Discussion thread 🔥

[bestsauce]

Note: this is a discussion thread only about the way we set things up on Github. Discussions on the book are for their relevant threads, as explained in README.

• Common milestones?

• All exercises or divide them into necessary+optional ones?

• Dividing exercises issues into each section instead of each chapter?

• Working all on a single document for notes?

Testing $\LaTeX$: $\displaystyle\int_0^1 \dfrac{x^2}{x+1}\ \mathrm{d}x$.

$$\boxed{\ \oint{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = - \overset{\color{white}{.}}{\frac{\mathrm{d}}{\mathrm{d}t}} \underset{\color{white}{.}}{\iint\Sigma} \mathbf{B} \cdot \mathrm{d}\mathbf{S}\ }$$

[doshgillio]

Hey there, interested in joining in. What text are you using and is it available online anywhere?

[BadiGard]

I'm interested in joining too :)

[MaxisJaisi]

Count me in!

[bestsauce]

@doshgillio @BadiGard @MaxisJaisi Sent you all an invitation (visit https://github.com/worstsauce to accept the invitation.)

Also is anyone having trouble configuring MathJax with Github?

@doshgillio We'll hopefully work on Sheldon Axler's Linear Algebra Done Right

[doshgillio]

@bestsauce lovely thank you, I'll source a copy. Would be interesting to know what level people are coming in from I'm a 3rd year maths undergrad who wants to better my understanding of a subject I have previously studied.

[bestsauce]

@BadiGard @doshgillio @MaxisJaisi Great! It seems now everyone accepted the invitation, now you need to:

1] Open two issues: https://github.com/worstsauce/study/issues/new both titled "Chapter 1". Label one of them with the Notes label and with the body:

Chapter 1: **Vector Spaces** 

- [ ] $\mathbf{R}^n$ and $\mathbf{C}^n$
- [ ] Definition of Vector Space
- [ ] Subspaces

and the other with the Exercises label and with content:

Chapter 1: **Vector Spaces**

**1.A**

- [ ] Exercise 1
- [ ] Exercise 2
- [ ] Exercise 3
- [ ] Exercise 4
- [ ] Exercise 5
- [ ] Exercise 6
- [ ] Exercise 7
- [ ] Exercise 8
- [ ] Exercise 9
- [ ] Exercise 10
- [ ] Exercise 11
- [ ] Exercise 12
- [ ] Exercise 13
- [ ] Exercise 14
- [ ] Exercise 15
- [ ] Exercise 16

**1.B**

- [ ] Exercise 1
- [ ] Exercise 2
- [ ] Exercise 3
- [ ] Exercise 4
- [ ] Exercise 5
- [ ] Exercise 6

**1.C**

- [ ] Exercise 1
- [ ] Exercise 2
- [ ] Exercise 3
- [ ] Exercise 4
- [ ] Exercise 5
- [ ] Exercise 6
- [ ] Exercise 7
- [ ] Exercise 8
- [ ] Exercise 9
- [ ] Exercise 10
- [ ] Exercise 11
- [ ] Exercise 12
- [ ] Exercise 13
- [ ] Exercise 14
- [ ] Exercise 15
- [ ] Exercise 16
- [ ] Exercise 17
- [ ] Exercise 18
- [ ] Exercise 19
- [ ] Exercise 20
- [ ] Exercise 21
- [ ] Exercise 22
- [ ] Exercise 23
- [ ] Exercise 24

(feel free to modify it to remove certain exercises if you want, it's not necessary here to solve all of them)

To set labels:

After making that we can discuss about the time schedule that you prefer (one chapter per week?) so that we can add milestones that fit here.

@doshgillio I'm a self-studier with no former background on linear algebra, so it's the first time I will study it, what about others? :)

[MaxisJaisi]

Dear @bestsauce , I've created my Notes and Exercises issues. Sorry for the delay; there were a few wrinkles on my part to sort out.

Perhaps we could ask knowledgeable people on Reddit about our MathJax loading problem... ?

I too have virtually no background in LA besides knowing a few things about matrices and linear maps.

[MaxisJaisi]

Test: $|a+b| \leq |a| + |b|$ Test II: $x \in \mathbf{R} \implies x^2 \geq 0$

[bestsauce]

@MaxisJaisi

Perhaps we could ask knowledgeable people on Reddit about our MathJax loading problem... ?

You're having problem with it? First what is your browser?

[MaxisJaisi]

@bestsauce Firefox. The same bug you described. MathJax won't load unless I refresh the page.

