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don't add 12 word phrase to create a wallet below - it is a honeypot

I really want to major math but i still need to wait a few years (i'm 15), however, i would like to know a good place to find studying material both for entry level college maths or american HS algebra/calc Every help is welcome.

I thought this channel had 7K from the production quality, but It's surprising to only be less than 1K subs

I have a bachelor's degree in math, and proofs is definitely where I started to struggle. Abstract algebra basically almost killed me, but that was partially because the teacher I had for it made it a lot more difficult than it should have been. Even other math professors at my university agreed that the way she taught it was just way too hard for undergrad. Most math programs have an intro to proofs type course that helps prepare people for proof classes. Overall, Real Analysis actually wasn't that bad for me mainly because every proof has a specific process in Real Analysis. If you know the process for a proof in real analysis, it's not super difficult. Abstract algebra is a completely different story. I had a few failed courses throughout my undergrad, but I still graduated with my math degree. I am very proud of myself for doing what I did.

No need to pretend it’s more complicated than it is. Bio is pretty easy, we’re not mechanical engineers. Chill

Excellent content I can't believe you have less than 500 subs, This is unbelievably underrated

I know no biology or organic chemistry, but this does remind me of "bridge". When you want to play it well, you suddenly realize that you need to study tons of techniques that have nothing to do with "fun" or "game", just like having to study the rules behind those mouthful chemical names when our initial plan is to understand life

This channel needs more recognition. Sooner or later I may or may not have to take o-chem. I’ll do everything I can to prepare for it

I think I can still remember what C2H5OH is (despite having scored a flat 0/20 at the chemistry oral of my engineer school entrance exam) 🍺 But that's my limit (well, I obviously also remember CH3OH, C3H7OH, ..., CnH(2n+1)OH)

I would say that the most important prerequisite of QM is linear algebra instead of complex analysis (more useful in QFT). I like that you use examples like hydrogen atoms and square wells instead of the cat non-sense. I do think the most important sequel to QM is solid state, and another pillar of modern physics, namely statistical mechanics, is worth mentioning and that subject has its own challenge.

Apologies for the scuffed audio at times. Help me reach 1000 subs so I can afford some better recording equipment

Having viewed a number of Caravaggio's works at the Borghese Gallery on a trip to Rome in September (playing Bridge, of course), I found him talented, interesting (because of his visual resistance to traditional Catholic taste) and worthwhile. Now, you bring up his behavior as a brawler and murderer - sure, but at least he didn't cheat at the table. I enjoyed much of his art, but that is a personal reaction.

This is funny

Epic

Wow lol cool channel

I like Rubik's cubes, and I learned how to solve one when I was five. When you turn a side the same way 5 "times", that's basically the same as one "time." Rubik's cube turns have a modulus of 4. I experienced acceleration when I ran headfirst into a wall.

This channel is pretty cool!

<-- 3lorian from your twitch stream in bridge. Awesome channel. You get a sub

I think the distinction isn't proofs vs. non-proofs, but rather problems that can be solved using a standard series of steps vs. problems that require more out-of-the-box thinking. Proofs can be just as formulaic and simple if there's no variation in the questions.. For example, in high school we had a proofs unit where we (for the most part) just had to prove some properties such as divisibility and rationality. Once our teacher showed us the steps to do this, we could pretty much just use these same steps for any question we got on the test, plugging in different numbers/expressions. I'd argue that there really isn't much of a difference between proofs and questions without proofs. Proofs are just regular questions where they give you the answer beforehand, and the question would be more difficult in most cases if they didn't give the answer. "Prove that if 2x = 4, then x = 2" counts as a proof, but it isn't any different from "find x if 2x = 4". You can turn any proof into a question just by phrasing it differently: instead of "prove that x is true", you can ask "is x true?" You definitely are right about students not being taught how to come up with unique solutions to problems themselves though. Most of high school math is just memorizing a few procedures that are taught by your teacher, and just plugging in different numbers. There is contest math however, which has questions that are not so straightforward, and I believe most students thinking of majoring math have tried it out.

Expert: This artist is probably the greatest artist of the 16th century, their use of colors is astonishing. Rob: I'll just put them in this yellow box!

real

Bit late I applied last week😅

Intro to fundamental analysis, real analysis, and modern abstract algebra made me understand what many students feel in a math class. Glad i did experience and knew that going further in math was not my jam, though makes stuff easier in masters of CS

I’m a senior in an arts degree who’s recently become obsessed with how math is developed and what constitutes rigorous proof… I don’t know if there’s a way to switch to math this late, but this video just makes me more passionate about that possibility.

