Tag Archives: mathematics

Mishkin Berteig


Breaking news: I did better than I expected! I thought I would get somewhere between 70 and 80. Sweet!!! I’m so happy!

Sabbatical Day 59 – Work and Work and School

Well, I apologize for the long time without posting.  Suffice it to say that I’ve had a pretty crazy couple weeks.  There’s been some work stuff and other work stuff, and some school stuff.  Here we go:

Work Stuff 1 – There have been some interesting challenges at work with culture.  It’s inevitable, I suppose, with being on sabbatical.  Me leaving has been a huge stress on the team in so many ways, but in particular, there’s been a great deal of adjustment in team dynamics.  I’ve had several tough conversations with people really concerned about what’s going on.  The dynamics will heal, but the stress is very very real.

Work Stuff 2 – Not connected to the earlier bit of work stuff, we had one of our senior employees ask for a change in role… and it’s a good thing… but it left us with no one to take care of marketing and content.  So, after consultation with my business partners Melanie and Travis, and in consultation with my wife, I have decided to volunteer to temporarily take on that role, part-time, until we can find a suitable person to do it full-time.  That will probably not be until the new year.  So, I’ll put in some extra hours in the afternoons.  I’m actually quite excited about the temporary return to the work I did early in the life of the business.

What will it mean in practical terms?  Well, I’ll be using some techniques from the Kanban method to act as a facilitator for the delivery of the marketing and content service.  I’ll get help from the rest of the team, of course, in both ideas about marketing and with people actually doing the work of marketing.  And I’ll be helping to evolve policies about how the work gets prioritized, chosen, and delivered.  It’s back to basics since I won’t have capacity for anything really sophisticated.

The one big change is that based on the advice and consultation with one of our external advisors, we are putting in place a new metric for our marketing efforts that will drive our strategy and activities.  I’m always wary of over-measuring, and of using metrics without extreme care.  Therefore, even the use of metrics is an experiment to me.  I will be monitoring how it affects the culture of our organization.

I’m also concerned about “coming back” during my sabbatical, no matter how limited.  That said, I also take personal responsibility for the health of the business.  There is a need, and since I have the flexibility to support it, I can’t do anything but rise to it.  Of course, there are lots of confidential details about the operation of the business that I’m not sharing here, but suffice it to say that I hope I’m exercising wisdom and judgement in doing this.

School Stuff – I had my first midterm exam last Thursday in Mathematics 3020 – Introduction to Abstract Algebra.  It was my first exam in over 23 years.  I’ve shared before that this class is pretty hard.  I studied somewhere between 15 and 20 hours in preparation for the exam in addition to the regular homework assigned for the class.  That’s more than I’ve studied for any exam ever in my life.  Honestly, I wish I had studied more.  In particular, I wish that I had started studying a week earlier… during reading week!

But I studied hard, and I was super excited (nervous and enthusiastic).  The morning of, I hadn’t had as much sleep as I wanted, so I had a half-cup of coffee (that’s way more than I normally have!)  I got to the Western Campus quite early just to make sure.  I did a quick last minute-review of some notes.  And then wrote the exam.

It was fun!

In fact, by the end of the 2 hour exam, I was super-high on adrenaline and the joy of math. I could barely contain myself.  I actually cried from joy.  I know that’s probably hard to relate to: someone crying from joy doing a mathematics exam… but that’s how much I love this field.  It’s challenging, it’s beautiful, and it gives me a deep sense of peace and harmony, that the universe has a foundation created by the Ultimate Intelligence.

The exam itself?  Well, I hope I find out soon how I did.  I suspect I did better than I feared and worse than I hoped… probably between 70 and 80% based on what I completed and a fudge factor for stupid mistakes.  I ran out of time and probably would have been able to finish if I had another 30 minutes (or if I had studied more).  I also confused the concepts of “well-defined” and “homomorphism” for a time and had to erase and re-do a question when I realized my mistake.

Again, it was incredibly fun.  And now I know what I need to do to prepare for the final!

Sabbatical Day 13 – Apple Watch Series 4

Well, yesterday Apple announced the new Series 4 watch.  Two big disappointments for me: no ceramic version, and Canada won’t get the EKG feature (at least not in any specified time).  Darn it!  I was really hoping to get a new one, but I really don’t see the point of doing so without those two things.  I have the Series 2 ceramic Apple Watch, and I love it.  So I’ll wait some more and maybe start looking for another vendor for my next fashion/fitness/tech accessory.