[bestsauce]

@MaxisJaisi Well that's more of a feature that is missing in the script rather than a bug, the only workaround for this now would be to refresh the page or load them in a different tab each time. (I will try to search a bit on this to see if there could be a more useful workaround, perhaps the script would reload itself whenever it hits a different url)

[MaxisJaisi]

@bestsauce Also, I'm fairly new to Github. I can see that you've assigned 6 & 7 to me via email, but I can't seem to find the exact notification here; it only says that you've assigned something.

[MaxisJaisi]

@bestsauce I see. Noted with thanks.

[bestsauce]

@MaxisJaisi Oh, also, you can create your own milestone here: https://github.com/worstsauce/study/milestones

Though it would be better to wait for others so that we can synchronize our work better (with a one chapter per week schedule ideally).

---

Yes, I've assigned these two issues you made because you forgot to assign them to yourself :) https://github.com/worstsauce/study/issues/7 and https://github.com/worstsauce/study/issues/6

[MaxisJaisi]

Ah, I see. :) By the way, where do you live, if you don't mind me asking? Our timezone might differ. I'm from Malaysia.

[bestsauce]

@MaxisJaisi Our timezones might differ but what's nice about this method is that we don't need to have our clocks synchronized. I'm from the UK so UTC+1.

[bestsauce]

I updated the instructions for using MathJax with Github, Chrome users can simply just install this add-on. Also this add-on doesn't have the problem outlined earlier (about the need to refresh pages).

[MaxisJaisi]

@bestsauce Just to clarify, solutions to exercises will be posted on each Exercise issue right? For example, if I want to do problems 1-10 in chap 1, my "written solutions" will be posted as comments.

[bestsauce]

@MaxisJaisi It's not necessary that you write all of your solutions there. Just put the ones that you're not sure about whether they're correct and then put the question label so that we can check them (and if you want some hint on an exercise for example put the help needed label along with which exact exercise you want help with). Is it clear for you now? :)

[MaxisJaisi]

Curly braces {} don't seem to work on MathJax. \{\} doesn't work, or am I missing something silly?

[bestsauce]

@MaxisJaisi Indeed, let me see if there's a solution to that.

[bestsauce]

@MaxisJaisi Found out one solution, replace \ with \, for example: $\{\}$.

Not the best solution but it works, if you happen to find out a better one please let me know.

[bestsauce]

@MaxisJaisi Found out a better solution: Use two \ instead of one, and it should work: $\\{\\}$ renders as: $\{\}$.

[MaxisJaisi]

@bestsauce Alternative one could just do away with MathJax when it comes to braces.

$\ \mathbf{R}$ $\cup$ {$\infty$} $ \cup$ {$-\infty$}

Doesn't look too bad, does it? (= Anyway $\\{\\}$is the best workaround, I believe. Thanks!

[bestsauce]

@MaxisJaisi Not too bad but then you have to write many $ to get it right, writing \ is faster.

[MaxisJaisi]

@bestsauce New chapter, today or tomorrow?

[bestsauce]

@MaxisJaisi Tomorrow :) Will finish what's left on my notes and the rest of the exercises today. In the meantime we may have someone who would want to join the group.

[MaxisJaisi]

By the way, I transferred part of my _LaTeX_ed notes I wrote down while reading the book onto the Notes section. They are quite brief (I didn't include the stock of examples I collected), require stylistic improvements, and they might contain mistakes. Certain proofs may be clumsy, so suggestions for improvement are appreciated.

[keyehzy]

I want to hope in this study group. I am still about to start chapter 1 but don't want to slow you down.

[bestsauce]

@masamu I sent you an invitation, go to https://github.com/worstsauce to accept it :smile: Once done, follow the steps here https://github.com/worstsauce/study/issues/1#issuecomment-294166204

By the way, did you get MathJax to work in Github?

[bestsauce]

@MaxisJaisi Thanks for that! Do you think it would be better to have a specific folder in the repository with your notes and exercises (so as to keep the issues pages distinct)? (Here's an example: https://github.com/worstsauce/study/blob/master/resources/Chapter%201/Notes-Maxis.md )

[keyehzy]

@bestsauce Yes, I'm set up and ready to go! Thanks.

[bestsauce]

@masamu Great! I already made two issue threads for you so that you can track your progress (you can change the one on exercises by deleting the exercises that you do not plan to make if you want)

https://github.com/worstsauce/study/issues/10 https://github.com/worstsauce/study/issues/9

If you need any help with regards to exercises or you have a question regarding a theorem or an exercise you may add the "question" or "help needed" labels in the respective thread with a comment detailing your issue and we'd be able to help.

Also is the May 7 milestone ok for you?

[MaxisJaisi]

@bestsauce Yes, a separate folder would be good; my issues look quite cluttered with the notes and exercises thrown in.

