6 Things I Wish I Knew Before Taking Real Analysis (Math Major)

🎓Become a Math Master With My Intro To Proofs Course!
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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.

[@BriTheMathGuy]

What I Wish I knew before becoming a Math Major! kzbin.info/www/bejne/rZyVaXWJlrGmsNE

[@dewman7477]

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.

[@youssephfofana9226]

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.....

[@briancannard7335]

@@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.

[@youssephfofana9226]

@@briancannard7335 Thanks, good to know. I Wii immerse myself in different sources...

[@kafrikotroll8610]

So what you do if someone has the problems you are referring to the start of the video how you overcome it?

[@jkim715]

Freshman Math Major: Calculus is cool Real Analysis: I’m gonna end this man’s whole career

[@joshuaramseur]

So true 😅

[@Abdulrahman.Knakriah]

Man I’m taking astrophysics in university of toronto this is my first year and I took real analysis and man… I need help💀

[@priyanshugoel3030]

I feel like this converges onto me.

[@citizencj3389]

@@priyanshugoel3030 uniformly.....and absolutely...

[@symptomesdelau-dela5442]

functional analysis and pde: im gonna end this man's life

[@suryaprakashvengadesan4930]

Berkeley's Real Analysis class taught by Dmitry Vaintrob, just assigned this video as an introductory assignment haha!

[@BriTheMathGuy]

Wow really?

[@suryaprakashvengadesan4930]

@@BriTheMathGuy yeah haha, great channel!

[@BriTheMathGuy]

@@suryaprakashvengadesan4930 Thanks very much!

[@walkerscoral]

Wish I had tour professor. My professor in real analysis didn’t know how email worked

[@devd_rx]

@@walkerscoral damn, he must be a sad guy

[@korbinmdavis]

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.

[@FsimulatorX]

What kind of professor would tell you they don't want you to pass? Are you in eastern Europe or something?

[@ToddlerAnnihilator666]

@@FsimulatorX Why eastern europe?

[@soupy5890]

@@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

[@ToddlerAnnihilator666]

@@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

[@questionable420]

Revenge arc. Inspirational.

[@WithASideOfFries]

This guy makes the first comprehensive beginner's perspective on real analysis that I've seen one semester AFTER I took it!

[@suryavarmanl9086]

😅 i completed my masters in mathematics

[@spydanig]

15 years after graduating as a math major, i still have nightmares about those exams lol. No joke.

[@BriTheMathGuy]

They're tough! Thanks for watching and commenting.

[@malloryabramovitz2238]

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

[@sarthakchavan9676]

What are you doing right now? As a profession. I'm also pursuing bsc degree in maths.

[@pinklady7184]

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.

[@entropyss]

@@pinklady7184 thank you for the advise, I will do the same now, that could have been added in the video.

[@christopherallan4298]

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!

[@Lola-wq9hn]

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.

[@BriTheMathGuy]

I've definitely been there, it's part of the process. You can do it!

[@nievsbest]

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.

[@benjaminhogan3157]

The secret to life baby!!

[@jiachen8353]

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.

[@xjuhox]

An undergrad course on topology without proper motivation *is* the killer.

[@BriTheMathGuy]

It definitely can be!

[@prem7676]

It's killer with motivation also😂

[@FsimulatorX]

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.

[@xjuhox]

@@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".

[@adanice49]

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

[@BriTheMathGuy]

It can definitely be a struggle. (especially at first) You can do it!

[@RamiSahyouni]

They taught us this course in our first year of university in 1998. It was a wakeup call for so many students!

[@frankduffy9271]

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.

[@tanya08cjm]

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!

[@robertlihou5780]

I’m taking intro to Real Analysis this fall. So glad I found this video. Thank you!

[@BriTheMathGuy]

Best of luck!

[@entropyss]

It's the first time I feel like I'm personally advised about going for a math major. Thank you.

[@BriTheMathGuy]

Happy to help!

