• Log InLog In
  • Register
Liquid`
Team Liquid Liquipedia
EDT 09:44
CEST 15:44
KST 22:44
  • Home
  • Forum
  • Calendar
  • Streams
  • Liquipedia
  • Features
  • Store
  • EPT
  • TL+
  • StarCraft 2
  • Brood War
  • Smash
  • Heroes
  • Counter-Strike
  • Overwatch
  • Liquibet
  • Fantasy StarCraft
  • TLPD
  • StarCraft 2
  • Brood War
  • Blogs
Forum Sidebar
Events/Features
News
Featured News
Power Rank - Esports World Cup 202568RSL Season 1 - Final Week9[ASL19] Finals Recap: Standing Tall15HomeStory Cup 27 - Info & Preview18Classic wins Code S Season 2 (2025)16
Community News
Google Play ASL (Season 20) Announced7BSL Team Wars - Bonyth, Dewalt, Hawk & Sziky teams10Weekly Cups (July 14-20): Final Check-up0Esports World Cup 2025 - Brackets Revealed19Weekly Cups (July 7-13): Classic continues to roll8
StarCraft 2
General
What tournaments are world championships? Server Blocker #1: Maru - Greatest Players of All Time THE BEST CRYPTOCURRENCY RECOVERY EXPERTS/GOTO WIZA Power Rank - Esports World Cup 2025
Tourneys
Esports World Cup 2025 FEL Cracov 2025 (July 27) - $8000 live event Sparkling Tuna Cup - Weekly Open Tournament Master Swan Open (Global Bronze-Master 2) Sea Duckling Open (Global, Bronze-Diamond)
Strategy
How did i lose this ZvP, whats the proper response
Custom Maps
External Content
Mutation #239 Bad Weather Mutation # 483 Kill Bot Wars Mutation # 482 Wheel of Misfortune Mutation # 481 Fear and Lava
Brood War
General
Google Play ASL (Season 20) Announced Simple editing of Brood War save files? (.mlx) BGH Auto Balance -> http://bghmmr.eu/ Ginuda's JaeDong Interview Series [Update] ShieldBattery: 2025 Redesign
Tourneys
[Megathread] Daily Proleagues [BSL20] Non-Korean Championship 4x BSL + 4x China CSL Xiamen International Invitational [CSLPRO] It's CSLAN Season! - Last Chance
Strategy
[G] Mineral Boosting Does 1 second matter in StarCraft? Simple Questions, Simple Answers
Other Games
General Games
Stormgate/Frost Giant Megathread Total Annihilation Server - TAForever Nintendo Switch Thread [MMORPG] Tree of Savior (Successor of Ragnarok) Path of Exile
Dota 2
Official 'what is Dota anymore' discussion
League of Legends
Heroes of the Storm
Simple Questions, Simple Answers Heroes of the Storm 2.0
Hearthstone
Heroes of StarCraft mini-set
TL Mafia
TL Mafia Community Thread Vanilla Mini Mafia
Community
General
US Politics Mega-thread Stop Killing Games - European Citizens Initiative Things Aren’t Peaceful in Palestine Russo-Ukrainian War Thread Post Pic of your Favorite Food!
Fan Clubs
INnoVation Fan Club SKT1 Classic Fan Club!
Media & Entertainment
[\m/] Heavy Metal Thread Anime Discussion Thread Movie Discussion! [Manga] One Piece Korean Music Discussion
Sports
Formula 1 Discussion 2024 - 2025 Football Thread TeamLiquid Health and Fitness Initiative For 2023 NBA General Discussion
World Cup 2022
Tech Support
Installation of Windows 10 suck at "just a moment" Computer Build, Upgrade & Buying Resource Thread
TL Community
TeamLiquid Team Shirt On Sale The Automated Ban List
Blogs
Ping To Win? Pings And Their…
TrAiDoS
momentary artworks from des…
tankgirl
from making sc maps to makin…
Husyelt
StarCraft improvement
iopq
Socialism Anyone?
GreenHorizons
Eight Anniversary as a TL…
Mizenhauer
Customize Sidebar...

Website Feedback

Closed Threads



Active: 571 users

The Math Thread - Page 25

Forum Index > General Forum
Post a Reply
Prev 1 23 24 25 26 27 32 Next All
Rodya
Profile Joined January 2018
546 Posts
Last Edited: 2019-02-22 00:18:15
February 22 2019 00:05 GMT
#481
Okay, I see what you were doing. Notice that x*sech^2(w^T x) is a vector - this is what you're saying is the gradient of f in this other problem. And that is indeed the correct answer.