[bestsauce]

@MaxisJaisi Ok, I'll move them there.

[MaxisJaisi]

Where should I put my notes for Chapter 2?

[bestsauce]

@MaxisJaisi I've created https://github.com/worstsauce/study/blob/master/resources/Chapter%202/Notes-Maxis.md for you, just edit it and save

[MaxisJaisi]

What should we do about @masamu ? He seems to have disappeared...

[bestsauce]

@MaxisJaisi A bit unfortunate that he didn't proceed, I'll leave his two issues open for a while...

[MaxisJaisi]

@bestsauce When typing out a solution to a problem, the equation

$T(x_1, \dots, x_m) = T(x_1(1,0,\dots,0)+x_2(0,1,\dots,0)+\dots+x_m(0,0,\dots,1)) = T(x_1(1,0,\dots,0))+T(x_2(1,0,\dots,0))+\dots+T(x_m(0,0,\dots,1)) = x_1 T(1,0,\dots,0)+x_2 T(0,1,\dots,0)+\dots+x_m T(0,0,\dots,1)$

overflows to the right. Any idea on how to fix this?

[MaxisJaisi]

Also, how do you write piecewise functions here?

[bestsauce]

@MaxisJaisi Only solution it seems would be to use \begin{align} ... \end{align}

$\begin{align}
T(x_1, \dots, x_m) & = T(x_1(1,0,\dots,0)+x_2(0,1,\dots,0)+\dots+x_m(0,0,\dots,1)) \\\\
& = T(x_1(1,0,\dots,0))+T(x_2(1,0,\dots,0))+\dots+T(x_m(0,0,\dots,1)) \\\\
& = x_1 T(1,0,\dots,0)+x_2 T(0,1,\dots,0)+\dots+x_m T(0,0,\dots,1) \\\\
\end{align}$

Result

$\begin{align} T(x_1, \dots, x_m) & = T(x_1(1,0,\dots,0)+x_2(0,1,\dots,0)+\dots+x_m(0,0,\dots,1)) \\ & = T(x_1(1,0,\dots,0))+T(x_2(1,0,\dots,0))+\dots+T(x_m(0,0,\dots,1)) \\ & = x_1 T(1,0,\dots,0)+x_2 T(0,1,\dots,0)+\dots+x_m T(0,0,\dots,1) \\ \end{align}$

---

Also, how do you write piecewise functions here?

\begin{cases}
x^2, & x\in\mathbf Q \\\\
x, & x\notin\mathbb Q
\end{cases}

Result

$$\begin{cases} x^2, & x\in\mathbf Q \\ x, & x\notin\mathbb Q \end{cases}$$

[MaxisJaisi]

@bestsauce Thanks. But what if I want to write $f(x)$ exactly to the left of the piecewise requirement?

[MaxisJaisi]

@bestsauce Nevermind, got it.

[bestsauce]

@MaxisJaisi Tried to transform your notes into a nice website but after a lot of trying it seemed to be not worth the effort,

I take my notes by hand, but if you want you can just upload the .tex files and I'll edit them which should be more efficient than transforming them into markdown.

[MaxisJaisi]

@bestsauce Sorry for the silence. I was caught up with a lot of things, and took a break (was on a holiday with my family throughout the past week). I'll send you the TeX files once I'm done with Chapter 3.

By the way, we seem to have slowed down quite a bit, and it's not clear if the whole project is still going forward. I've learned a lot from this, and feel that it's a shame if this group dies out. I suppose we could discuss on reorienting ourselves a bit? Chapter 3 is a big chapter, and it's very important. I think completing Chap 3 would make studying the subsequent chapters much smoother, so it's crucial that we finish it.

[bestsauce]

@MaxisJaisi

By the way, we seem to have slowed down quite a bit, and it's not clear if the whole project is still going forward. I've learned a lot from this, and feel that it's a shame if this group dies out. I suppose we could discuss on reorienting ourselves a bit? Chapter 3 is a big chapter, and it's very important. I think completing Chap 3 would make studying the subsequent chapters much smoother, so it's crucial that we finish it.

Yeah sorry for that, I was pretty busy these weeks and didn't have much free time. How about we take a one week pause (instead of constantly pushing the milestone) and then be more strict with the schedule (I'll have much more free time after that so I can dedicate the necessary time)?

And yes, I think after finishing Chapter 3 we can move on a lot faster.

[MaxisJaisi]

@bestsauce That sounds good to me.

[bestsauce]

@MaxisJaisi Ok, I updated the milestone now!

[celiopassos]

I'm interesting in participating. I have been using this site to check my answers, but some are either missing or proven differently. I look forward to post some of my solutions here and see if you guys can point out a mistake I could've possibly made.