7 Ways to Level Up Your MATH SUPERPOWERS

[@energiam880]

I have recently submitted a Ph.D. in metallurgical sciences. I took a brain holiday for 4 weeks, then realized, even after 6 years of a doctorate, I was hungry for more knowledge. Particularly mathematical knowledge, a skill that I haven't really sharpened in my materials science research project (other than qualitatively interpret known equations). So I found your videos incredibly useful, particularly your calculus section. I want to be able to model complex fluid flows pertaining to liquid-metal castings, which is quite fiendish (not only is it's a fluid flow, but the fluid evolves with time, due to solidification). There are computational fluid dynamic modelling packages that model real-world industrial processes (such as metal castings), with easy to use interface. But there is still a long way to go to accurately predict defects within metal castings, and that's where better mathematical modelling comes in. That topic is currently above my pay grade, it was above the scope of my research problem, but it's something I'm itching to learn more about! And Your videos are certainly a step in the right direction! If I can model something as complex as that, than I can just about model anything! Again, many thanks for your videos and inspirations!

[@nonamesleft9699]

Hi dr, i have a few maths related questions since I’m an aspiring mathematician. I’d really appreciate it, if you could answer them please! 1) how do you revise math? To preface this, when i first learn a topic i understand all the intricate details and how techniques work. However when i review it, i realise i lost all these nuanced understandings, how can i mitigate this? 2) How to improve mathematical thinking/problem solving ? To clarify this, for example if you were given a puzzle (which you are unfamiliar with), how would you go about solving this accurately? 3) what does it mean to understand a topic? Knowing all the intricate details, or being able to apply it, etc... 4) How to be critical about your own problem solving? In order to improve and spot errors. 5) how to think clearly and efficiently? Thank you!

[@bonifaceyogendran2294]

Great advice. I spent one summer learning LaTex by transferring my handwritten notes to digital. It refreshed lots of materials and I learned a new skill.

[@DrTrefor]

That’s actually a pretty good way to do that, two birds with one stone

[@lisaitocummings9280]

Thank you Dr. Bazett! Just finished up my finals last week so this is perfect timing! Think I'm going to tackle projects #1 and #4 this summer, thanks again for the superb videos!

[@DrTrefor]

Glad to hear you’re all done!

[@giuseppedeluca4465]

"summer is an awesome time to NOT do math" Italian universities: "so anyway you have like 5 exams in three months, have fun lmao byeeeee"

[@DrTrefor]

Lol

[@KyleBroder]

Another thing they could do is take more math courses, I took 4 math courses during the summer, I couldn't wait for the next semester to roll around 😂

[@jerrysinger2985]

Wow

[@joshlau9279]

It might be too late now, but also don’t forgot to take advantage of paid undergraduate research opportunities! I’m just getting started with a project funded with an NSERC USRA and having a blast! It’s also great that I have a supervisor to talk to whenever I get confused about things.

[@joshlau9279]

P.S. Awesome shirt, it helps people such as myself feel included and welcomed in the mathematical community! If only there were more accepting individuals during Alan Turing’s lifetime, I would have loved to know what ideas he would have come up with if not for his early demise.

[@DrTrefor]

Very happy to hear you are doing a USRA, I thought that was one of my best experiences as an undergrad for sure. RIP to Alan Turing, such a loss to have died so young and in such tragic circumstances.

[@DrTrefor]

For those outside Canada, USRA is an undergraduate research opportunity with a prof over the summer for a little bit of cash, and definitely great idea to find similar in other countries.

[@carterrodriguez2749]

My calculus teacher told me that teaching is by far one of the most selfish things you can do for yourself in college. The reason being, if you can teach it to others than you’re also just mastering the skills in whatever class you take. I just thought of that when you mentioned your 7th point. Love your videos

[@lanog40]

“One of the most selfish things” Was there a typo here?