Now going back to the original problem, let me just write the answer so you can see the differences: (1/2)(sum from i to m)x^(i)(w^Tx^(i)-y^(i)) / |w^Tx^(i)-y^(i)|. Apologies for misreading your answer. You are using some shortcuts to calculate the whole gradient at once. Which is fine, but I wasn't expecting it.

Let me give you a quick calculus review. So, the output of f(w) is a number (it looks like a loss function). However, f(w) is a multivariable function, it has as many variables as there are elements in w. Now, I'm assuming that w is a vector, not a matrix, although it definitely could be, lets assume for now that it is a vector. You talk about the derivative of f with respect to w, however think about the function g(z) = z_1+2z_2+3z_3 where z=(z_1, z_2,z_3) is some vector. Now you probably can guess that the 'derivative' of g is equal to (1,2,3), but strictly speaking, you can only take a derivative with respect to a single dimensional variable (i.e. something that varies over the real numbers and therefore isnt a vector). Thus we can't calculate dg/dz, we can only calculate dg/dz_1, dg/dz_2, and dg/dz_3. So we simply DEFINE dg/dz to be the VECTOR (dg/dz_1, dg/dz_2, dg/dz_3), which you can easily check is equal to (1,2,3). Similarly, the derivative of f(w) is defined to be the vector (df/dw_1, ..., df/dw_D). You can check your work and see that the answer I gave you can be found using either your method or the method of partial derivatives. I'm actually lying a bit to you here, but it's very useful (and I'm sure your teacher expects you) to think of the derivative of g/f this way. It will help to demystify some of your derivations and let you check your work using basic calculus.

Earlier you mentioned that you were anxious about taking derivatives of matrices - so since you've mentioned it again, let me briefly justify the fact that d/dw (w^T x) = x. Let x be an arbitrary matrix, then we can think of it as a linear transformation that maps vectors w to xw. Therefore, if we denote that linear transformation by f(w), we have f(w) = xw. Now, a derivative is supposed to be the best linear approximation of a function at each point. But a linear transformation is linear everywhere, so it is ITSELF the best linear approximation to ITSELF at every point. Thus the best linear approximation (i.e. the derivative) of f(w) is x. So d/dw(f(w)) = x. Hopefully it gives you some peace of mind at least, even if it isn't a rigorous argument.
Banned for saying "zerg players are by far the biggest whiners in sc2 history" despite the fact that this forum is full of such posts about Terrans. Foreigner Elitists in control!
Deleted User 3420
Profile Blog Joined May 2003
24492 Posts
February 22 2019 00:09 GMT
#482
how are you so nice here when you're so mean to foreign pros in power rankings

just teasing, thanks for all the responses. I'll check this out closely when I am done with dinner.
Rodya
Profile Joined January 2018
546 Posts
Last Edited: 2019-02-22 00:17:18
February 22 2019 00:13 GMT
#483
Oh, and you asked about whether since x^(i) is a vector, that x is a matrix. You haven't defined x yet, I have no clue what it is. It's possible that in your book, the notation used is that x^(i) is the i'th column or row of x. If that is the case, then x would be a matrix. If your book does not use that notation though, then x isn't anything - it is undefined, so don't think about it and don't let it appear in your derivations unless you define it first.

edit: I'm an enigma.
Banned for saying "zerg players are by far the biggest whiners in sc2 history" despite the fact that this forum is full of such posts about Terrans. Foreigner Elitists in control!
Deleted User 3420
Profile Blog Joined May 2003
24492 Posts
February 22 2019 23:02 GMT
#484
I solved the last two derivatives on my own... they were horrible and long but they used the same concepts.

In other news, I am being forced to turn my homework in using latex, and it includes graphs and stuff. This does not seem worth it, it is making my homework take SOOOO long to do, and I expect that people outside of academia don't really end up using this so I am not sure why the professor wouldn't let us write it on a damn piece of paper
Rodya
Profile Joined January 2018
546 Posts
February 23 2019 00:52 GMT
#485
If your professor is okay with it, you can cut down the time it takes to put graphs in the document by using snipping tool (or screen shot) to take a picture of the graph, then use \includegraphics{mypicture.png} to insert the graph crudely into the doc. You can also manually adjust the size of the picture.

You gotta include \usepackage{graphicx} in the preamble though to do that.

