Interactive Online Tutoring Services

December 11, 2022


Filed under: introduction,Tutoring — Rob burchett @ 4:12 am

Hi, my name is Rob Burchett. I’ve been tutoring Math and Physics for over ten years in York Region and Toronto. I can tutor in-person or online. You can find some information in regards to my tutoring at the left under categories: Tutoring.

I apologize for the current construction going on at my website, soon I hope to have it back to normal. I have been tutoring continuously and have not had a long break. My website was attacked by malware and 5 years of data was lost. I’m working to put some of it back at the current time.

I’ve had success tutoring many students over the years. I also work on creating my own math some of which I have posted to this blog under the category, Concept sharing, math concept sharing and also under the category, Mathematics.

This is work of a basic nature, you do not need a degree from University to understand it. Incredibly, I hope to one day change grade 11 Mathematics, to make it much better!

December 10, 2022

Where I’m currently working

Filed under: Tutoring — Rob burchett @ 9:43 am

I am working with my own students, tutoring grade 10 and 11 Math in person and online. I also tutor online with Brainiacs Online, online tutoring grade 10, 11 Math and grade 11 Physics. I am looking for new students in grade 9,10 or 11 Math and Physics and can be reached by phone or text message at 647-218-1407 or email:

November 24, 2016

some characters

Filed under: Art,doodles — Rob @ 4:10 pm


September 30, 2016

Angela at Second Cup

Filed under: Art,portraits — Rob @ 6:12 am


February 29, 2016

Degree from the University of Toronto

I thought I would post my degree from the University of Toronto.

January 7, 2015

Adult education and Staff Training certification

August 21, 2009

Oxford Learning letter of recommendation

Letter of recomendation from Oxford

January 22, 2023

Division by zero

Filed under: division by zero,Mathematics — Rob burchett @ 5:07 am

With the advent of concept sharing of a point we may have a definition of division by zero.

A simpler classification of surfaces

Filed under: a simpler classification of surfaces — Rob burchett @ 5:05 am

It seems we can start differently and have a simpler classification of surfaces both 2 and 3 dimensional.

January 20, 2023

The explanation

Filed under: knots,Mathematics,the knottedness and chirality of the trefoil — Rob burchett @ 7:05 am

The explanation:

  1. Crossings in R^3 or S^3 (positive space)
  2. Label 1+,1-,ect. The locations of D-joinings/crossings (mixed space)
  3. Place a, b at each D.
  4. Move to negative space: move crossing now a sharing as we are capable of having 2 parts or more at a vertex with a and b always moving along.

1+,1-,ect. Are the specific locations in R^3 where we put the other concept sharing diagram back together.

But in the moving diagram they have some freedom. They can travel along as they are labels, reachable through moves of the diagram (that is moves are reversible) or they can stop at a specific pair of locations and the a, b pairs move on forward. This is still reversible as I can get back to this D, as I can reverse from forward motion. At the end, after I go all the way back I come back to the same location.

So 1+ and 1- label the crossing 1, where the original locations can be traced back from. I am placing the labels on specific locations. I mean that this is where the crossing is so that I can trace back to the original location which matches moves in this space then are fully reversible and take full advantage of the new freedoms. Then all these diagrams are equivalent and complete as long as we don’t cut the diagram or change the order of locations.

Then R1,R2,R3, isotopy have their equivalents as well. I have rotation of the locations, creation of labels, joinings, movements of joinings and labels through sharings. And that’s all (complete).

Let there be another diagram D(2) in R^3 and we wish to compare this to the original diagram. Move it to mixed space and then to negative space. Concept share it and one part of it moves off. If we can make a congruency between this and the other diagram in negative space then the two diagrams in positive space are also congruent.

So we need to look for a match of the labels, joinings when we simplify the diagrams.

If they are the same, then the information should be contained in one diagram. That is, movements of one diagram should be able to produce the second one. So we need to look at one diagram to see if we can produce another(using all moves available)

Let’s look at T. To cut down a lot of the moves, let’s apply a simplifying method.

Now I only need to apply S1,S2,S3 and isotopy(2) and I can obtain any diagram of T. Then reform the diagram to go back to R^3.

But the only new diagrams I can obtain will be through the application of the new moves to the T-invariant. That is all possible moves of the invariant. None yield the unknot or any achirality.

The new moves are rotation (which isn’t usually considered) and movement of labels and joinings through sharings. 

January 12, 2023

Trefoil invariant

Filed under: knots,Mathematics,supplemental on knots — Rob burchett @ 3:59 pm

So starting with the standard diagram for the Trefoil knot. I place this in the new space and I have the sharings D1,D2,D3. These have the associated moving parts a1,b1,a2,b2,a3,b3. Then I move the outer loops inward (green and red) forming the sharings Q1,Q2,Q3,Q4,Q5,Q6. These have the associated moving labels r1,s1,r2,s2,r3,s3. Then I form the joinings (a1(r1), (b2(s2), (a3(r3), (b1(s1), (a3(r2), (b3(s3) (all red). Now this can be further decomposed to eventually form the “circle”.

January 11, 2023

The third move

Filed under: knots,Mathematics,supplemental on knots — Rob burchett @ 9:18 am

Showing the third move. After reduction, only Q-types are involved.

January 5, 2023

Showing necessity to keep orientation of joining

Filed under: knots,Mathematics,supplemental on knots — Rob burchett @ 7:08 pm

Here I show why we must keep to the same orientation when we reform a joining after we undo it in negative space.

January 4, 2023


Filed under: abstract art,Art — Rob burchett @ 4:50 am

January 2, 2023

Perspective drawing of my parent’s house

Filed under: Art,perspective drawing — Rob burchett @ 7:04 am

Drawing of hands

Filed under: anatomical art — Rob burchett @ 6:59 am

This is a pen and ink of my hands.

General philosophy

Filed under: general philosophy,Philosophy — Rob burchett @ 6:24 am

It is important to understand that we are all imperfect, so not to judge anyone, as has been written. That is the reason we are all equal. That is also the reason we all need each other so much.

Therefore use what you have to take care of yourself and beyond this, to help others. For they in turn will help you, wanting your further help. It is only logical.

We are not beings of pure energy but have physical, social, mental, vocational…many needs which must be taken care of.

Living well, day by day will allow you to climb higher, slowly, to greater levels of awareness.

It has been written that it is possible in one day, to gain the whole world but what does it profit you, if you lose yourself?

Try not to waste anything. You do not know how long you have with what you have. Remember what has been written that with the lord, one day is as a thousand years and a thousand years is as one day.

Time is not strictly linear. In the sense that you can use the power of novelty to get you over some roadblocks which might be in your path. Just working hard might not do it quickly enough.

Be careful what you say. But also realize there is also jesting, as long as you state you are jesting. Also it is alright to change your mind.

Trust and rapport take time to build. Keep steady and you can do this well. As is said, do for others what you want them to do for you.

You’ve got to move between a lot of different areas. Maybe more than you realize. Be careful, try not to neglect anything. Somethings you may have not been near in a long time. Giving things a rest is useful-but not for too long.

Don’t let your imagination block you or your reasoning bog you down.

Watch the passage of time. Keep up with everything. Remember, you might not have that much more time in this set of systems.

What you are accusing others of, you may be guilty of yourself. Remember what is written, take the log out of your own eye before trying to remove the speck that’s in your brother’s eye.

Next Page »

Contact us today to get started