[@DrTrefor]

It’s totally true! Helps others, the really also helps yourself

[@manamsetty2664]

@@lanog40 no it's not a typo

[@shubhamsatyaprakash54]

It is the channel where I find blissfulness and ecstasy. Thank you Prof. Trefor.👋

[@ogunsadebenjaminadeiyin2729]

Reading mathematical jargons bores me when reading Advanced Control Theory concepts and journals. Engaging and lively as usual. 👍😎

[@KyleBroder]

If students are going to read articles from the arXiv, perhaps they should try to find survey articles. Or better yet, ask a professor that they know who, in particular, knows their mathematical ability and taste, and can point them to a specific reference. The arXiv is filled with a lot of nonsense that can be distracting and a massive time sink.

[@DrTrefor]

It’s definitely true. Curating the right papers to read is not a trivial task by any means.

[@aashsyed1277]

thanks for telling, i will learn these!

[@physira7551]

Thanks

[@Probably-Bobby]

I'm halfway through Strogatz' infinite powers, such an interesting read! It blows my mind that some ideas from calculus go all the way back to Archimedes. I like the idea of learning a topic, though haven't decided what field of math I should tackle this summer... I'm leaning towards PDEs, or logic/proofs as you suggested, though I'm unsure if that will be as useful to me as a physics major. Numerical analysis also interests me, although at the moment my python knowledge is far too rudimentary to get me very far haha. So much to choose from, so little time! Great video as always!

[@DrTrefor]

Isn't it a cool book? Definitely PDE is very useful for physics, although you are almost certain to be required to take that course at some point so might not have as much an advantage. One possible option is a more proofy linear algebra. A great intuition and understanding of linear algebra is SO useful in physics and you can't possibly do enough of it:D

[@carlng8438]

Really appreciate the enthusiasm with which these videos are delivered. Thanks for making these kinds of videos. That LaTeX intro video helped me learn to write LaTeX for a Numerical Methods course I was taking!

[@DrTrefor]

Glad it helped!

[@I0MSammy]

@@DrTrefor Yeah seriously Dr Bazett, I have notifications on, on your videos because your're so inspirational for students. Thanks so much for the content, your videos in particular on laplace transforms and convolution were very helpful to me in DE since you made it more intuitive.

[@homamhassn4144]

I am 14 years old and I watched all your courses

[@michaelterrell5061]

Same

[@homamhassn4144]

@@michaelterrell5061 Is your main interest in mathematics My main interest is physics I study mathematics so that I can study physics

[@michaelterrell5061]

@@homamhassn4144 Same here. In fact the man on you’re profile picture(Nobel prize winning theoretical physicist Richard Feynman) is one of my favorite physicists ever.

[@homamhassn4144]

@@michaelterrell5061 of course I know Him that's why he is in my profile picture And He has a very deep understanding of the laws of physics and the world in general. Not just a scientist, he is a great thinker

[@michaelterrell5061]

@@homamhassn4144 One of my favorite thinkers as well, and an amazing teacher as well.

[@silversky216]

Thank you professor for helping us! Thank you so much. And congratulation for surpassing 100k, many more to come :)

[@DrTrefor]

Thank you!!

[@ankitkothawade603]

I m gonna do all of this. Math book & research paper wasn't in my list . Thanks for the idea. And most importantly, Thanks for the encouragement!!!

[@DrTrefor]

Haha you’re welcome!

[@scottboyer7774]

my #1 favorite math KZbinr these days :)

[@DrTrefor]

Thank you!!

[@johnwoods978]

thanks a lot for your energy! it really gives motivation for learning :)

[@angelmpc1725]

Your videos are incredible, Dr.Bazett. I'm really looking forward to that new series on game theory!

[@ayoubsbai6339]

Thank you for the suggestions~

[@sodiumhyposulfite5902]

Thank you for your cool videos and useful suggestions! I do hope to see some videos in the future centering on real or complex analysis: there could be, for instance, a trilogy of Fourier Series- Real Complex Analysis in the style of Stein. Anyways, thank you so much for the nice videos!

