Interactive Online Tutoring Services

September 27, 2020


Filed under: business improvements,Tutoring — Rob @ 4:28 pm

Due to the pandemic I am currently tutoring online only. I am charging $25-$35 an hour for math tutoring from grades 6-10. In over ten years of tutoring I have had great success.

September 23, 2017

Working in the fall term

Filed under: business improvements,Tutoring — Rob @ 7:58 am

I am currently working for Oxford Learning in north Richmond Hill. I tutor students in mathematics and physics up to and including the grade 12 level. I also teach privately one-on-one a student from Durham College in Mechanical Engineering Technology. Currently, I am still seeking other students.

August 12, 2017

new student from Wilfred Laurier

Filed under: student updates,Tutoring — Rob @ 8:02 pm

I am helping a new student from Wilfred Laurier University. She is taking an online course over the summer which is designed for her to go at her own pace.

June 15, 2017

New student

I have a new student through ‘ Tutor by Numbers’ he is in grade 12 and is trying to get into Durham College for Automotive Engineering. I have met with him 4 times and will likely be reviewing with him in the summer.

March 9, 2017

reference from the Learning Disabilities Association of York Region


March 3, 2017

working in the spring term

Filed under: business improvements,Tutoring — Rob @ 7:03 pm

I am working at the Prestige private school located in Richmond Hill. I am tutoring six groups of four students from grade levels 2 to 11 in math.

January 28, 2017

Tutor by Numbers

Filed under: business improvements,tutor by numbers — Rob @ 5:12 pm

I am starting a new branch of my business called “Tutor by Numbers”. I am seeking students from grade 4-11 who would be interested in meeting in-person in my local area of Markham/Vaughan. I am specifically looking for but I am not limiting myself to students with learning disabilities.

I am Currently having great success tutoring a student with a learning disability through the Learning Disabilities Association of York Region. He recently received a grade of 100% on two quizzes in math.

Anyone interested in this service can call me at 416-227-1657 or email me at

January 25, 2017

working in the winter term

Filed under: student updates,Tutoring — Rob @ 10:35 am

I am teaching two students, in person, at J.D.L. consulting in Richmond Hill. One student is in grade 9 and the other in grade 10. I also continue teaching a student in grade 8, through the learning disabilities association of York region.

November 15, 2016

working in the fall term

Filed under: student updates,Tutoring — Rob @ 9:32 pm

I am still working for JDL consulting in Richmond Hill. I am teaching grade 4 and 5 math. I still continue to tutor a grade 8 student through the learning disabilities association of York Region.

April 26, 2016

Student doing well

Filed under: student updates,Tutoring — Rob @ 6:12 pm

My new student in grade 7 mathematics is doing very well. He received a grade of 88% in algebra last week. Moving forward he is studying fractions.

April 13, 2016

New student

Filed under: business improvements,student updates,Tutoring — Rob @ 4:06 am

I have a new student that I started to tutor in math yesterday. I found him through the Learning Disabilities Association of York Region. He is in grade 7.

February 29, 2016

Degree from the University of Toronto

Filed under: Tutoring,university degree — Rob @ 1:51 pm

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

March 10, 2015

Continued success

Filed under: business improvements,student updates,Tutoring — Rob @ 5:52 am

I am having continued success tutoring grades 8 and 11 at the moment. My students’ grades have improved dramatically.

January 7, 2015

Adult education and Staff Training certification

February 14, 2010

Frequently Asked Questions

Filed under: frequently asked questions,Tutoring — Rob @ 3:36 pm

1. How effective is this tutoring?

A: I have been able to raise grades into the mid nineties

2. Do I have to buy a number of sessions?

A: You do not have to buy any set number of sessions. I can charge you after a set of five sessions or if you prefer, you may pay as you go.

3. What kind of equipment do I need?

A: A basic computer system, high speed internet. You can write to me using a mouse or type your questions to me using a chat window. I am using meeting software. If you have a writing tablet this will work well too.

4. How is payment made?

A :After a face-to-face meeting you can pay me cash as we go. I also accept cheques. You can pay by interact email money transfer as well. For online meetings I am using interact email money transfer.

5.Are you available on demand?

A: No. A specific time to meet is arranged.

August 21, 2009

Letter of recomendation from Oxford

May 4, 2021

Central ideas

Filed under: knots,Mathematics — Rob @ 7:55 pm

The main idea is simple. That two points can exist together and still be two points. Since points have no extent, this is possible. We have to have a new plane for this where we can take away the one point that already exists-where I want to put the two points together. For then there is no confusion, and I have two points there and not one. Then there must exist another level where I can take one point away and still have something there.

