXTBOOK!  At the start of his career Mendeleev was one of the many professors with a high teaching load and not-so-high salary.  His famous table was a result of frustration with his students and the teaching materials that he was provided with.  Contrary to a relatively common belief, Mendeleev was NOT the first scientist to attempt organizing and classifying the elements.  Other classification systems were widely published in textbooks but Mendeleev’s class was unable to make sense out of those classification systems. Hence, Mendeleev set off to create his own way of organizing the elements and presenting them to his students.  Soon the famous periodic table appeared in an ordinary textbook for university level chemistry class.

Richard Dedekind was absolutely appalled by methods of teaching calculus at university level.  He was unhappy with all the gaps in students’ knowledge of math in general as well as in subject-specific areas.  This frustration with poor pedagogy of calculus has inspired his works on integers.  In fact, it inspired him to push the ‘boundaries’ of algebra so far that some mathematicians were doubting that his works should even be considered a part of the realm of algebra (for those who are specializing in history of sciences, I’m just trying to say that he has altered the ‘image’ of algebra).

David Hilbert always surrounded himself with as many talented students as he could, especially during the mature stages of his career.  He claimed that tuning into their ideas and bouncing his own ideas against them motivates him to expand his academic views and provides him with inspiration to keep learning.

There are countless examples of other scientists and mathematicians who were motivated by teaching such as Kolmogorov, Alexandrov, etc. (each of them deserves a BOOK  – not a paragraph).

Of course, there are equally as many successful and famous scientists who were sure that teaching is not their thing, which is fine, and deserves a discussion as well – but maybe in a different post 🙂

P.S.: mini-bibliography/inspiration sources:

A Well Ordered Thing: In the Shadow of the Periodic Table by Michael Gordin

History of Modern Algebra  by Leo Cory

Hilbert by Constance Reid


First Timer’s Guide to New York

This May I went to New York for the first time.  The first thing I explored in NY was the Museum of Mathematics (MoMath 🙂 )

bodies of constant width
bodies of constant width
the famous 'bicycles'
the famous ‘bicycles’


then I headed to MoMa, cause, let’s be honest – where else would you pay $15 to see 🙂 masterpieces 🙂 like







or this


… unfortunately photography was not allowed at the special exhibition of Gauguin.

Moma also has an amazing staff! From a conversation with one of them I found out that they have memorized the rules of the museum, but never bothered to find out the reasoning behind them… for instance, my simple and innocent question “Why talking on the cell phone is not allowed but talking to each other IS allowed” totally confused the staff.

on my way to MoMa I stumbled upon a Russian store where I found these Chaburashki



After MoMa I headed south


Astro Gallery of Gems remains my favorite place in New York! I can’t imagine that some of the exhibited fossils and minerals have been existing for millions of years!



I wish I could spend more time at the Central Library



or walk into the Central Park through the Engineers’ Gate


but too many other things were planned for this trip – like riding through the abandoned City Hall station


attending the Museum of the City of New York


the Jewish Museum



and The Metropolitan! (or just the Met :):):) )


Walking down the Fifth avenue felt a lot like walking down an endless hallway.  I just had this persistent feeling of being indoors all the time.  However, there were endless interesting and pleasant things like seeing the Empire State Building from my hotel window


or this Luna Bar – made SPECIFICALLY for women….. I wonder what would happen if a man eats it…..?


or being greeted by fresh flowers before brunch on my last day there


New York is a puzzling city and I have much more to tell then I could fit into this photo-post.  I would definitely want to go there again to explore the museums and the architecture.

(If you would rather read this post in Russian, see it at my new blog page at the Vorkug Sveta (Around the World) magazine )



Math, Outreach

Geek Street Fair powered by Google – Toronto Distillery District


Last Thursday I, along with a great group of volunteers, had a pleasure to participate in the Toronto Distillery District Geek Street Fair powered by Google.

The event was designed to demonstrate how fun and exciting STEM subjects can be.

Read more about this event at out new website at

Math, Outreach

Math Kangaroo, Mentorship, Girls in Gear

It has been a long time since I posted any updates, and I want to thank all the guests who have been reading my webpage during that time.