Also, http://detexify.kirelabs.org/classify.html is your best friend. Just draw any symbol and it will tell you how to make it, and if you need a special package to do so.
Banned for saying "zerg players are by far the biggest whiners in sc2 history" despite the fact that this forum is full of such posts about Terrans. Foreigner Elitists in control!
Deleted User 3420
Profile Blog Joined May 2003
24492 Posts
February 23 2019 01:35 GMT
#486
that symbol classifier - whoever made that is a hero
Acrofales
Profile Joined August 2010
Spain17983 Posts
February 23 2019 01:47 GMT
#487
Latex is great. Drawing graphs with latex is absurd. Just use whatever and include them as images. Tikz is awesome for making pretty diagrams, but there are much better and easier ways of drawing graphs.

Yes, nobody outside of (computer) science uses it, but you're being the trained as a computer scientist, so I don't see the problem with learning it. We had to learn it in 1st year CS, and once you get the hang of it, you'll never want to use Word again ever.
Deleted User 3420
Profile Blog Joined May 2003
24492 Posts
Last Edited: 2019-02-23 01:50:18
February 23 2019 01:49 GMT
#488
Well I don't use word either(unless I am forced to), I just write stuff on paper and then scan it to pdf. As long as the handwriting is legible I can't imagine latex being superior to that, but maybe I am wrong?

I suppose I would want it for publishing any papers, though...
Acrofales
Profile Joined August 2010
Spain17983 Posts
February 23 2019 09:58 GMT
#489
On February 23 2019 10:49 travis wrote:
Well I don't use word either(unless I am forced to), I just write stuff on paper and then scan it to pdf. As long as the handwriting is legible I can't imagine latex being superior to that, but maybe I am wrong?

I suppose I would want it for publishing any papers, though...

"As long as the handwriting is legible" is the key point there, though. Remember that your professor is going to have to correct and grade this work for everybody in your class, not just you.
Mr. Wiggles
Profile Blog Joined August 2010
Canada5894 Posts
February 23 2019 18:10 GMT
#490
LaTeX is one of my hidden shames, since I use it quite a bit but have never actually spent the time to sit down and learn how it really works. In that sense, a lot of it is 'magic' to me since I mostly know the proper rituals and incantations but would have a hard time rebuilding my collection of useful patterns from scratch.

For graphs (if we're talking figures) I've never used LaTeX directly. I usually use gnuplot (ugly) and then include the PNG into the LaTeX document. There's much nicer graphing libraries out there, I've just never spent the time to find them.

For drawing graphs (if we're talking graph-theory) I've mostly used the Tikz library, as mentioned. I found the Tikz automata library very useful for drawing things like DFAs, NFAs, etc. in courses that required it.

In some math electives I took I ended up using LaTeX for all the coursework. The profs seemed to appreciate it, and I found that it actually cut down on the writing time overall.
you gotta dance
neptunusfisk
Profile Blog Joined July 2012
2286 Posts
February 23 2019 23:19 GMT
#491
On February 24 2019 03:10 Mr. Wiggles wrote:
I usually use gnuplot (ugly) and then include the PNG into the LaTeX document.


Gnuplot can export to vectorised formats...
maru G5L pls
Deleted User 3420
Profile Blog Joined May 2003
24492 Posts
February 26 2019 16:12 GMT
#492
I wanted to verify a true or false section on my homework that I did, it's abstract algebra groups. I just want to make sure I am understanding this stuff correctly. Note that the * denotes that the set does not contain 0

T/F:

1.) Q(under addition) us a subgroup of R (under addition): true

2.) R* (under addition) is a subgroup of R (under addition): false (no identity in R*)

3.) R* (under multiplication) us a subgroup of R (with addition): false (they need to be same operation right?)

4.) {1,-1} (under multiplication) is a subgroup of R* (under multiplication): true

5.): {2^k : k in Z} (under multiplication) is a subgroup of Q* (under multiplication): false (no zero in Q* so no inverse for 2^k... am I understanding that right?)

Acrofales
Profile Joined August 2010
Spain17983 Posts
February 26 2019 16:45 GMT
#493
5) seems true to me. look at it again, but the lack of 0 doesn't matter.
mahrgell
Profile Blog Joined December 2009
Germany3943 Posts
February 26 2019 17:20 GMT
#494
At first glance I would also consider 3 true.
Acrofales
Profile Joined August 2010
Spain17983 Posts
February 26 2019 17:29 GMT
#495
On February 27 2019 02:20 mahrgell wrote:
At first glance I would also consider 3 true.