Today I cycled to school again.  I love the exercise – and while I’m in better shape than I used to be, I’m still not in “good” shape for cycling.  It’s an 8.5km ride each way and it takes me about 30 minutes.  Lots of hills.  There’s a segment on city streets.  This morning I left at the same time as Verity so that we could travel together for that segment.  Then there’s a bunch of walking/cycle paths along the Thames river valley.  It’s a lovely start to the morning.  The only thing is that I get _really_ sweaty!!  After I cycled home, I jumped in the pool – without looking at the temperature – and it was freezing!!!  I could only do 6 lengths before I had to get out because of the cold.  I’m not sure of the temperature, but I’m guessing it was somewhere between 15 C and 18 C.  Not dangerous, but super uncomfortable!

One of my in-progress projects is to help Haifa with her driving and preparing for her road test. Today we went out for about half an hour to practice parallel parking and three point turns.  She made great progress, but I started getting super tired.  I think I ate something that didn’t agree with me and so we ended a bit sooner than I expected.  Then I took a 4 hour nap!  I’m likely to be up late tonight.  Anyway, I suspect that my dad’s garlic allergy is affecting me.  I have to try avoiding garlic to see if that is the case.

Tonight I’m doing my first official homework assignment for school.  It’s a sheet of six questions adapted from the textbook for Math 2155.  Here are a couple example questions:

Rewrite the following English statements as logical statements. (a) John and Bill are both telling the truth or neither of them is.

Make truth tables for the following formulas: (a) ¬[P∧(Q∨¬P)]

Honestly, it feels a bit like busy-work for me.  My computer science degree covered all this stuff in depth, and even worse, I got into this stuff as a kid somewhere around grade 7 or 8 so I’ve been doing logic and truth tables like, forever!  Anyway, I’ll get it done quickly and hopefully I won’t make any stupid errors.  That’s my most common problem with math.  I’ll let all y’all know when I get my grades.  Here’s hoping for 100% on my first assignment…  Incidentally, Verity is struggling with the same problem with her math in grade 9 – it’s super easy, boring review.  I feel for her.


Sabbatical Day 6 – First Day of Class

I attended my first day of university classes since 1995!  I cycled to class.  It took about 35 minutes which was 5 minutes longer than I planned.  I showed up about 10 minutes to start and there weren’t too many spots left so I ended up at the back of the class in “Mathematics 3020 Introduction to Abstract Algebra”.  I intend to change that for next class on Tuesday – hopefully I will be able to sit in the 2nd or 3rd row instead of the 5th.  I am the “old guy” in the room.  Everyone looks very young.  There was a guy sitting almost right in front of me who answered a lot of the questions.  I answered one, but otherwise shut up.  I took seven pages of notes.  So far, it is stuff that I already know.  I’m trying to decide if I work ahead in the textbook or if I just follow along.  The textbook is pretty well-written (I’ve read up to where we ended the class today) so I could really leap ahead without too much trouble.  I cycled back home immediately after class, ate a terrible lunch, and then fell asleep for four hours.  My day hasn’t had much else to it.

Tonight I’ll do the last little bits of my leadership book:

  • Write acknowledgements
  • Get an ISBN
  • Start the project on lulu.com

I’m expecting I will get final edits tomorrow and be able to finish the export for lulu.com at that time… and then it will be published!  I’ll have completed one of the projects on my board.

Sabbatical Countdown T-30 Days

I recently finished catching myself up on my basic differential and integral calculus.  I actually think I understand it better now than I did when I took calculus in high school and in university.  I may be fooling myself 🙂  I finished reading and doing many exercises in Quick Calculus 2nd Ed. and I can highly recommend it for anyone who wants to brush up on their calculus.  It’s fast-paced, focuses on core concepts and techniques, covers both theory and application, and does it all in a slim easy-to-consume volume.  Of course, it doesn’t have the depth of something like Stewart’s Calculus which is a common textbook, and I’m peeking into that too, but it satisfies the requirements of getting back up to speed after a time away.  I’m also continuing to use Khan Academy for further practice and depth, and will continue to do so probably throughout at least my first term back in school.

