• Log InLog In
  • Register
Liquid`
Team Liquid Liquipedia
EDT 08:53
CEST 14:53
KST 21:53
  • 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
TL.net Map Contest #21: Voting10[ASL20] Ro4 Preview: Descent11Team TLMC #5: Winners Announced!3[ASL20] Ro8 Preview Pt2: Holding On9Maestros of the Game: Live Finals Preview (RO4)5
Community News
Chinese SC2 server to reopen; live all-star event in Hangzhou16Weekly Cups (Oct 13-19): Clem Goes for Four1BSL Team A vs Koreans - Sat-Sun 16:00 CET6Weekly Cups (Oct 6-12): Four star herO85.0.15 Patch Balance Hotfix (2025-10-8)80
StarCraft 2
General
Weekly Cups (Oct 13-19): Clem Goes for Four RotterdaM "Serral is the GOAT, and it's not close" Chinese SC2 server to reopen; live all-star event in Hangzhou Weekly Cups (March 17-23): Clem Bounces Back DreamHack Open 2013 revealed
Tourneys
$1,200 WardiTV October (Oct 21st-31st) SC2's Safe House 2 - October 18 & 19 INu's Battles #13 - ByuN vs Zoun Tenacious Turtle Tussle Sparkling Tuna Cup - Weekly Open Tournament
Strategy
Custom Maps
Map Editor closed ?
External Content
Mutation # 496 Endless Infection Mutation # 495 Rest In Peace Mutation # 494 Unstable Environment Mutation # 493 Quick Killers
Brood War
General
BW General Discussion Is there anyway to get a private coach? BGH Auto Balance -> http://bghmmr.eu/ BSL Season 21 OGN to release AI-upscaled StarLeague from Feb 24
Tourneys
[Megathread] Daily Proleagues 300$ 3D!Community Brood War Super Cup #4 [ASL20] Semifinal B Azhi's Colosseum - Anonymous Tournament
Strategy
Roaring Currents ASL final Current Meta [I] Funny Protoss Builds/Strategies BW - ajfirecracker Strategy & Training
Other Games
General Games
Stormgate/Frost Giant Megathread Path of Exile Nintendo Switch Thread Dawn of War IV ZeroSpace Megathread
Dota 2
Official 'what is Dota anymore' discussion LiquidDota to reintegrate into TL.net
League of Legends
Heroes of the Storm
Simple Questions, Simple Answers Heroes of the Storm 2.0
Hearthstone
Deck construction bug Heroes of StarCraft mini-set
TL Mafia
TL Mafia Community Thread SPIRED by.ASL Mafia {211640}
Community
General
Things Aren’t Peaceful in Palestine US Politics Mega-thread The Chess Thread Russo-Ukrainian War Thread Men's Fashion Thread
Fan Clubs
The herO Fan Club!
Media & Entertainment
Anime Discussion Thread Series you have seen recently... [Manga] One Piece Movie Discussion!
Sports
2024 - 2026 Football Thread TeamLiquid Health and Fitness Initiative For 2023 MLB/Baseball 2023 Formula 1 Discussion NBA General Discussion
World Cup 2022
Tech Support
SC2 Client Relocalization [Change SC2 Language] Linksys AE2500 USB WIFI keeps disconnecting Computer Build, Upgrade & Buying Resource Thread
TL Community
The Automated Ban List Recent Gifted Posts
Blogs
Our Last Hope in th…
KrillinFromwales
Certified Crazy
Hildegard
The Heroism of Pepe the Fro…
Peanutsc
Rocket League: Traits, Abili…
TrAiDoS
Customize Sidebar...

Website Feedback

Closed Threads



Active: 1182 users

Teaching Vectors Properly (For Everyone) - Page 9

Forum Index > General Forum
Post a Reply
Prev 1 7 8 9 All
decerto
Profile Joined November 2011
244 Posts
Last Edited: 2012-02-05 11:05:10
February 05 2012 10:39 GMT
#161
On February 05 2012 19:11 Jombozeus wrote:
I am currently taking Calc B in my college freshman year, and I've taken regular math in highschool with only introduction to vectors. So I am what you would call a stereotypical -meh- math student that would be learning vectors.

I read through your explanation of vectors 3 times and I have not a single fucking clue what its saying.

Which I guess proves you wrong.


Physics vectors and real numbers 17, (1,2) or (3,4,5) are just a special case of vectors called n-tuples with n being the dimension. They are the vectors of vector spaces R, R^2, R^3 which are called euclidean vector spaces after the famous mathematician Euclid who developed the geometry in these spaces in his book "Elements".

Vector spaces are just sets of elements like the real numbers with additional structure, like how to combine them etc(that big list of things he wrote).

These elements can also be functions, complex numbers and polynomials etc so long as they obey those properties he wrote. And because they do obey those property's it gives rise to a lot of new property's that can be derived like the inner product etc.

And just like sets you can have subsets(smaller sets that are contained in the original set) which when they obey these property's they are subspaces

Linear algebra is just the study of these Vector spaces and their subspaces and mappings between vector spaces which preserve linearity(maps a line to a line).

But Im curious if vectors are just a further special case of tensors?, only In first year so I havent come across them properly
rabidch
Profile Joined January 2010
United States20289 Posts
February 05 2012 10:42 GMT
#162
when i see average high school students being taught the way as outlined as OP and the majority of them understanding it quickly, i'll agree with the OP. otherwise not.
LiquidDota StaffOnly a true king can play the King.
Lpspace
Profile Joined April 2011
4 Posts
February 05 2012 14:12 GMT
#163
On February 05 2012 17:46 paralleluniverse wrote:

Show nested quote +
This is one example why I think you shouldnt try to teach. If you want to explain fundamentals you have to get it right otherwise you are hurting the understanding more than you help it in the long run.