[@benno291980]

I took Set Theory before Real Analysis I, and it was immensely helpful

[@BriTheMathGuy]

I bet it was!

[@youssephfofana9226]

Any books on proofs technique you can recommend??? Great video

[@benno291980]

@@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

[@youssephfofana9226]

@@benno291980 plz can u be more precise about the book...i could not find it. Thanks...

[@benno291980]

@@youssephfofana9226 looked it up; it's called "Naive Set Theory" by Paul Halmos

[@jaredngota289]

The key tips are really amazing and helpful.I hope to see more of this

[@weltonspratley4367]

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

[@FsimulatorX]

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.

[@jhonybraavo]

any book suggestion?

[@spiderjerusalem4009]

or just the naive notions of set theory, not to the level akin to filters&ultrafilters

[@georgesealy4706]

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.

[@luoduwz9789]

Fabulous expression and ideas. Especially the 3rd of them which can make me more clear in proofing, I guess ;D. Thanks a lot~

[@antonbashkin6706]

Really cool, interesting advice, thank you!

[@dhickey5919]

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!

[@surrealistidealist]

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...

[@asifmahmud5646]

Great content. Thanks for sharing your insight

[@BriTheMathGuy]

Thanks very much! Have a great day.

[@Therock151214]

You sir talk the most sense.

[@BriTheMathGuy]

Glad to hear it :) Thanks for watching!

[@RandyKing314]

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

[@davidbrisbane7206]

Definitions are so important as pointed out by my maths professor, who said that good defintions are 90% of the proof of theorems.

[@alex_8704]

Thank you. This is a very interesting and useful video. The best of this sort I've ever seen.

[@BriTheMathGuy]

Glad you enjoyed it!

[@garvitgupta8485]

Thank You for your suggestions ✌

[@Anothercrazytoo]

thank you for spending your time to create this video.

[@moglie2904]

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.

[@kirstentrimble379]

Thank you for this pep talk

[@tauceti8341]

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,

[@user-yk7jk4lh9p]

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))))

[@ilovetiananmen]

Awesome video! Thank you!

[@BriTheMathGuy]

Glad you liked it!

[@sieni221]

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.

[@alexandertownsend3291]

Good luck work hard and perservere.

[@BriTheMathGuy]

You can do it! Best of luck!!

[@tanya08cjm]

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!

[@haskaru3777]

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!

[@BriTheMathGuy]

Best of luck to you and your student this semester!

[@trongtue8384]

Can ask this kind of math do have number or need to caculate anything or you just write proof

[@brandonzappanti4330]

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 🙂

[@johnroy4424]

Thank you so much!! Starting Real Analysis later today.

[@BriTheMathGuy]

Best of luck!

[@JoelRosenfeld]

It’s funny how big KZbin 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!

[@BriTheMathGuy]

I appreciate that!

[@rickt10]

Knowing, not just understanding, but knowing definitions verbatim, agree 100%. It was the thing I had the hardest time finally understanding.

[@ssss855167]

Thank you very much for your valuable ideas...

[@BriTheMathGuy]

You're very welcome. Have a great day!

[@ofb12345]

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

[@theunknown4209]

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.

[@Chrissymae1]

"I think 90% of a math degree is just straight not giving up" PREACH!

[@luyombojonathan6688]

Thank you sir for this effort

[@MathematicsforU]

Good Content. I agree with your point.

[@BriTheMathGuy]

Thanks for watching and have a great day!

[@PhrontDoor]

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.

[@CalBruin]

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.

[@maxwellmogadam399]

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

[@neon75105]

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!

[@kagayakuangel5828]

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.

[@newyorkguy158]

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.

[@BriTheMathGuy]

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.

[@alexandertownsend3291]

@@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.

[@fouzuliffath3057]

Really helpful . just started my Msc in Maths

[@ishaangoud3180]

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!

