6 Things I Wish I Knew Before Taking Real Analysis (Math Major)
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- Опубликовано: 29 июл 2024
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What I Wish I knew before becoming a Math Major!
ruclips.net/video/wk28BSaLszo/видео.html
Hey there. I am planning of taking a real analysis course but I'm so scared of the rigorous mathematical maturity involved in it. I am planning to get a leg up by looking at the material and seeing what I have to know. What are the main proofs techniques I can get a hang of in order to succeed in the course? I have only taken two proofs courses but I did kind of bad but want to get better.
Hi there, i find the book online. I haven't purchase yet; but before i do i want your opinion whether or not is it saved to take the course as independent study????
Thanks.....
@@youssephfofana9226 Analysis is a course worth taking from all possible sources. All your life. There's never can be "enough" of this only "true" mathematics.
@@briancannard7335 Thanks, good to know. I Wii immerse myself in different sources...
So what you do if someone has the problems you are referring to the start of the video how you overcome it?
Freshman Math Major: Calculus is cool
Real Analysis: I’m gonna end this man’s whole career
So true 😅
Man I’m taking astrophysics in university of toronto this is my first year and I took real analysis and man… I need help💀
I feel like this converges onto me.
@@priyanshugoel3030 uniformly.....and absolutely...
functional analysis and pde: im gonna end this man's life
Berkeley's Real Analysis class taught by Dmitry Vaintrob, just assigned this video as an introductory assignment haha!
Wow really?
@@BriTheMathGuy yeah haha, great channel!
@@suryaprakashvengadesan4930 Thanks very much!
Wish I had tour professor. My professor in real analysis didn’t know how email worked
@@walkerscoral damn, he must be a sad guy
Just took a real analysis exam with 20 proofs, 5 definitions, 10 T/F, 5 open-ended questions, and 3 T/F questions where you have to prove your answer. In an hour. Dropping out now. This was my last math course...
I knew all the material, there just wasn't nearly enough time to write everything.
Edit: I didn't drop out. After commenting this, I got angry because the prof said he didn't want me to pass so I studied hard and memorized every proof from 4 chapters of the textbook to do well on the final. Passed the course and I'm gonna graduate now.
What kind of professor would tell you they don't want you to pass? Are you in eastern Europe or something?
@@FsimulatorX Why eastern europe?
@@ToddlerAnnihilator666 From what I've seen from some online math groups, there seems to be a stereotype of certain areas and their math faculty, I couldn't elaborate too much as I don't quite understand it or have the experience to speak on it's validity
@@soupy5890 Ok you are indeed correct. I was lucky to attend uni with fairly down to earth staff/professors. But those that transfered from other unis say that to keep their employment rates (and other statistics) higher they purposely fail students after certain qouta has been met
Revenge arc. Inspirational.
This guy makes the first comprehensive beginner's perspective on real analysis that I've seen one semester AFTER I took it!
😅 i completed my masters in mathematics
15 years after graduating as a math major, i still have nightmares about those exams lol. No joke.
They're tough! Thanks for watching and commenting.
I took it 4 years ago (graduated with BS in Math in 2017) and had a nightmare last night!! I guess they'll never stop... sigh
What are you doing right now? As a profession.
I'm also pursuing bsc degree in maths.
The more practice with mock exam questions, the more your confidence grows. I frequently visit Mathematics Stackoverflow and MathOverflow, considerably the best hubs where I view tough exam-like questions and others' solutions. I learn much by brain-picking gifted mathematicians there. Don't mind me, as I am only an intermediate in mathematics.
@@pinklady7184 thank you for the advise, I will do the same now, that could have been added in the video.
The video is quite helpful. Thanks for the suggestions. Struggling with the real analysis right now. Questions are not super hard, but I'm nowhere near solving them. It's frustrating that after so many hours of hard-working, I still have a hard time writing down proper proof without oversimplifying or complicating things. Whereas my classmates are gifted, discussing recondite ideas with prof all the time.
I've definitely been there, it's part of the process. You can do it!
I'm actually kind of surprised to hear that (at least some) math programs use real analysis as the first proof-based course. At my school, they used the discrete math as the "intro to proof" course. As a computer science major, it was hard enough for me to pass this class when we were writing proofs about sets; I can't imagine having to throw calculus into the mix!
Agree on repeatedly failing and trying then finally getting it. That's probably the best thing that I gotten out of being a math major. There's no way I'm giving up on anything after completing my degree.
The secret to life baby!!