[@badwolf8112]

"It has often been said that a person does not really understand something until after teaching it to someone else. Actually, a person does not really understand something until after teaching it to a computer, i.e., expressing it as an algorithm … An attempt to formalize things as algorithms leads to a much deeper understanding than if we simply try to comprehend things in the traditional way." -Donald Knuth

[@jessewolf6806]

The great analysts did not need to teach computers about limits in order to understand, discover, and invent modern mathematics.

[@continnum_radhe-radhe]

This is amazing... 🔥🔥🔥

[@jorgebuitrago2982]

Thank you Dr.Bazett. My daughter and I look forward for your videos on Game Theory

[@DrTrefor]

Love that you and your daughter can learn together, when my son is a bit older I definitely want to do that!

[@garthgriffith4237]

Thank you for this video. Very helpful

[@maestro_100]

Thanks Alot For The Advice Sir!

[@axisepsilon514]

Omg did u read my mind? I was actually going to start a channel over the summer lol. Mainly talking about my journey as college student studying cs, stat and math!

[@DrTrefor]

That sounds really cool! Please do share link in comments if you start it:)

[@jeremylane3139]

One I'll just throw into the mix if you want to really flex your mathematical problem solving skills: try math competition problems. For instance, try some Putnam problems. They can be hard, but they're also extremely rewarding when you solve one of them.

[@jueedhar1545]

I am planning to learn basic mathematical modelling in biophysical systems over the summer (I am engaging with a biophysics lab group over the summer as intern) ! Also, would love to follow up the Game theory series coming up :) This is going to be a fun summer !!

[@DrTrefor]

Very cool!!

[@badwolf8112]

Richard Southwell on KZbin has a Category Theory playlist, and there was recently a category theorist Emily Riehl interviewed on Sean Carrol's Mindscape podcast, also on KZbin. Category Theory is one of the most abstract branches of math.

[@NothingMaster]

The last person with Math SUPERPOWERS was Grothendieck, though I don’t think he ever did any programming, but in his head.

[@DrTrefor]

He was truly amazing

[@NothingMaster]

@@DrTrefor: He was a genius amongst geniuses.

[@gardenmenuuu]

Great content as usual.I have been kinda addicted to this channel ,watching each and every series haha....anyways can you tell me which software or programming does presh talwakatr(mind your decisions use?) or to make simple animations of math equations like that..except for manim?

[@DrTrefor]

Pretty sure he is doing the same thing as me, just PowerPoint. I actually asked him once. He replied back but didn’t actually answer, so it is just a guess.

[@gardenmenuuu]

​@@DrTrefor Are you using microsoft power point or what?Your animations are so nice and so are your presentation!!You aren't far from a million subs in just some time I guess

[@gardenmenuuu]

..

[@christianchavez2202]

Very good video! I will share it with my classmates.

[@DrTrefor]

Appreciate that!

[@continnum_radhe-radhe]

Sir , please make a video on gamma,beta function

[@Aaron-jk4qh]

Watching this from Germany makes me feel sad, I still have 2 months of studying ahead ;(

[@DrTrefor]

Oh no!

[@huseyinnuriz]

in turkey usually we have 3 months for summer holyday. but this year govenment decided to make it 2 months and my school is prepearing a camp which will last 1 month. that means i can rest only for 1 month lol.

[@swatimahapatra9806]

This was truly amazing since summer break started and I was planning on working out with some projects. Specifically I was interested to do something in the applied branch so thought of doing some modelling of structural behavior during earthquakes. Is it possible to get some ideas from you regarding this topic?

[@LexiRoze]

Love these ideas, and I need that shirt!

[@jorgeespinoza3938]

About your last point, it comes to mind this quote from french moralist and essayist Joseph Joubert: "To teach is to learn twice"

[@hellocomputer8622]

Hello Sir.. i wanted to program a calculator for solving complex integration. Thank you for introducing me to LaTeX

[@DrTrefor]

That would be cool!