[@aryankumarprasad1574]

If I ever have to teach a course on Real Analysis, this video is going to be on the syllabus

[@BriTheMathGuy]

Thanks so much!

[@siamrahman1409]

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 ;)

[@FsimulatorX]

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

[@nahidhkurdi6740]

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.

[@natashadavina7592]

watching this when im gonna have my finals tomorrow

[@BriTheMathGuy]

Best of luck!

[@parthasarathidash8061]

Finals during Pandemic..Nice

[@YamahaC7SRG]

Great video. Here's what you must know before becoming a math major. Real Analysis (aka 'Advanced Calculus') is usually the first proof-based course in college and it isn't normally taken until FAR TOO LATE to realize you don't understand proofs at all and you may NEVER be able to handle proof-based courses, making a math degree effectively unattainable for you. Real Analysis is usually taken in your junior year and these proof-based courses make up your last two years of college yet they are a COMPLETE CHANGE OF DIRECTION from what you thought math was all about. It's almost criminal that this isn't revealed and emphasized EARLY ON in college, but it is not. Math profs at university have pure math PhDs and were born knowing how to do this stuff (no kidding). They assume you are the same. College advising sucks and no one will tell you the following. Being good at 'plug 'n chug' will not help you with proofs. You can be an A+ student in all calculus courses and fail proof-based courses such as Real Analysis. If you happen to be reading this before it's too late, get Laura Alcock's book 'How to Think About Analysis' and STUDY IT CAREFULLY. If you can't follow her material, you are probably in the wrong major. Her presentation is, by far, the best I've seen. Even applied math majors will normally get a big dose of proof-based courses that may stop them - dead in their tracks. Get lots of help or change majors, NOW! Asking the prof for help is a waste of time. Get online and find someone on Wyzant or something like that who is good at pure math and do one-on-one tutoring. But, good luck! If you can't do proofs, a Math PhD is not going to happen. So, even if you complete an Applied Math program, you better have computer science skills in order to get a job in a relevant field (except teaching public school). You won't be teaching at University without a PhD in math.

[@xHannaHx33]

Stoooop u r gonna make me cry 😭😖😫 I’m taking it rn!!!!

[@YamahaC7SRG]

@@xHannaHx33 How is it going?

[@xHannaHx33]

YamahaC7SRG it is the 2nd week and I’m lost 😭 can’t find good KZbin profs that explain it well!!!

[@YamahaC7SRG]

@@xHannaHx33 What book are you using and what section are you lost on? If I can find the book online, I'll take a look at the section. Remember, get help ASAP. Don't wait. Perhaps try Wyzant. Upper level math is not commonly found on KZbin. If this is your first 'proofs' class, it will make or break you.

[@xHannaHx33]

YamahaC7SRG AFriendlyIntroduction toAnalysis (2nd edition). It’s my first proofs class and it’s online which honestly isn’t helping. What’s wyzant??

[@andresarroyo1809]

I come back to this every time the textbook feels like its killing me

[@davidbrisbane7206]

Very good advice.

[@BriTheMathGuy]

Glad you think so!

[@supremegalacticcommander2783]

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.

[@sanjursan]

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.

[@jonatankelu]

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.

[@tmendoza6]

that was a great vid!

[@tmendoza6]

and so many professors play down teaching what proof techniques are

[@BriTheMathGuy]

Thanks very much for saying so and watching! Have a great day.

[@ahmedhasabo6647]

Nice and very valuable vedio thanks a lot

[@richardxue1506]

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.