I totally feel you. The key here is really not giving up. I am taking analysis right now and it’s extremely difficult to me. But I still force myself to try again and again.
An undergrad course on topology without proper motivation *is* the killer.
It definitely can be!
It's killer with motivation also😂
Killer in what way?
For context I'm considering taking Real Analysis as my elective (mainly out of curiosity and for the challenge) but I've heard often that Topology helps a lot with understanding real analysis and should be taken before analysis.
@@FsimulatorX If the presentation is just abstact and formal, then you might ask 'what is all this, and what are the practical examples that lead to these definitions?' For example, the Euclidean space R^n is a prototype for a toplogical space. A well motivated book is Topology now! by Messer".
They taught us this course in our first year of university in 1998. It was a wakeup call for so many students!
I would love to see a top level summary of what you learn in real analysis and what it allows you to go into next.
I’m taking intro to Real Analysis this fall. So glad I found this video. Thank you!
Best of luck!
This subject really shook me in my first sem class. It takes so much time to absorb, and is just So different. Watching your video's making me realize how students first upon entering college-level math need to be given intro transition classes into each subject each semester. Like, u need some storytelling and constant context to get through that!
Thank you. This is a very interesting and useful video. The best of this sort I've ever seen.
Glad you enjoyed it!
Fabulous expression and ideas. Especially the 3rd of them which can make me more clear in proofing, I guess ;D. Thanks a lot~
The key tips are really amazing and helpful.I hope to see more of this
It's the first time I feel like I'm personally advised about going for a math major. Thank you.
Happy to help!
You sir talk the most sense.
Glad to hear it :) Thanks for watching!
I came here after crying my eyes out because of a real analysis assignment. I really wish I knew this beforehand, it’s so disheartening to be in a class where you feel so inadequate
It can definitely be a struggle. (especially at first) You can do it!
Great content. Thanks for sharing your insight
Thanks very much! Have a great day.
Being an undergraduate engineering student I didn't have an acquaintance with RA. I was really good at calculus, but RA kicked my butt when I got into grad school. I needed to strengthen my pure mathematics background for what I was into. And as you mentioned, it is NOT calculus. So I had trouble with the abstract nature of it. It still bugs me after all these years! And that is why I watched your video. Thanks.
Really cool, interesting advice, thank you!
My God, what you just said here about the essential importance of knowing definitions really opens my eyes to so much, not just in math, but in life and the world in general...
Definitions are so important as pointed out by my maths professor, who said that good defintions are 90% of the proof of theorems.
Thank You for your suggestions ✌
Thanks Bri! What you're providing are the axioms to have when you walk through the classroom door. That way, Real Analysis axioms are the second set of assumptions you learn instead of the first!
As someone attempting to self study real analysis, this is so useful! This entire video managed to put into words what I’ve felt for the past month. It’s been really hard to even do the most basic proofs, but this has given me some jump off points to speed up progress. Thank you.
It’s funny how big RUclips is. You are clearly doing a great job, you have videos that are well made and well targeted and raking in the views. This is the first video I’ve seen of yours. Keep up the great work!
I appreciate that!
thank you for spending your time to create this video.
so glad i was able to take geometry and abstract algebra before RA. i had never seen non-E geo before then, so that solidified the importance of definitions. the set theory and structural concepts of ab. alg. helped me get my mind right. RA was still a challenge, but it’s like i was looking at calculus from “the other side,” so i really felt like i was going somewhere in my math understanding
Thank you for this pep talk
Awesome video! Thank you!
Glad you liked it!
oh, I started real analysis book by myself just bc I found it interresting to learn something abstract myself PS: i am electrical engineer at high school. Nearly every question seems unsolvable while deffinitions are so simple and logic. I really felt stupid bc I couldnt proof such clear things like intersection with such simple deffinitions. But now I see that it's not that simpel as I though))))
Thank you so much!! Starting Real Analysis later today.
Best of luck!
I will be teaching Real Analysis this semester. In preparation to the semester, I was planning to find a tasteful video on the history of RA. Then instead I found this video! These things came to me naturally when I was once a student, so, I was blind to most of the issues. But by experience I know, these are exactly where my students may struggle. I will share this video with my students. They'll surely appreciate it. Thanks for the excellent video!
Best of luck to you and your student this semester!
Can ask this kind of math do have number or need to caculate anything or you just write proof
2:38 induction
definitions. alarm bells.
I remember when I was sitting in an upper-division class and remember the panic when the professor would right Defn. -
Now I understand. LOL
5:20 Start at what You know and The answer you want, meet the 2.