I’m also just at the start of brushing up on linear algebra, which I have very little interest in.  I kinda have to force myself.  I’ve got an old textbook called Linear Algebra with Applications.  I also downloaded two linear algebra texts onto my iPhone, and I’ve still got a bunch of Khan Academy units to do… but I have to push myself harder because of my lack of interest.  It’s not that I don’t see the applications… I do… it’s just that linear algebra has so many numbers!!!

That’s not a contradiction: I love mathematics, but I’m not a big fan of numerical manipulation (calculation).  The difference is that mathematics is about seeing relationships, structures and concepts whereas calculation is simply about getting formulaic answers from numerical data.  Calculation is boring to me (usually) because it doesn’t represent an intellectual challenge.  As a result, I hate doing bookkeeping.  On the other hand, I love designing complicated spreadsheets.  And, back to mathematics, I like doing proofs and other activities that represent problem-solving and discovery.  I love learning about cool relationships between mathematical structures and concepts.  And the numbers don’t matter except incidentally.

Preparing for School

I’m working on getting ready for school. I will be taking two classes starting in September: Mathematics 2155 “Mathematical Structures” and Mathematics 3020 “Introduction to Abstract Algebra”. Both of these cover material I am broadly familiar with, but… My calculus and my linear algebra are very rusty. So, I’ve been using Khan Academy and a couple of old textbooks to try to catch up enough so that I’m not out of my depth when I start. I’m comfortable with basic differential calculus now, but I do need to memorize a few more standard derivatives. I’ve just started on integral calculus and linear algebra.

I’m really tempted to also start a few more “projects”… I’ve got a hankering to study French (again), do some electronics fiddling, and even try my hand at some sculpture (inspired by our recent family trip to Paris).  But, I need to be realistic about my capacity.  I’ve still got lots of work to do before my sabbatical starts including training, client consultations, and handing off more things to my colleagues.  Then, when September comes, I’m going to have to make sure that I’m completely focused on family and school.  After that has settled in, then maybe I can bring on another project or two 🙂

Sabbatical Countdown T-53 Days

I have been approved for a sabbatical by my business partners (Melanie and Travis) and I have most of the needed things in place in our business (www.berteig.com) so that it will thrive while I am away, and I begin a full year sabbatical starting September 4th, 2018!

This has been a long time coming.  I started thinking about a sabbatical at least 6 years ago.  I’ve been over-stressed, over-worked, and going through a lot of both business and personal challenges.  With Melanie, I started the business in 2004.  We had a number of up and down cycles in the business with the latest down cycle ending in 2014.  It’s been solid growth and maturation of the business since then.  We have grown from 5 employees (including partners) to our current 15 employees.  We have established a solid reputation in public training, private training and coaching/consulting work. Our employees know how to run things.

I have also been considering going back to school for many years.  Both my father and my mother went to get Masters degrees in their late 30’s.  I’m in my 40’s and I’m ready to do the same.  I’ve considered an MBA or EMBA, but they don’t appeal to me.  I’ve considered other possibilities related to business such as leadership.  But really what I want to do is Mathematics.  Several months ago, in anticipation of the possibility of a sabbatical, I applied to University of Western Ontario (“Western”) and after a bit of back and forth on my first degree, I was accepted.  Just in the past  two weeks, I have received confirmation that many of my mathematics courses from my first degree will be allowed as alternatives to the normal prerequisites.  So, starting in September, I will be taking two math courses.  One is a second year course and the other is a third year course.  I’m super excited.

I also, and more importantly, will be spending a lot of time with my family.  I’ve been so busy with work that my four kids know me mostly as a worker.  Travelling, late nights in the home office, weekend interruptions, etc.  The cost of running a small, struggling business.  My kids, being that they are human, have various challenges they are facing and I hope to be more involved in helping them face their challenges and overcome them.  Better late than never.  I’m not the dad that I thought I would be (i’ll probably expand on that more later).

So, as I count down towards my sabbatical, I will start documenting here my interests and my passions and my experiences.  Stay tuned for mathematics, family, philosophy, religion, fiction, and all the other things that make up my life as I experience much less work for a year.