Here are several events that took place recently:

Mathematics Kangaroo Contest took place on March 23rd across Canada.  All three University of Toronto Campuses were involved.  The students and the staff had a great time! Visit to register for the 2015 Math Kangaroo Contest!


Math In Motion…Girls In Gear  (April 5th).  It was a great honor for me to be one of the guest speakers and to teach grade 9 students about ancient calculation aid – abacus. Then they even made their own abaci and took their creations home!

Girls also braved the Design Challenge task that required them to build a container for an egg that needed to be thrown off the third floor! Guess what – most eggs survived this adventure without a slightest crack!


Mathematics Mentorship – Poster Presentation Event. 25 high school students were paired up with UofT Math department graduate students and professors for a semester-long mentored studies.  The students demonstrated their newly acquired knowledge during the end-of-the-semester poster presentation session.  Please see the details of other outreach programs offered by the U of T Math department at


Math, Outreach

Kangaroos are coming!!!

Last weekend all of the University of Toronto campuses hosted the last preparation session before the Mathematics Kangaroo Contest of 2014! The students and the instructors had a great time. The kids couldn’t wait to write the contest!

The contest will take place tomorrow! Math students all over Canada will be writing it. If you are planning to participate, you still have the entire Saturday night to try some of the contest problems from last year.

You can find them here

Good luck for tomorrow’s contestants! Have some good night sleep and we will see you on Sunday morning!

Math, Outreach

Math and Comp. Sci. High School Teachers’ Workshop

 Today I was honored to be one of the speakers at the Math and Comp. Sci. High School Teachers’ Workshop at the University of Toronto at Mississauga.

Here is the link to the workshop program

I was speaking about methodology of history of mathematics, math education reforms in the US and in the USSR and various ideas that modern teachers can  draw from them and successfully use in the modern classroom.

I could not only attend one other talk –  Nifty Computer Science Assignments by Daniel Zingaro – and it was a great! We learned about various ideas for assignments that stimulate the students to go above and beyond the course content.  


Math, Outreach

Happy Pi-Day!

The Math Kangaroo Camp is over, and I have to say that it was an absolutely amazing March Break week! The weather prepared a surprise for us on Wednesday – 10 cm of snow in just several hours, just when all of us thought that the spring is on its way.


Then on Thursday the temperatures dropped drastically, but the Math Academy students braved the icy wind and went on a mini Filed Trip to the Fields Institute.

Friday – Pi-Day! That is a great rhyme, and certainly a great way to end the March Break week!

Congratulations to all of the camp participants and instructors! Can’t wait till the Summer Math Kangaroo Camp already!

Math, Outreach

Math Kangaroo Campers get antiquated with Platonic solids

Math Kangaroo Campers were making platonic solids this morning. They did a great job! See the pic at

Lifestyle, Reviews: books and art events

Collected Curiosities: Darwin, Banksy, Tstar Nicholas II, etc

 Darwin said that men endowed with mathematical talent “seem to have an extra sense” (Lecture at the Fields Institute)
Banksy trouble:
According to a group of my friends I was the last person (if not on the entire Earth, than in North America:)) who did not know the name of a graffiti artist Banksy. When they told me that he is famous for hiding his identity I asked why he does that and if anyone asks him to reveal his identity.  Asking that was a big mistake.  Not only my friends got upset, but I also did not get the answer to my question.  If there is anyone else who did not know about Banksy, here is his website
Tango was brought to Paris in the 1910’s by rich Argentinian young men who toured Europe and actively participated in Paris’ night life. Soon tango became so popular that there were tango lectures, tea parties, exhibitions, etc. (Tango! : the dance, the song, the story by Collier)
Stravinsky wrote the first act of “Petrushka” ballet in an attic of a small house near a hospital where his wife was placed before the birth of their son. (Stravinsky by B. Yarustovsky)
Russian tsar Nicolas II likely was the first monarch who saw tango being danced. He even liked it! (Tango! : the dance, the song, the story by Collier)
Apparently soap is the most recommended souvenir to buy in Marselles, France. (internet)
Robert Hooke convinced his contemporaries that ‘minute bodies’ (very small organisms and very small things in general) are capable of having complex structure.  In his book Micrographia (1665) he illustrated that a flies have 360 degree field of vision as well as many other intricacies of small organisms and plants. His work was especially impressive because before the seventeenth century smallness was considered an obstacle to having a complex structure. (Micrographia by Robert Hooke)
Grad School, Research