This can be what I call placement space. It is a space where a location may have another ‘location of a location’. Basically a location is mobile. Then two locations may share the same placement (location of location) and I call this a “sharing”. A special type of sharing may exist in the manipulation of diagrams which I call a “joining”.

I use the knottedness and chirality or achirality of knots to demonstrate the usefulness of these ideas.

March 1, 2021

Filed under: knots,Mathematics — Rob @ 8:24 pm

February 18, 2021

The achirality of 4(1)

Filed under: knots,Mathematics — Rob @ 4:01 pm

February 15, 2021

Filed under: knots,Mathematics — Rob @ 9:02 pm

February 13, 2021

Filed under: knots,Mathematics — Rob @ 4:27 pm

This note is showing the two final diagram reached after the Reidemeister moves in R^3. These diagrams also have to be equivalent in P^3. Then I can set up a congruency of locations between the two diagrams.

January 14, 2021

Filed under: knots,Mathematics — Rob @ 7:15 am

This post is describing the push move (named by Murasugi), which is an extra move in knots which doesn’t effect the knot. In R^3, this is seen as the curve being mapped to itself by a rotation of the curve upon itself. In P^3 we see this as a movement of joining pairs around the curve. The cyclic order of the joining pairs gives us the shape of the knot diagram.

January 8, 2021

Filed under: knots,Mathematics — Rob @ 3:39 pm

This page is showing the different moves possible in the two different spaces. The top space is R^3 and the bottom space is placement space (P^3). Placement space is described in the posts below. The idea that leads to placement space is described in the quick view, below.

There is a link between R^3 and P^3. Also in P^3 we can create a D-sharing- a type of crossing. In turns out in placement space there are two types of basic crossings. I’ve labelled these D and Q. These are shown in some detail in the diagrams below.

Applying moves S1,S2,S3 counterparts to the Reidemeister moves to take us from one diagram to the next. I use Reidemeister moves to go from one diagram to the next, but do not use these to prove knottedness or chirality.

These moves all involve Q-sharings only and I’ve drawn them above. In order that I only apply these moves to Q-sharings a transformation is applied to the trefoil. This transformation is described in the posts below. I’ve shown it in a diagram above.

Then these S1,S2,S3 have counterparts in the space R^3 above. This then leads us to a diagram with the same shape as the original, but with possibly an unknotted case or a mirror image case.

To rule these out we put back in the cyclic permutable set {a(1)r(1),b(2)s(2),a(3)r(3),b(1)s(1),a(2)b(2),b(3)s(3)} which was removed during the transformation in placement space. It might be possible to obtain a mirror image or an unknot because I am applying the moves generally.

That is I allow all possible paths by Reidemeister moves which lead back to the diagram with the same shape. It turns out I can only reform the original configuration, not the unknotted or mirror image case.

For future work I can say that the shape of the knot need not be one shape alone, also in larger knots such as the Perko pair, I can remove the D-sharings and put new D-sharings in, changing the writhe of the knot which is the number of positive crossings minus the number of negative crossings.

January 1, 2021

Filed under: an extension of calculus,Mathematics — Rob @ 5:49 pm

December 29, 2020

Quick view-abstract

Filed under: knots,Mathematics — Rob @ 9:29 pm

As a quick way to understand my starting point think of something which can be called two disjoint points (named by Kauffman), but not two points separated, but two points together. Then to have this I must first remove the notion of the single point, otherwise I would have both one and two points here. So some other structure is here. Then this is placement space. For a detailed explanation of this see the beginning of all the posts below.

What I’m trying to show is that in placement space P^3, I can move the joining pairs cyclicly and these can reform to make D-sharings. The joining pairs come from an original set of D-sharings. These two sets of D-sharings are related by a set of Reidemeister moves, in R^3 so these are equal knots.

Then for the Trefoil, I can start with the simple representition and show that there are no reformations that lead to the unknotted case and also do not lead to the mirror image, in the same shape, after any number of Reidemeister moves.

I also consider future work which could be done.

December 23, 2020

Clearer explantion for the Trefoil

Filed under: knots,Mathematics — Rob @ 11:23 am

This is showing a more clear exposition of the final conclusion for the trefoil, as well I show the way to finding a minimum diagram with a different shape than the original knot diagram.

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