6:30 Notations, quantifiers, symbols,
Im in university right now as a maths major straight out of highschool and my first course is real analysis 3 weeks in right now. It has been tough.
Good luck work hard and perservere.
You can do it! Best of luck!!
You can do it! .. It IS hard to digest, but get yourself s many resources you can to understand how to deal with all the elements that make up the subject. Best wishes!
"I think 90% of a math degree is just straight not giving up"
PREACH!
Do you have any tips on how to (improve) remember(ing) math theorems and definitions? Most of the times I sort of get the point of how you can use it and understand what it does, yet I always struggle to memorize the more precise/small parts like for example some given requirements, preconditions or exceptions.
Good question.
I think it's achieved by solving problems
You gotta understand certain concepts at a very fundamental level
Real analysis was by far the most troubling undergrad math course I've taken as a math major. Don't know why I still have the textbook I don't understand 95% of the text lol
I took Set Theory before Real Analysis I, and it was immensely helpful
I bet it was!
Any books on proofs technique you can recommend??? Great video
@@youssephfofana9226 I had a skinny little (80 pgs or so) book called Set Theory that was used in class. Sry can't remember the author but it might've been my prof (last name Bradley). Very concise explanations on axioms, (well) ordering, proof by induction, etc
@@benno291980 plz can u be more precise about the book...i could not find it. Thanks...
@@youssephfofana9226 looked it up; it's called "Naive Set Theory" by Paul Halmos
Here's a nugget: Take Set Theory if it's offered or study it on your own. This is like the "introduction" to Real Analysis. This will get you thinking about the abstract logic when studying real numbers and knowing how to "speak the real analysis language" when it's time to discuss integration and differentiation utilizing sets because you're not going to be computing hardly anything, but writing nothing, but proofs and more proofs
My university does not offer a set theory course but it does offer an Intro to mathematical concepts/proofs course that covers logic, proofs, sets, functions, relations and number theory.
any book suggestion?
or just the naive notions of set theory, not to the level akin to filters&ultrafilters
Is Algebra (not just Linear Algebra) necessary for studying Ananlisis?
Great video, I graduated from my math BA program in January and many concepts that were still fuzzy are finally starting to click now and it happens at the most random times so I would agree that persistence is key, I don’t think I would have done well in Real Analysis if I had not taken a proof course first. Set theory is your friend 🙂
I come back to this every time the textbook feels like its killing me
But 50% of the screen was literally unused the whole video 😂
Is that supposed to be some metaphor!
Thank you very much for your valuable ideas...
You're very welcome. Have a great day!
watching this when im gonna have my finals tomorrow
Best of luck!
Finals during Pandemic..Nice
Knowing, not just understanding, but knowing definitions verbatim, agree 100%. It was the thing I had the hardest time finally understanding.
Thank you sir for this effort
Hi!! How much time should i spend working in a proof based problem? What do i do next if i cannot solve it?
Can you please suggest any good online video on proofs of mathematics. And how to approach them as a beginner . Is the approach different from what I have been doing while studying till high school.
If I ever have to teach a course on Real Analysis, this video is going to be on the syllabus
Thanks so much!
1) The real Analysis course is nothing like a Calculus course. It's logistically rigorous and proof-based. It's not taking derivatives, factoring, plugging, etc.
2) Be familiar with some proof techniques, such as mathematical induction.
3) Be extremely familiar with definitions: definition matters. You need definitions to start a logistic proof that your professor like.
4) Write down the definitions you know and write down what you want to prove (the conditions and the conclusions). It can be a great way to trigger a correct proof.
5) Be familiar with logistic quantifiers, all kinds of notations.
6) Persistence is key. You have to stick to learning and trust yourself. Never giving up is important to nail this class.
Good Content. I agree with your point.
Thanks for watching and have a great day!
Really helpful . just started my Msc in Maths
I hated that I didn't know proof as well as I needed, so I took a break, studied a HUGE amount of proof-related material. It's an advantage you have as an older student where you don't care how long it takes to graduate. My goal was simply to not complete a course/class unless I considered myself to have mastered the material.
It means that for every epsilon greater than 0, there exists an n in the Natural Numbers such that for all n greater than some k (also a natural number), then the absolute value of the sequence (X_n) is less than epsilon. There!
I enjoy your videos Prof. How can i set up that kind of board you write on?
I read and went through all the questions from Richard hammock's book of proof. I don't know if this is the same this as pure logic, but it is beautiful. To me, real analysis sounds like it builds on the bones of logic. But what kind of course or subject lies at a deeper more fundamental level. Like the three rules of thought and a proof for the existence of truth.
