It's Really Hard For Most People
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- Опубліковано 2 тра 2024
- In this video we discuss one of the hardest math subjects for undergrads to learn, Topology. We also take a look at a wonderful book titled Introduction to General Topology. It was written by George Cain.
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Thank you:)
topology looks so fun. I love the difficulty of advanced math
As someone who knows nothing about topology, I am glad you like it.
It is pretty fun. And based on such a simple idea.
Why what ifbthe topoogy.makes you frustrated and depressed. I need to feel like a math genius.
Haven't studied topology, but I really like the layout of the book - the old school style: definition, theorem, proof, example. And all with clean notation, no messy subscripts and superscripts flying around that get introduced for one section and then dropped for the next section because too many have accumulated. Unfortunately, clean layouts like these are hard to come by, especially in newer books.
can you do a video about the balance between reading and note-taking for advanced math? I can never decide whether or not to spend time refining very detailed notes from the textbook or just use scratchwork to get through proofs
I thought Hausdorff was that guy who Played KnightRider in the 80s TV series
No that would be Hasselhoff, he was also the guy who sang 'Looking for freedom' when the Berlin Wall went down. What a legend
I can say none of your videos are complete with out the Math Sorcerer book 'sniff' test!
The dedication must have been to his father. The George Cain that wrote this book taught at Georgia Tech thru 2001, died in 2015. Fall of 1988 I took real analysis from him. We used a book by Bartle. There were classes and a weekly 2-hour lab where he would have us work problems on the board and grill us on our methods. Towards the end of the course he called me into his office and asked me had he been too hard on me. I guess some of the other students had said something to him. I was sort of confused and told him no. I was an engineering student and it was my first proof-heavy math class, though not my last. Want to learn proofs, try writing it out and explaining it to someone that's as good or better at it than you.
The compositors have done a wonderful job on this book: typeface, layout, and print quality are all top notch. I'll bet it's pretty expensive.
I love your approach to learning, that if you're interested in something you can just dive in and get wet. I've never even taken a calculus course but I enjoy reading a bit of graph theory here and there and a bit of topology here and there.
So many ways to enjoy math as a hobby!
Topology by Muncrez sp? Wow, there is a section that states "now we are going to introduce a deep concept" 7 page proof. My first PhD course, ouch. Ucsc student but the prof was from UCB. I didn't shave, eat, and studied it 18 hours a day. I will never forget the class size was 2.
Here's me who have never heard of topology😂
Plus I am not even able to write a newborn proof😭
Does he mention why he focuses on pseudometric spaces? Do they have interesting examples that aren't metric spaces?
Doughnut = Coffee Cup: that's why Topology is so hard.
Do you offer tutor over zoom? I am trying so hard to understand this statistics class
Does it have the 3 Urysohn theorems: Lemma, Metrization, Extension?
Any chance of a video on studying Dynamical systems? i feel like its an area of math only some people see but for any university degree where you encounter differential equations it is criminal to not let these students study these systems and talk about the state spaces asosciated with them, showing them graphically where the solutions sit, writing ODE in standard form , using Lyapunov stability analysis etc ? im a 2nd year physics undergrad and im taking the pure math class of dynamical systems right now, would be interesting and pleasent to hear your insight on this topic!
Thank you so much for such inspiring videos....ypur videosare always awesome..please let me know how to study trigonometry... Thanks a lot... Sanvie from India
What school did you go to for undergraduate?
I would advise strongly against this book. This is 'old school' topology, at a time where students has a much stronger background.
Yeah a 1994 book is already old by today's very low standards, imagine books from the 50's etc. Look for more recent introductions, there should be many.
A very good book, with a lot of examples is Munkres Topology : you will get much more than you need to start Topology, but I think it works very well for an introduction text.
An 'old school' book that is very well written is Kelley's Topology... But again, you need some solid background.
Pseudometrics, for an introduction on topology is a big NO. It is a useless nuance for a beginner. Better start with any introduction text on metric spaces (or functional analysis) and go from there. Ypu can also see by the very good state of the book that Sorcerer did not study this book, did not try to do the exercises... Notice that this is the case for many of his reviews (some do point out to great references, that is the only reason I am a subscriber)
Would love to see your personal notes
Is a Hausdorff space just saying any two distinct points are isolated and that there exists a neighborhood around x that does not contain y?
What you described is called a T1 space, which is weaker than being a Hausdorff space (aka T2). For a Hausdorff space, you need _both_ x and y to have neigbourhoods which do not intersect one another. Another way to phrase it is that x has a _closed_ neigbourhood that does not contain y.
Here is an example of a T1 space that is not Hausdorff:
The underlying set is an arbitrary infinite set X. The topology on X is the cofinite topology, i. e. a set is closed iff it is finite or all of X.
Point set topology is easier than measure theory.
Hardcover $58
Paperback $191
yeah, ok.
i believe in the free consumption and distribution of knowledge. that's why you should definitely *not* use a crafty internet search or open archive to access most academic literature. remember do NOT do this
Not a very liquid market I guess…
@@keeganandre1708yup never do such a thing.
@@keeganandre1708 how else?
I don't enjoy the difficulties. I ended up learning some topology to understand some other things in quantum dynamics. Topology is important in fields.
Interesting 😮
How does he record this type of content tho?
Is this complex as in representing a complex system like the markets as matrices of a system of linear equations or leontief matrix that includes the government, or complex like what the heck did I just read?
Option 2. It's a whole nother animal.
Topology is not an intuitive domain, so people used to ingrained pattern recognition will struggle with the absolute logical reconciliation of it
I had difficulty with proofs. My pretend were weak. I got help from a book titled “The Art of Reasoning” by David Kelley. Well worth it.
topology is one of those things i use daily in my graphics programming but never have actually had to take a class for and do by hand
The book is too shiny.
Munkre's Topology... Smirking 😅
I found topology quite difficult; almost as difficult as real analysis.
For some one who can't wait you are certainly taking your time geting to it.
Why do I even watch this in english, I can't understand shit
Watch it in Spanish.
Math is an universal language ❤❤❤..
Is a cup a deformed donut or handcuffs 😂🧐🤪😵💫🤔🙃
Handcuffs = Genus 0: you're OK.
Handcuffs = Genus 1: you're in trouble.
Handcuffs = Genus 2: you're going to jail.
What you went through in the video is basic info, why would you need to prove it? It's union and intersection. It's kids stuff to be honest. It's so simple stuff and you're trying to make it like it's harder than calculus or you need background for it.
Watch out guys! Math genius over here
@@allthesepollitos8891 😜😂😁