[@MadScientyst]

Having accomplished 2 Math Degrees so far...I highly recommend a std Web Search for: 'real analysis prerequisite courses', reason being that there are a couple of basic lower-level Math courses which WILL help greatly such as: *Discrete Math (emphasis on Logic & Induction, Boolean Algebra, etc) *Abstract Algebra I/II (sometimes called Mathematical Methods in undergrad programmes) *Introductory Analysis (basic methods of proof, etc). However, apart from these there are the more 'specialized' courses route such as: *Advanced Linear Algebra *Set Theory *Point-Set Topology In hindsight, I presonally summarize Real Analysis as (Advanced) Calculus I-III using R.A. methods & similarly for my personal Major & all-time favorite topic 'Complex Analysis,' Calculus I-IV using C.A. methods. Footnote: make no mistake, these advanced 'Analysis' type courses require committment, dedication & HARD WORK to SUCCEED! Be prepared to FAIL (& YES I failed, did a few repeats along the way), but KEEP practising as commented in this Video. You'll eventually appreciate the sheer beauty, mystery & wonder of the mathematical Universe...as I have. So, good luck on your journeys, my mathematical friends!!

[@Skylitzz_]

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.

[@whydontiknowthat]

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.

[@nias2631]

So how'd it go?

[@heyo8674]

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.

[@valentinlishkov9540]

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

[@Dhruvbala]

I'm a freshman in an introductory proof course, and I have a feeling that this will really help me out later on

[@BriTheMathGuy]

I hope it does. Best of luck!

[@youssephfofana9226]

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...

[@Dhruvbala]

@@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

[@joshuaisemperor]

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.

[@kingwoomy8781]

Good question.

[@pianoforte17xx48]

I think it's achieved by solving problems

[@moeyali123]

You gotta understand certain concepts at a very fundamental level

[@jacktrainer4387]

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.

[@sevenkaylive]

But 50% of the screen was literally unused the whole video 😂 Is that supposed to be some metaphor!

[@audience2]

Agree with this completely. I was just thrown into real analysis (it was my very first lecture in university) and had to painfully realise this myself as the lecturer didn't say it.

[@SHAKTISINGH-fj1bf]

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.. 😑😑

[@jahnabidas108]

I watched this video before starting the real analysis course so I couldn't understand what he was talking about back then. Now, 2 months later, I can understand and relate to each and everything he is saying. I followed what he told and I can say I am starting to get a grip, still very very very far from the end but I am moving atleast. Edit: I think I'm gonna fail this semester 😭

[@VSS031]

Update???

[@DouglasHPlumb]

I couldn't do it in university - it was my 8th class, I had 7 other courses. The pressure was too much so I dropped it and the idea of getting a double major in math and engineering. Without the pressure I now use it to escape the insanity around me and find it very interesting - lots of little puzzles but no harder than puzzles you would find in a book of puzzles. Of course, a book of puzzles is a waste of time since you can get the same pleasure and learn something practical and useful like real analysis. If you take your time, it's not that hard - stop at something you don't understand until you do - if that takes a week, no big deal. I don't know why anyone would solve puzzles when a desire to be challenged can be met with so many useful subjects like philosophy and math and these really develop your mind. You know it's working when you start to find sitcoms and movies boring. I'm 56 and can still learn this kind of stuff although it is harder than when I was in my twenties.

[@Tuffadandem]

I have 4 semesters of Real Analysis in my degree. I'm on my third. To be honest with you, Real Analysis is the toughest course I have ever done.. My proof Kung Fu wasn't really good on starting Real Analysis, so I struggled, A LOT. I think I'm kinda getting it these days though.

[@davidorndorf306]

Taking PSU MATH312H (Intro Real Analysis) right now so the timing of this video was perfect

[@georgesealy4706]

Good luck.

[@infinimente]

This channel is Gold.

[@BriTheMathGuy]

Thanks very much!

[@jpnesseth]

All of this is why they should teach Real Analysis *before* Calculus. If you're balancing a checkbook, you don't need Calculus. However, if you're using Calculus, you need to understand the tools you're using.