At 6:49, you mention taking an "introductory proof class to understand real analysis". Can you please recommend any book or materials that one can review? Thanks,
„Book of Proof“ „How to prove it“
Bartle and sherbert is fine
Does that mean you gotta memorize definitions (as in verbatim)?
Currently doing a major in applied math and computer science and Real Analysis was one of the most dreaded courses. Unfortunately got stuck with Real Analysis, Complex Analysis and Stochastic Processes all in one semester haha. But who doesn't love a good challenge ;)
lol how did it go man? I'm thinking of taking real analysis, abstract algebra and stochastic processes on the same semester. Complex Analysis sounds dreadfully worse though XD
Yes, yes, his point number 4! Sometimes, just start "Since, (definition) and (definition), then because of .... we see that (conclusion.)" Write this in "math" to practice. Trust me, you will be on your way.
Lol watching this one day after my real analysis exam has me like, wow....CAN DEFINITELY RELATE!!!
By the way, you're the one who taught me what a topology is. Absolutely love your video on that, it was extremely helpful and I love this video.
It's ℝeal lol.
It's sorta sad the way the math program is made though, before this level, no one will know what's about to hit them. I only knew that everyone said they "hate" real analysis. Never heard nor saw anything else about it. Now I understand that it's an analysis based course, which I kinda like tbh, and kinda hate.
I loveeeeee finding solutions to problems lol it makes me feel like a jackpot winner LOL, but on the other hand, I HATEEEEE all of these seemingly random, yet connected and absolutely necessary theorems and definitions.
I stopped counting them when we hit topology. LOL.
I do however have a very LONGGGGGG list of almost all of the definitions and theorems stockpiled into a MS Word document hahaha...
Crazy stuff.
Tbh, Advanced Calculus was much harder for me than ℝeal analysis because at least by the time I hit ℝeal analysis, I was already exposed to a great many of the definitions that we would need to use.
How was your 2nd Real Analysis class compared to your 1st one? I did really well in my first class (my school calls it Advanced Calculus 1), and I start the 2nd class of the sequence next week.
How did the second one go?
Hello Sir, I too have problem in proving ,your advice gives me direction what to do
Hii, can you a video/series on introduction to proofs and like the basic understanding which we should have as you mentioned in your video.
Re. Real Analysis vs Calculus sequence:
In some teaching sequences, Real Analysis is taught _before_ Calculus. There is a certain logic in doing so, theory before application. Hence why Calculus was usually feared being the final class taken. In the most of US (United States) for the last 40 (or 50?) years, that is reversed because more practical teaching that way.
In Mathematics Departments' defense, they are teaching to a much larger audience than potential math majors; Chemistry, Physics, pre-med, econ, engineering, Comp Sci, and possibly any other are all required having mathematics, and in most cases, Calculus and Differential Equations. So makes much more sense that the first year(s) courses are calculus then switch to the more rigorous theoretical framework of upper division (junior & senior level) classes which are geared specific toward math majors. Unless one is doing Harvard's Math 55, they are not likely to study Real Analysis in their first year.
In my current undergrad experience its interesting the courses which definetly are built upon complicated niche rigorous proofs are often the classes where you arent required to do those proofs, because many students who find calculus appealing end up reaching into areas like differential geometry and geometric calculus those courses are often taught at the undergrad levels with out too many proofs even tho there “past” calculus they require real analysis to work
I agree with you about not giving up and persisting. Sometimes the first encounter with some new material is like hitting an impenetrable wall. You have to persist in battering that wall, until it gives way to your understanding.
Not giving up is the key! Can't tell you how many times I had to repeatedly stare at problems or theorems before I could get my head around it.
@@BriTheMathGuy When I first tried abstract algebra I saw the material and just about had a panic attack. I am not ready for it yet. I am brushing up on my fundamentals first before I try again.
Very good advice.
Glad you think so!
trying something different this semester by starting early since am bored,thanks for tips but am looking for content to learn.
1:47 what are the other two?
Issue:
What is a differential of an irrational argument?
Let a= some rational approximation, and A be the irrational number itself (if that makes sense).
Then A - a > dA and there is no way a + dA > A
that was a great vid!
and so many professors play down teaching what proof techniques are
Thanks very much for saying so and watching! Have a great day.
Hi , if anyone would recommend some books for kind of beginners in geometry, algebra , and in analysis... need them soooooo much
IM IN MY FIRST YEAR THANK U FOR THIS VID IT MOTIVATED ME A LOT
I did Real Analysis some 25-26 years ago & I still get nightmares about it every now & then. But I’ve learned to appreciate it more over the years.