While I can't remember the exact definition of a subgroup, so maybe it just isn't even defined properly if the operators are different. But mostly R* doesn't have 0, so doesn't have the ident for addition, and thus is not a group with addition, and therefore also not a subgroup.
mahrgell
Profile Blog Joined December 2009
Germany3943 Posts
February 26 2019 17:45 GMT
#496
On February 27 2019 02:29 Acrofales wrote:
Show nested quote +
On February 27 2019 02:20 mahrgell wrote:
At first glance I would also consider 3 true.

While I can't remember the exact definition of a subgroup, so maybe it just isn't even defined properly if the operators are different. But mostly R* doesn't have 0, so doesn't have the ident for addition, and thus is not a group with addition, and therefore also not a subgroup.

For the multiplication the 1 is the same as the 0 for the addition.
Acrofales
Profile Joined August 2010
Spain17983 Posts
Last Edited: 2019-02-26 17:57:15
February 26 2019 17:52 GMT
#497
On February 27 2019 02:45 mahrgell wrote:
Show nested quote +
On February 27 2019 02:29 Acrofales wrote:
On February 27 2019 02:20 mahrgell wrote:
At first glance I would also consider 3 true.

While I can't remember the exact definition of a subgroup, so maybe it just isn't even defined properly if the operators are different. But mostly R* doesn't have 0, so doesn't have the ident for addition, and thus is not a group with addition, and therefore also not a subgroup.

For the multiplication the 1 is the same as the 0 for the addition.

Yes... so?

A group is not a subgroup of an other just because it is a group and the elements are a subset. It has to include the identity.


And googling it:
https://en.wikipedia.org/wiki/Subgroup

Including the identity is not enough either, it definitely needs to be a group under the same operator, so can't simply redefine the group operator in the subgroup. So (3) fails on both those points.
mahrgell
Profile Blog Joined December 2009
Germany3943 Posts
February 26 2019 18:55 GMT
#498
On February 27 2019 02:52 Acrofales wrote:
Show nested quote +
On February 27 2019 02:45 mahrgell wrote:
On February 27 2019 02:29 Acrofales wrote:
On February 27 2019 02:20 mahrgell wrote:
At first glance I would also consider 3 true.

While I can't remember the exact definition of a subgroup, so maybe it just isn't even defined properly if the operators are different. But mostly R* doesn't have 0, so doesn't have the ident for addition, and thus is not a group with addition, and therefore also not a subgroup.

For the multiplication the 1 is the same as the 0 for the addition.

Yes... so?

A group is not a subgroup of an other just because it is a group and the elements are a subset. It has to include the identity.


And googling it:
https://en.wikipedia.org/wiki/Subgroup

Including the identity is not enough either, it definitely needs to be a group under the same operator, so can't simply redefine the group operator in the subgroup. So (3) fails on both those points.



At least we learned a more theoretical version, where it is enough to be isomorph to a subgroup (by the your/wiki definition) of supposed supergroup to be considered a subgroup in a group theoretical point of view.
How you name your elements and ops really doesn't matter then. And then obviously your isomorphism images the identity of one group onto the identity of the other group.

Now there is a trivial isomorphism (ln(x)) between (R+\{0}, *) and (R,+).

This is in fact, what led me to my initial thought. But at least right now, I can't expand this to {R\{0},*}. Which leads me to believe that this is indeed false, just for very different reasons.


Melliflue
Profile Joined October 2012
United Kingdom1389 Posts
Last Edited: 2019-02-26 19:02:54
February 26 2019 18:58 GMT
#499
I think (3) is highlighting the issue about the operator and not the identity (Travis is correct, different operator so not a subgroup). Needing the identity was the purpose of example (2).

(5) is true and I don't know where the confusion came from. The lack of zero in Q* is irrelevant. The inverse for 2^k is 2^(-k) so you are fine when k ranges over Z.