[@I0MSammy]

This summer I am using codecademy to learn Python, learning MATLAB, building electronics projects with Udemy, reading University physics by Young and Friedman (only the electricity chapters), taking a class in Data Networks, and maybeee even learning Discrete Maths now! There are not enough hours in the day! I think I will split it all into 1 hour blocks and try to do each at least 3 times per week. Thanks for everything Dr Bazett, you're awesome! :)) P.S would this Physics book count? It is calculus based Physics.

[@DrTrefor]

That sounds like quite the summer!!

[@julioosorio604]

Hello Dr. Bazet, I am working on a work for my master's thesis nonlinear control and MPC but there is not much information, could you make some topics: Feedback Linearization | Input-State Linearization Feedback Linearization | Input-Output Linearization Greetings from Lima, Peru

[@bardock-yk2xg]

What a great video! Might start studying linear algebra this summer, any textbook recommendation?

[@DrTrefor]

I find most intro linear algebra texts all pretty similar so it doesn't matter too much. I do have a lin alg playlist on the channel so be sure to check that out!

[@tommyhuffman7499]

Great video!

[@djt6fan]

Dr. Trefor, do you have a suggestion on how to learn to read a math book? I could pick up a pure math book, but I probably wouldn't understand the majority of the proofs, and pure math notation. I understand mathematics on a sort of intuitive level, well enough to be able to use it to solve problems in engineering, which you can imagine, are really far away from pure math. I can't really understand stuff like epsilon-delta definitions for example, without watching a video that clearly explains what's going on. How does one build up to such a level, where I should be able to grapple a math textbook, and come out on top? A book on logic? On proofs? What's the first step?

[@DrTrefor]

This is actually kinda common and don’t feel bad at all about that. I think you should work through an introduction to the basics of sets, logic, and proofs. My discrete math playlist covers some of this, but you also want to be doing plenty of practice. With that foundation, you can then build up to more complicatied things

[@nobirapals974]

I recommend How to Think Like a Mathematician by Kevin Houston! It’s on my uni’s Foundation of Mathematics course. Maybe you’ll like it, it’s quite a light fun read!

[@DrTrefor]

Thanks for the recommendation, I’ll check that one out!

[@stevehof]

OMG, Game Theory is coming soon! YEEESSSSSSSSS!

[@DrTrefor]

I'm legit so excited. It is such a cool topic and is so rarely taught in math programs

[@Ash-bc8vw]

Looking forward to Game theory videos 😀

[@DrTrefor]

You and me both!

[@ItsTornHD]

Chaos by James Gleick is a fantastic book about chaos in math

[@DrTrefor]

Thanks for sharing!

[@maurocruz1824]

Hi Treffor. Any suggestion for Category Theory?

[@radwizard]

Do not skip on your skills over the summer. If you don't use it, you quickly lose it when you first learn something new.

[@DrTrefor]

Totally true!

[@nobirapals974]

I’ve been wanting to learn LaTex and Number Theory for this holiday but I’ve been postponing it with some Harvest Moon lol, thanks for the motivation!! (I’ll start tomorrow, promise😅)

[@DrTrefor]

Haha I’ll hold you to that!

[@bonifaceyogendran2294]

Just saw your comment. I made a comment above saying how I learned LaTex. I dedicated one summer to transfer my handwritten notes to digital. This helped me refresh materials and learn LaTex.

[@nobirapals974]

@@bonifaceyogendran2294 that’s a brilliant idea! Thanks for the suggestion lol

[@NeonArtzMotionDesigns]

Would analyzing the Rubik's cube algorithm to solve it be a good mathematical modeling project?