“You study math and what…???” – How math and history majors merged into one

As a student of the Concurrent Teacher Education Program I knew that eventually I will need to have two teachable subjects. Despite of all difficulties I really enjoyed my math classes and I did not even think of studying anything else. By the end of the second year I had a lot of math courses under my belt but my academic adviser kept reminding me that I need to choose the second teachable. Since I was interested in history before it seemed like a natural choice. I chose to complete a double major (Major of Mathematics and Major of History). I did not choose to complete the specialist because it contained many computer science courses and computer science was not my primary interest at that time.

Having such a combination of majors made me the “laugh of the town” among my friends for some time but I was confident in my choices. Turned out that this combination of academic interests was an asset for me while applying to the History of Science graduate program later.

first posted at

Math, Outreach

Freshmen, this one is dedicated to you :)

If you happen to be going into your first year of university, I have some pointers to give you here (

first-week-of-the-first-year-of-university over here (

more on specific math classes here (

Let me know if that was helpful :):):)

Math, Outreach

Wikipedia: teacher`s enemy or a friend?

Much of Wikipedia's appeal lies in the way it creates a community.

One of my high school teachers used to say that “Wikipedia is an enemy of research”. I have heard similar phrases throughout my university career, at OISE and at my teaching practicums. All those teachers were making valid points. First of all, Wikipedia is too easily editable. Many articles (especially historical or political ones) are biased or inaccurate. Moreover, we never know who the author of the article is and who the editors are, hence, we cannot be sure that they are professionals. The ready availability of Wikipedia articles might give the students a false idea of what research is, leading them to think that in order to understand a subject one just needs to click on several links. Over-relying on Wikipedia promotes poor time management skills because many students use it to cram before their tests, so it is understandable why many teachers would encourage their students to opt out of using Wikipedia altogether. Such an aggressive reaction always surprised me. I can certainly see how the overuse of Wikipedia can negatively impact students’ research skills and how inaccurate information may lead them astray but as teachers we need to face reality. As much as we want our students to consult reliable sources, they tend to consult Wikipedia when faced with anything unfamiliar.

I was reviewing the topics that would be presented at the CMS camp and I was shocked by their level of difficulty. I have taught a gifted math class before but the enhanced curriculum never covered game theory, advanced combinatorics or Diophantine equations.  I thought it would be interesting to see what Wikipedia had to say about them (since the students probably looked all of them up already). I was pleasantly surprised. Most topics were covered in great detail and I did not spot any inaccuracies. Moreover, the descriptions contained links to interesting mathematical facts and theorems that could lead the students into interdisciplinary ways of thinking. For instance, after typing the word “Triangle” in Wikipedia search box I was expecting to see a one-screen description with a picture of a triangle. Wikipedia went above and beyond my expectations listing all interesting facts about triangles, related theorems and formulas, historical notes and more. There were at least 10 different formulas for finding the area of a triangle! (As a teacher I was lucky to meet students who knew one formula (A = ½(bh) ) and I was extra lucky if that student could explain why the formula is working.) There were other links to applications of mathematical concepts and numerous highlighted keywords linked to the relevant articles. Each page contained detailed diagrams, sometimes even the interactive ones. Many links made me regret that I did not think of consulting Wikipedia before preparing some of my lesson plans.

For me it is always important to motivate students to explore math in their own way and at their own pace. Wikipedia is a useful tool to get the student started on a topic. The first paragraph of a typical Wikipedia page is a concise summary that allows the student to quickly see if they are interested in the presented material. For instance, if a student heard an unfamiliar term he or she can quickly look it up and get a rough idea of what branch of math it belongs to, etc. Of course as teachers we need to be able to explain to the students which sources are suitable for effective research and which are not, but this part comes later, when the initial interest in a topic is present already. Wikipedia is just one of the numerous objects in our lives which have their designated uses but can be dangerous when misused. For instance, we never hear anyone calling a kitchen knife an enemy of human fingers. Wikipedia can be turned into teachers’ helper as well if the teachers will clearly define its role for the students. After all the phrase “Do NOT use Wikipedia” may cause more students to use it simply to ‘rebel’.

original at

image from