No shit. That's the whole point of this post.

The very first picture depicts a complex number as a vector.

Yet, students get it drilled into them that you cannot multiply 2 vectors (which is correct), but then why can you multiply two complex numbers if they are vectors? The answer requires an understanding of vector spaces, and that when complex numbers are presented as a vector over the reals, there is no vector multiplication, so complex multiplication isn't vector multiplication. But when complex numbers are presented as a field, the field multiplication is complex multiplication.


Well if that's the point, here's an example issue from your posts. The reason you can multiply two complex "vectors" together is not that the complex numbers form a field. It is because the complex numbers form an algebra over the reals. There are plenty of other interesting vector spaces which you can extend to algebras but do not have a field structure. For example, look at the multiplication defined for lie algebras which gives rise to a whole lot of "zero divisors".
zag
Profile Joined September 2010
Australia60 Posts
Last Edited: 2012-02-05 14:38:14
February 05 2012 14:29 GMT
#164
edit: was plainly wrong sry
Envy is the highest form of recognition
Caloooomi
Profile Joined July 2010
Scotland188 Posts
February 05 2012 14:35 GMT
#165
I like it. Started off learning vectors and didn't grasp it as well as other maths topics which ended up hurting me in the long run!
Booga booga booga~
gyth
Profile Blog Joined September 2009
657 Posts
February 05 2012 15:09 GMT
#166
You should only need to explain enough to understand the content and not teach something that is wrong

Physics teaches the difference between scalars and vectors. That can't be done by using a mathematically rigorous definition of a vector.


Complex numbers are often introduced as vectors.

Introduced as the same special case R^2 vector used in physics. It is almost like teachers got together and agreed upon how vectors should be taught outside of university level linear algebra courses.
The plural of anecdote is not data.
Prev 1 7 8 9 All
Please log in or register to reply.
Live Events Refresh
OSC
11:00
Mid Season Playoffs
Nicoract vs GgMaChineLIVE!
SKillous vs sebesdes
Solar vs Cure
WardiTV672
Liquipedia
Replay Cast
10:00
SC2's Safe House 2: Playoffs
CranKy Ducklings135
Liquipedia
[ Submit Event ]
Live Streams
Refresh
StarCraft: Brood War
Rain 10656
GuemChi 3547
Horang2 3036
Bisu 2114
Hyuk 1492
Flash 1174
Jaedong 879
hero 738
firebathero 556
Mini 368
[ Show more ]
Soma 367
BeSt 307
Stork 292
EffOrt 291
Hyun 284
Light 259
Soulkey 228
ZerO 212
Last 185
Snow 143
Barracks 113
PianO 111
yabsab 104
Free 88
Killer 87
Aegong 80
JYJ77
ToSsGirL 73
Mind 65
Pusan 65
Rush 63
ggaemo 50
Movie 44
Sharp 33
zelot 22
ajuk12(nOOB) 20
soO 17
scan(afreeca) 16
Noble 14
Sacsri 13
Shinee 12
ivOry 12
SilentControl 10
HiyA 9
Bale 5
Terrorterran 4
Mong 1
Sea 0
Dota 2
qojqva1380
Dendi492
BananaSlamJamma218
XcaliburYe205
420jenkins151
canceldota64
League of Legends
JimRising 368
Counter-Strike
olofmeister2005
zeus668
x6flipin583
oskar123
edward105
Other Games
summit1g5985
singsing2405
B2W.Neo634
hiko282
XaKoH 187
Pyrionflax166
Hui .165
Sick161
Happy51
Mew2King47
Trikslyr14
ZerO(Twitch)6
Organizations
Counter-Strike
PGL269
StarCraft 2
Blizzard YouTube
StarCraft: Brood War
BSLTrovo
sctven
[ Show 14 non-featured ]
StarCraft 2
• AfreecaTV YouTube
• intothetv
• Kozan
• IndyKCrew
• LaughNgamezSOOP
• Migwel
• sooper7s
StarCraft: Brood War
• iopq 14
• BSLYoutube
• STPLYoutube
• ZZZeroYoutube
Dota 2
• C_a_k_e 459
• Noizen71
League of Legends
• Jankos2944
Upcoming Events
OSC
3h 7m
Tenacious Turtle Tussle
10h 7m
The PondCast
21h 7m
OSC
23h 7m
WardiTV Invitational
1d 22h
Online Event
2 days
RSL Revival
2 days
RSL Revival
2 days
WardiTV Invitational
2 days
Afreeca Starleague
3 days
Snow vs Soma
[ Show More ]
Sparkling Tuna Cup
3 days
WardiTV Invitational
3 days
CrankTV Team League
4 days
RSL Revival
4 days
Wardi Open
4 days
CrankTV Team League
5 days
Replay Cast
5 days
WardiTV Invitational
5 days
CrankTV Team League
6 days
Replay Cast
6 days
Liquipedia Results

Completed

Acropolis #4 - TS2
WardiTV TLMC #15
HCC Europe

Ongoing

BSL 21 Points
ASL Season 20
CSL 2025 AUTUMN (S18)
C-Race Season 1
IPSL Winter 2025-26
EC S1
Thunderpick World Champ.
CS Asia Championships 2025
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

Upcoming

SC4ALL: Brood War
BSL Season 21
BSL 21 Team A
BSL 21 Non-Korean Championship
RSL Offline Finals
RSL Revival: Season 3
Stellar Fest
SC4ALL: StarCraft II
CranK Gathers Season 2: SC II Pro Teams
eXTREMESLAND 2025
ESL Impact League Season 8
SL Budapest Major 2025
BLAST Rivals Fall 2025
IEM Chengdu 2025
PGL Masters Bucharest 2025
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.