Taking PSU MATH312H (Intro Real Analysis) right now so the timing of this video was perfect
Good luck.
I am in Real Analysis now :) And I am elated with the concept of convergence and the Topology as well! I am fond of Topological Groups!
This Video Is Very Helpful For Those Students Who Are Going to Study University level Mathematics
Sir, can you recommend an introductory class for proofs for analysis.
About the sandwiching "technique" that is mentioned here: I remember using it in Euclidean Geometry in my early teens. Then I considered it natural so that everyone should be using it. I tried to teach it to one student two years my junior, but it seemed easier said than practiced for him.
hey could someone help me with this, my goal is to be able to understand stochastic calculus one day. in order to get there I know probability is a must, and to understand probability in depth as I read on blogs I understood I need measure theory. SO, in order to be able to do measure theory do I need to take some proof theory classes? and in order to do measure theory do I need real analysis?
damn someone please throw some light down this rabbit hole!
You don't necessarily need proof based classes, but in my opinion you should certainly know real analysis before you delve into measure theory. The reason for this is not really that real analysis is a prerequisite for measure theory, but that you will understand measure theory MUCH better and deeper if you know real analysis.
I had a master of science degree in mechanical engineering and even had taken two graduate course in Classical Mechanics and Mathematical Physics when I decided I wanted to get a masters degree in mathematics. Real Analysis was the first course. I was blown away and had to drop it. I wish this video had been around all those years ago! It was like approaching math in a completely different way. I just couldn't wrap my head around it.
I'm a freshman in an introductory proof course, and I have a feeling that this will really help me out later on
I hope it does. Best of luck!
What's book do you use for introduction proof???
The name and the author precisely the ISBN# will be great. I'm looking forward as independent study.
Thanks...
@@youssephfofana9226 hmm I don't have the ISBN, but it's called "Analysis with an Introduction to Proof" by Steven Lay. Here is the link: www.pearson.com/store/p/analysis-with-an-introduction-to-proof/P100001370585/9780321747471
Does it also apply to people who r into theoretical physics?
Nice and very valuable vedio thanks a lot
Proofs class first. Definitions, yes!
This was so helpful.
Velleman's How to Prove It opened the world of math to me. I thought I'd need proofs for Calc 1, but aside from delta/epsilon🤷♂️ Everyone should be obliged to take a course based on Velleman before embarking on a math major. He goes thru symbolic logic, quantifiers, everything.
is there a problem with sound volume?
Maybe - hope I've fixed it.
1:50 what are the big three areas: Algebra, Analysis and... Geometry? Statistics/Probability?
Number theory
I want good books for real analysis,which books do you recommend for students?Thank you
Personally I like this one: (here is a video review I did of it)
ruclips.net/video/1mxaWclWtH4/видео.html
Love your content sir one more thing i want to ask that what was your phd topic umm just asking usually 😅
I’m taking real analysis this next year, and I feel relatively good with the things you mentioned since I’ve already taken an intro proofs course, and 2 abstract algebra courses. The only thing that worries me is the fact that I haven’t taken any type of calculus in 2 years. But nevertheless I still feel confident.
you don't really need to 'know' calculus, but it does help knowing calculus so that the motivation behind learning analysis is there. When you know the end goal, you gain a greater appreciation for the machinery they build up in the class.
So how'd it go?
Real Analysis as the FIRST proofs-based course? That's insane, I had my own introduction to proofs class and apparently talking to some computer science students my introductory class was three discrete math classes combined. Then I picked up a Real Analysis book to see what it's like and the first Unit just casually summarized everything I learned in that class. I'm still trying to read the book; it's intense and the exercises are brutal, but I find RA VERY rewarding. I was forced to switch Real Analysis with Abstract Algebra and Probability Proofs for the upcoming year, but hopefully I can take RA soon.
I can relate every bit of word you said .
One of the most difficult thing for me as a beginner is to use mathematical definitions to proof certain theorems...these theorems makes you realize that you don't know the actual meaning (essence) of the topic.. 😑😑
Can anyone provide a list of good analysis texts for self-study ? Thanks for any & all suggestions.
Spivak - Calculus (pretty challenging problems, great writing. I used this way back when I first learned analysis)
Abbot - Understanding Analysis (This is easier and arguably better if you wanna use it for self study. The author motivates real analysis from the paradoxes and hard problems that may arise from regular calculus)