Edit: To the above, being isomorphic to a subgroup is not the same as being a subgroup. There are times when the distinction is not important so we treat isomorphic subgroups as subgroups (mathematicians are often lazy like that). Sometimes however it can cause problems and it is important to remember they are different.
Deleted User 3420
Profile Blog Joined May 2003
24492 Posts
February 27 2019 02:13 GMT
#500
ah right, the identity in 5.) is 1.. not 0. the confusion was that I was thinking 2^0 = 1 .. temporarily forgetting that the member of my group is 2^k, not k. if that confuses you don't worry about it, my thinking clearly didn't make sense. glad I posted them though!
Prev 1 23 24 25 26 27 32 Next All
Please log in or register to reply.
Live Events Refresh
CranKy Ducklings
10:00
Master Swan Open #94
Liquipedia
[ Submit Event ]
Live Streams
Refresh
StarCraft 2
Hui .289
BRAT_OK 75
ProTech67
MindelVK 27
StarCraft: Brood War
Britney 57039
Horang2 3346
Shuttle 2707
Bisu 2582
Barracks 1624
Flash 1578
Jaedong 1462
EffOrt 896
BeSt 682
firebathero 404
[ Show more ]
Larva 338
ToSsGirL 248
Soma 220
sorry 154
Last 144
Soulkey 128
Hyun 88
Rush 86
Light 71
Sea.KH 56
ZerO 55
JYJ52
Shinee 48
JulyZerg 46
Aegong 46
sas.Sziky 45
Free 37
scan(afreeca) 21
sSak 20
zelot 18
Terrorterran 9
IntoTheRainbow 8
Dota 2
Gorgc5107
qojqva2247
XaKoH 473
XcaliburYe415
420jenkins99
LuMiX1
Counter-Strike
fl0m2528
sgares216
Heroes of the Storm
Khaldor309
Other Games
singsing2113
B2W.Neo1946
Beastyqt1212
crisheroes368
Fuzer 238
ZerO(Twitch)15
Organizations
StarCraft 2
Blizzard YouTube
StarCraft: Brood War
BSLTrovo
sctven
[ Show 15 non-featured ]
StarCraft 2
• Berry_CruncH360
• Adnapsc2 26
• Dystopia_ 6
• AfreecaTV YouTube
• intothetv
• Kozan
• IndyKCrew
• LaughNgamezSOOP
• Migwel
• sooper7s
StarCraft: Brood War
• BSLYoutube
• STPLYoutube
• ZZZeroYoutube
Dota 2
• C_a_k_e 3153
League of Legends
• Nemesis1391
Upcoming Events
BSL20 Non-Korean Champi…
16m
CSO Cup
2h 16m
BSL20 Non-Korean Champi…
4h 16m
Bonyth vs Sziky
Dewalt vs Hawk
Hawk vs QiaoGege
Sziky vs Dewalt
Mihu vs Bonyth
Zhanhun vs QiaoGege
QiaoGege vs Fengzi
FEL
19h 16m
BSL20 Non-Korean Champi…
1d
BSL20 Non-Korean Champi…
1d 4h
Bonyth vs Zhanhun
Dewalt vs Mihu
Hawk vs Sziky
Sziky vs QiaoGege
Mihu vs Hawk
Zhanhun vs Dewalt
Fengzi vs Bonyth
Sparkling Tuna Cup
2 days
Online Event
3 days
uThermal 2v2 Circuit
4 days
The PondCast
4 days
[ Show More ]
Replay Cast
5 days
Korean StarCraft League
6 days
CranKy Ducklings
6 days
Liquipedia Results

Completed

CSL Xiamen Invitational
Esports World Cup 2025
Murky Cup #2

Ongoing

Copa Latinoamericana 4
Jiahua Invitational
BSL20 Non-Korean Championship
BSL Team Wars
CSLPRO Last Chance 2025
CC Div. A S7
Underdog Cup #2
IEM Cologne 2025
FISSURE Playground #1
BLAST.tv Austin Major 2025
ESL Impact League Season 7
IEM Dallas 2025
PGL Astana 2025
Asian Champions League '25

Upcoming

ASL Season 20: Qualifier #1
ASL Season 20: Qualifier #2
ASL Season 20
CSLPRO Chat StarLAN 3
BSL Season 21
RSL Revival: Season 2
Maestros of the Game
SEL Season 2 Championship
uThermal 2v2 Main Event
FEL Cracov 2025
HCC Europe
ESL Pro League S22
StarSeries Fall 2025
FISSURE Playground #2
BLAST Open Fall 2025
BLAST Open Fall Qual
Esports World Cup 2025
BLAST Bounty Fall 2025
BLAST Bounty Fall Qual
TLPD

1. ByuN
2. TY
3. Dark
4. Solar
5. Stats
6. Nerchio
7. sOs
8. soO
9. INnoVation
10. Elazer
1. Rain
2. Flash
3. EffOrt
4. Last
5. Bisu
6. Soulkey
7. Mini
8. Sharp
Sidebar Settings...

Advertising | Privacy Policy | Terms Of Use | Contact Us

Original banner artwork: Jim Warren
The contents of this webpage are copyright © 2025 TLnet. All Rights Reserved.