[@DrTrefor]

I love that idea! Many deep connections to various topics in discrete math there as well that you can explore for sure

[@xoxoxoxoxoxoxo6921]

before watching this video I've delved into complex analysis

[@DrTrefor]

Ooh that’s a good one. I actually want to make a series on this.........eventually:D

[@trexbattle]

I’m taking linear algebra as a web class at penn state, Show that the pure imaginary numbers (elements of C of the form 0+bi) form an additive abelian group. Show that they are a sub space of C as a real vector space.

[@elltwo8393]

Which resources would you recommend to learn some category theory?

[@DrTrefor]

One video series I've heard recommended (but haven't watched myself) is here: kzbin.info/aero/PLGCr8P_YncjVjwAxrifKgcQYtbZ3zuPlb

[@Satya1621]

Waiting

[@Enem_Verse]

Sir your videos are sooooo helpfull thank you soo much Sir please make some videos of statistics hypothesis testing

[@DrTrefor]

I do want to do some more stats for sure:)

[@mayukhmalidas]

Sir can you suggest some online free summer schools for maths ?

[@biomec5690]

What a great shirt! Where can I find one?

[@DrTrefor]

If you can believe it it was a random pizza shop in Denver called pizza pi, had nothing much to do with math

[@biomec5690]

​@@DrTrefor It looks like going to "Pizza Pi" in Denver will be my math summer project, then

[@marwanbasem193]

How can one contact you if he has an idea or wanna check a solution to one of his problems?

[@johnny3475]

I have a research training program in the summer. And then I start my directed study with the professor in fall. Any recommendations to learn Graph Theory?

[@DrTrefor]

That's awesome! I actually don't have a great resource in mind, but graph theory is a very standard subject and I know there is a tonne of interesting resources for you. Have fun!

[@LeBartoshe]

Great shirt. Hit the bell and smashed the like button.

[@DrTrefor]

haha, awesome

[@LeBartoshe]

@@DrTrefor Gotta keep the balance

[@Satya1621]

I’m looking for Matlab, Maple videos for Math

[@interest21stcentury74]

Thank You So Much for this academic year dr!!! I’m intending on learning about Graph Theory and Matrices in this summer, it is interesting for me, and like it’s said, that education is a lifelong journey and it isn’t constrained towards an institution. Now is when I know that Math is the most interesting thing to learn about and understand in real life. I now know things I didn’t expect to know in the first place. I hope your videos reach the world!! You got your support from Lebanon!

[@interest21stcentury74]

Sorry for the errors, I just finished my exams and english is my second language 😂😂

[@mathadventuress]

where do you get your tshirts??

[@mathadventuress]

@@williams322 just got your notification and I am still in the search for these amazing shirts.

[@aashsyed1277]

ok

[@MS-il3ht]

I basically forgot everything I "learned" in high school; including some algebra. So this is what I revise now. Taking logics classes has basically forced my brain into switching to a math degree next semestre...

[@DrTrefor]

That's cool! I think you are definitely not alone with a story like that. Wish we focused more on logic in HS.

[@MS-il3ht]

@@DrTrefor I agree. Thanks for your videos! - They have been incredibly helpful in changing my academic path and figuring the basics out so far.

[@hikmatullahpakhtoon3694]

I always thinking to study python C++. but as in undergraduate it seems like its impossible to study any of these language meanwhile this BS duration. Anyway Dr i am Physics student and i love your math tutorials.

[@DrTrefor]

Definitely possible to gain the basics at least working independently in your own time:)

[@hikmatullahpakhtoon3694]

@@DrTrefor thank you sir for encourage me.

[@adadnahahachaad1065]

Can you please suggest books about modeling for complete beginners? I have always wondered how people model things using math.

[@DrTrefor]

There is a great book by Bernardo Galvao-Silva

[@adadnahahachaad1065]

@@DrTrefor Thank you so much Dr. Iam honored by your reply

[@Coolblueocean2001]

Nice shirt on my favorite mathematician!

[@rodrigocortez5643]

Thanks for the disappointment pal, not even math can be saved from the woke ):

[@qadimonotheisttheasian24]

are you a homosexual? btw I liked your videos