Tips to be a better problem solver [Last live lecture] | Ep. 10 Lockdown live math

Tips on problem-solving, with examples from geometry, trig, and probability.

Notes by Ngân Vũ:

Mistakes:
50:35, there should be a dx in the integral
54:40, if you notice the mistake here and are inclined to complain, keep watching

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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Video timeline (thanks to user "noonesperfect")
0:34 9-Problem Solving Principles/Tip
1:15 Question 1 (Probability)
2:08 Who is Ben Eater?
4:25 Inscribed angle theorem, θL=2*θs
5:58 Tip-1
7:48 Tip-2
8:16 Question 2
9:34 Answer 2
10:29 Tip-3
15:17 Tip-4
22:48 Question 3
25:56 Answer 3 (Marked incorrectly, Answer: Option D)
26:31 Answer 1
27:28 Explanation for Q1, Floor function
30:38 Tip-5
32:53 Tip-6
33:36 Question 4
34:43 Answer 4
36:37 Question 5
38:10 Answer 5
41:48 Probability graph in Desmos
44:08 Revisiting an alternating series sum for ln(2)
47:29 Tip-7
51:08 Tip-8
55:23 Audience questions through tweets
57:28 Tip-9
58:29 Python programming for various probability question
1:04:31 Arts created using Desmos graph tool with mathematical expressions
1:05:54 Thank you, appreciation to the team and all.
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The live question setup with stats on-screen is powered by Itempool.

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Music by Vincent Rubinetti.
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Stream the music on Spotify:

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

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Various social media stuffs:

[noonesperfect]

0:34 9-Problem Solving Principles/Tip
1:15 Question 1 (Probability)
2:08 Who is Ben Eater?
4:25 Inscribed angle theorem, θL=2*θs
5:58 Tip-1
7:48 Tip-2
8:16 Question 2
9:34 Answer 2
10:29 Tip-3
15:17 Tip-4
22:48 Question 3
25:56 Answer 3 (Marked incorrectly, Answer: Option D)
26:31 Answer 1
27:28 Explanation for Q1, Floor function
30:38 Tip-5
32:53 Tip-6
33:36 Question 4
34:43 Answer 4
36:37 Question 5
38:10 Answer 5
41:48 Probability graph in Desmos
44:08 Revisiting an alternating series sum for ln(2)
47:29 Tip-7
51:08 Tip-8
55:23 Audience questions through tweets
57:28 Tip-9
58:29 Python programming for various probability question
1:04:31 Arts created using Desmos graph tool with mathematical expressions
1:05:54 Thank you, appreciation to team and all.
_Water Sip:_ 23:26, 23:36, 34:06, 37:28, 1:03:42

[Sharpgamingvideos]

You are setting the bar right now for the future of mathematics education, and you are setting it VERY high.

[madhurima]

Why should you watch his videos?
1. You will learn to think intuitively.
2. You will get better at Mathematics (not just the course work but also the daily life mathematics).
3. Your problem solving skills and spatial thinking abilities will improve dramatically.
4. He is the best teacher possible.
5. He is just awesome :)

[NXaiUL]

Petition requesting Grant to make a series teaching python in his unique way.

[saurra]

I just applied your tip on a higher level maths worksheet than mine and holy shit it works!! Hopefully I get better at Maths. Thank you!

[EayuProuxm]

Problem solving tips
1. Use the defining features of the set up.
2. Give things (meaningful) names
3. Leverage symmetry
4. Try describing one object two different ways
5. Draw a picture. [Have some numbers? Make them coordinates!]
6. Ask a simpler version of the problem
7. Read a lot, and think about problems a lot.
8. Always gut-check your answer!
9. Learn at least a little bit of programming

[andrexeme_swag]

Oh, it's a shame this series has to come to an end. I was fond of it and your constant enthusiasm. As always, you left me astonished at the terrific quality of your content and thus I'd like to thank you for putting your efforts into such a generous project. You're awesome!

[Leonardo-lbrs]

Tip 5 : Draw a picture. This tip is also very useful when solving problems related to mechanics.

*Grant is like Bertrand Russell, thinks like a mathematician and talks like a poet.*

[arongil]

Thank you so much for putting together this absolutely splendid lockdown math series. It's been a pleasure to watch each and every one. In particular, it's been extremely gratifying to review (and expand upon) ways to conceptualize exp(x), because it is such a lively function with so much to explore about it. Wishing you happiness during the times of quarantine ahead :)

[Twisol]

That "double projection" proof of the Pythagorean identity almost took me right out of my seat!

[warmpianist]

For probability problem, you can also try to find the probability of being even if rounded nearest, or round up as well. The answers are quite surprising in some ways. By the way, you should be able to answer right away for round up, given that you know the answer for round down. Hint for round nearest: there is pi.

[PleegWat]

My professor would say he doesn't need to draw a perfect circle. He just needs to state the curve he drew is a circle.

[nobody]

31:22 - 31:42 You are officially the Bob Ross of math.
Edit: I don't know why my timestamps were messed up.

[komalvenkatesh]

Feels like our favorite TV show just ended with a touching last episode. Thank you so much Grant! You're a wonderful person. <3

[matron]

Those were great, can’t say more than tank you, thanks Grant.

[AbhishekGNair]

Please consider doing more lectures on lockdown math, Grant. You're just awesome at the math and I love the way you look at problems. It breaks my heart to see you go.

[TopGunMan]

I've always struggled with problem-solving. My process usually involves a lot of coffee, degrading into confusion, sleepiness, frustration, and possibly paper violence. Thanks for talking about this stuff.

[varunraju]

Grant, your videos are absolutely incredible! This series has been so helpful for me - I am a high school student from India hoping to pursue Physics at university this year, and I have stayed up for almost all your lectures because they always have little things that are so fascinating and are never taught conventionally. You have really inspired me with this lockdown series, and I just wanted to let you know that what you are doing is something truly amazing. I have been homeschooling for the past four years and your videos, especially the calculus series, have been extremely useful (and very beautiful!). You are one of the reasons I want to study Physics. Thank you so much, and please, for our sake, never stop what you're doing!

[segalanicolas]

I am grateful for this whole channel and this particular series of lives which brightened my lockdown and most certainly the lockdown of other math fans. Looking forward to re-watching it all and watching the videos coming out later.

[sandeepbharadwaj]

Thank You so much for this entire series Grant.I developed a deeper understanding and liking in maths thanks to you.I missed a few of the episodes because it is a bit late here .Nevertheless, wanted to thank you for the amazing visual intuitions you always provide