Real Advanced Mathematics
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- Опубліковано 28 кві 2024
- We go over a mathematical proof where we discuss the definition of a Ring. This is really cool and it can help you. We look at the amazing book by Hungerford, it is titled Algebra. Amazing Book on Abstract Algebra!!
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Thank you:)
Abstract algebra is so cool 😎
I love Abstract Algebra also:)
Thank you for your comment!
Your videos are the best! You have inspired me to study math, and I want to study mathematics or physics as my career.
Yeah he also gives a clear explanation on his videos
I love this particular proof. I remember studying this and thinking why such an obvious thing is being proved. Thanks for sharing!
the only guy on youtube who makes math intresting!
Been doing ring theory all day (using Fraleigh), great book, especially the exposition on the fundamental ring homomorphism theorem
Was just doing some ring theory yesterday!
Looking at this and other "higher" math, we see the great emphasis on formalism and an axiomatic approach -- always with proofs. And so often proofs aren't necessarily proof in the everyday sense, rather, more of a picking apart and analyzing of why something works. With the proof you just showed we get a deeper sense of how things hang/hold together and bootstrap themselves up into more powerful abstractions and generalizations. But I worry about K-12 math. No explanations of the abstractions. Zero formalism. It's like visiting a circus where they turn you into the circus animal doing conditioned tricks. You never understand why or what, instead, just the old "When you see this, do this." Tragic.
i will never understand why u need to prove why a triangle is a triangle lol
@@thetester7988 A proof is using logic. With logic, ephemeral intuitions become traceable, reliable -- on paper, then out in the real world. There's no end to the amazing things you can find in math.
Waiting for the Alcubierre Drive.
Hi, Math Sorcerer. Can you make a video on the Darboux's theorem? I really love your explanations and just finished your integral course on Udemy. I'm now looking to advance my Calculus knowledge.
OK. You inspired me to do something new. I had not studied math since 1970 - not that I remember anyway - and I always regarded mathematics as something esoteric, something that I never really needed and never would need. (Like illiterates, innumerates are experts at conceilement.)
Then I heard you talking about doing mathematics for the hell of it, because it's fun. because it's beautiful, and because it's worth doing for its own sake. I spent two weeks in a short course for Accuplacer Math, took that test, and tested into College Algebra. I registered for that class today at our Community College - ten weeks in the summer term. So, all that fretting about it taking years to run that oh-so-hard High School Algebra gauntlet was all for nothing. That could be done in two weeks. My unrealistic goal is to do "hard math" - and to give me a target, I want to do calculus based Physics next year. I'll give myself a year to learn enough math to be able to do that. What I like about math is it helps me focus. I have a short attention span and am very distractable but I can do math for hours... . I kinda wish I'd discovered this in 1970. Thanks, Math Sorcerer. Great channel, too!
I’m retaking trig bc I failed. I need to know how it feels to effectively learn. To retain, to recall, to make use of what was learned and compound as you go deeper into math.
What's the best maths book for jee advanced preparation?
What do you think about measure theory? I'd love to see some videos on that topic, focusing on the intuition/motivation part rather than formal proofs.
Hello The Math Sorcerer. I'd like to ask you what you think about the book "Engineering Mathematicsr" by K.A. Stroud & Dexter J. Booth. I'm self-learning math and I'm currently using this book. What do you think about this book?" is good for beginners?
After studying both real analysis and abstract algebra. I'm convinced abstract algebra is a lot harder (except for topology on R in real analysis)
I have to agree! Analysis seems hard but it easier than abstract algebra once you start getting deeper
@@Coffeyhandle exactly! For me it came down to absolute value inequalities and epsilon delta definitions. After that it's a lot easier to get through
@@PodcastClips910but measure theory persists!
@@Coffeyhandle never heard of this area of mathematics but I'll take your word for it. I want to take algebraic topology tho, do you have any thoughts on that? I read on math stack exchange that it can be brutal lol
Product of sums = sum of sums = nested for loop 🧐
Make a video on your book collection
Can a person in his thirties who is self-taught in mathematics (who has not obtained a bachelor’s degree in mathematics) obtain a doctorate in pure mathematics and work in the field of research?
Only if you believe sir
God, I love this channel
Abstract algebra is my thing. Did everything undergrad can do for credit
I feel lucky that I get to end at abstract algebra, and even that's being generous since its not required
Can you please do a podcast with Chitrang murdia, mit graduate and phd from Uc Berkeley. He is a physicist and also mathematician hailing from india. He had also won gold medal at international physics Olympiad back then in 2015. Please do a podcast with him on beauty of physics and mathematics. I think you can get his contact email or something on Google.
yaa
This so cool
Principia Mathematica by Bertrand Russell and Alfred Whitehead. Next perhaps...?
That's some heavy lifting!
I'm doing abstract next semester. Wish me luck!
I had that book for abstract algebra but it was thiner and less brown at university. Groups are alright never really got on with rings.
Can you suggest an affordable proof writing book
"how to prove it: a structured approach" is the book the math sourcerer generally suggests, but proofs by Jay Cummings is cheaper to buy brand new and its really good too
I'd suggest not getting a proof book and rather studying the book you want to read, you'll learn it over time
Library should have books.
Discrete math by Rosen, I think it’s free online, or likely cheap to find a used copy
One of the best books that looks at proofs from a procedural viewpoint with full explanation is "How to Read and Do Proofs" by Daniel Solow. It is supported by a series of Video's that consolidate the material in the book. The book contains examples and a lot of exercises for each method. Answers to the odd numbered exercises are provided via a URL to a library of solutions. Finally examples are taken of well documented proofs from all areas of mathematics, Geometry, Number theory, Analysis etc., Well worth a read.
Im watching this video and I dont know anything about advanced math. My most hardest math class was pre algebra lol
Are you the type of man who has sacrificed their life for the sake of maths and science?
LIKE EINSTEIN?
Volume in this vid is lower than your usual...
Absurd book , impossible to learn from.