[@marcustumelomakofane4578]

everything you just mentioned I already learnt in my first year in extreme detail… I go to Nelson Mandela Metropolitan University. Real Analysis was literally a walk in the park

[@kevinsmith2349]

I took Real Analysis in the early 80's and I wish I had this video to watch back then before I took it. I honestly was not ready for it and the prof (who wrote the textbook) never really gave any overview on the topic or discussed any of the techniques required to do the proofs. He kind of assumed we knew how to do "Proof by Contradiction" or "Proof by Induction" etc. In fact, one of our assignments was to prove the Dedekind Cut Theorem. I think everyone got lost on that one.

[@chinmaypadhan5936]

I can relate every bit of word you said .

[@RajSingh-oz5zq]

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.

[@alexbyard9358]

My freshman math class was on functional analysis and measure theory

[@sam-eg7ff]

IM IN MY FIRST YEAR THANK U FOR THIS VID IT MOTIVATED ME A LOT

[@walterstevens3874]

Proofs class first. Definitions, yes! This was so helpful.

[@tumelotlhaodi8577]

trying something different this semester by starting early since am bored,thanks for tips but am looking for content to learn.

[@jtchavda4718]

This Video Is Very Helpful For Those Students Who Are Going to Study University level Mathematics

[@the_nuwarrior]

6:10 in my case I learned that in Calc 1, induction, And first order logic

[@javiermd5835]

Where I live it’s really different. The “Calculus” you learn in your first year is something in the lines of Spivak’s. A rigorous approach where you do both computations and proofs, but without introducing topological notions. That’s introduced in your second year. The same goes for nearly every subject you encounter. If I’d have to give my two cents though, I think both ways have their pros and cons. What I think it’s mandatory is a transition course that covers sets, maps, logic, proof techniques, etc. 1/4 out of 80 sophmores that take the math degree drop in the first year or earlier.

[@mateusvitor2774]

Damn no wonder people drop out, analysis needs some math maturity

[@mateusvitor2774]

Which is hard to have as a first year

[@javiermd5835]

@@mateusvitor2774 yeah the rate of failing is quite high in the first year. The same applies to linear algebra, for example. It’s not in the realm of, say, Sheldon Axler’s LADR, but it is quite abstract for people coming from high school. For example, the last part of that course covers the dual space, which a significant leap in abstraction for people who are still coming to terms with vector spaces and linear transformations.

[@mateusvitor2774]

@@javiermd5835 agreed. I remember taking linear algebra during my second semestre. First exam was proof only, very different from, for example a calculus test during the first semestre.

[@javiermd5835]

@@mateusvitor2774 when I first took linear algebra literally half of the class was people who had already failed. I remember that in the first test only 33% of people passed. There were lots of really bad grades (in a scale from 1 to 10 most people were in the 1-3,5 ballpark). I know this situation is not as common in other countries, I’d like to know why because I don’t think people here are more stupid to be honest.

[@Lawrance36]

Thank you advice, so helpful

[@BriTheMathGuy]

Glad it was helpful!

[@sanjursan]

Definitions are the times tables of higher math. Know them cold and they will serve you well.

[@Jack_Callcott_AU]

I studied real analysis with the late Prof. Rudolf Vyborny, a Czech emigre, in the 1980_s . It was one of the most intellectually fulfilling studies in my life.; but it is hard and challenging for sure. I would encourage anyone who feels a bit overwhelmed by the rigour of the subject to persist and to believe that they will get there in the end.

[@nexovec]

It annoyed me into oblivion that in my math class I had to do "proofs" that weren't proofs - more like a basic vague sketch of ideas that really has no structure - at all and it was almost like the teachers were actively trying to persuade us that proofs don't exist. I can't even talk to my classmates now, because just a slight derail from the beaten path of plug and chugging leaves them confused, and that's kinda sad, being unable to really share these great ideas with anyone as an EECS undergrad(At least I hope that's the reason) :D It's a lot of work to learn this properly though

[@rampadmanabhan4258]

This is so true! I'm in my final year as an Electronics undergrad and in most of our classes that involve maths to some extent, the teachers really don't care about rigour and we just take most things for granted...