I was first introduced to proofs from a textbook called discrete math and its applications by Rosen, and honestly I’ve never felt so humbled. Growing up I’ve never made below a high A on a math test. Calc 1 2 and the highschool algebra and trig were easy… simply learn an algorithm, follow the steps and you get the solution. However when our textbook started introducing simple proofs I’ve never felt anymore stupid, sometimes the idea would be simple, for example proving the sqrt(2) is irrational. However I had no idea how to formulate my ideas, and I felt so humbled. Needless to say I passed the course, and made me consider switching from computer science to mathematics. Currently I’m still majoring in computer science, but I really want to give a course like real analysis or abstract algebra a shot….

What website are you showing us at 0:55 ?

05:55 Isnt the number of all proofs theoretically countably infinite since every proof is a sequence of symbols ;P

I feel like I'm going through the opposite process right now: I started as a comp-sci major, but I am trying more math classes this semester and I'm currently loving number systems (another proof based class, before real analysis). This video has given me the confidence that I would be a great math major.

Is it really normal to not have taken a proof based class before real analysis? My uni requires you to take an introduction to proofs, and proof based linear algebra/calc 1 + 2 in first year. Second year you do more proof based linear algebra, so by the time you get to real analysis you have a good amount of experience with proofs.

Im a stats and data science major and was guessing this would be about real analysis and was right. Been avoiding this vid cuz it seemed clickbaity but since im procrastinating, i clicked anyway. Im kinda tempted to take real analysis at some point. Its not necessary at all to take it, but my proofs class has been neat enough to where im curious.

I don’t know I’m watching this when I’ve already graduated with a math degree. Started as Physics though then switched to Math pretty late.

It was never fun, it was always work. The real challenge is... How do you take someone like me into the world Bridge? In my case I was looking for something to do that did not involve a bar or a church.

Am i dumb if i cant solve that calculus question about finding the area but was able to prove xy≠0?

5:55 I made the comment, "the number of proofs is uncountably infinite." Many people have addressed this in the comments and I want to apologize for making this misleading remark. While researching for the video I came across this statement and accepted it as fact without checking it myself. While the statement as given is not technically inaccurate since we would first need to define a rigorous logical system and without this we can't comment on the validity of any statements (is this confusing or what?), under a few simple assumptions such as: 1) Languages have a finite number of characters; and 2) Proofs are finite, we can show that the number of proofs is a countable union of finite sets, which is countable. Sorry for the misleading statement. It will happen again! I appreciate all the comments point this out 😊

5:55 "... the number of possible proofs in uncountably infinite..." It certainly is not! It's infinite, but not uncountably infinite. This guy needs to take some math classes.

I am currently taking AP Calculus AB and will be taking BC next semester. I REALLY want to go into a math major in college cause I feel like that would be the only major I would enjoy. We did proofs in Geometry, it was a struggle at first because I had no idea on how specific I am supposed to be, but now I think I have gotten a lot better, but only for the geometry level.

5:59 the number of possible proofs is *countably* infinite

5:58 the number of proofs/theorems in general is actually countably infinite not uncountably infinite. Since all proofs/theorems are of finite length, the set of theorems is the infinite union over all possible lengths, and for each length k there is a finite amount of theorems as words/mathematical signs are a finite set. So it's an countably infinite union of finite sets which ends up as just countably infinite

This video is about 14 months too late

As someone who has a backround in international math competitions, I personally think that the lack of exposure to proofs is the single biggest problem in a lot of school systems. It's just a lot of fun to do a wide range of math exercises, especially doing little variations on things you have seen a lot.

Who says I have a brain? Unacceptable.

I would add that many of these students are probably better served studying applied maths, whether has part of a different degree (physics, CompSci, engineering) or as part of a dedicated applied maths degree, which does exist. A lot of the thinking and type of problem structures in that are closer to the high school maths you talk about.

Analysis is hard.... But like.... Honestly things get harder afterwards that it seems easy now

for anyone doubting about mathematics: remember that math is creative. if you love math and enjoy finding creative and original solutions to problems, you are on the right track. if you have the patience and discipline to work hard at it every day, not only are you in the right field, but mathematics will be a BREEZE. dont let anyone scare you away! best of luck

Oops too late

By the way, did you know that Edgar Allen Poe was first translated to French by Charles Baudelaire?

The thing that made proofs kind of click for me is realising that I should just see proofs as an explaination for why something is true based on prior knowledge. Usually if I am stuck on a proof, it's a sign I need to look over or organize my notes again, and once I have all of my axioms, theorums, and everything in one place, then I can piece them together like a puzzle.

Well since high school geometry on khan academy has a structure of 2 column proof, I had to adapt fast since it was rigorous as hell. From algebra 1 to high school geometry felt like getting wooped by Euclid and his book of elements.

My geometry classes in high school went over proofs a bit, but I didn't really learn proofs until linear algebra. I think that helped with Real Analysis. I made it through, but that's when I decided grad school wasn't for me. I just didn't have the talent to go further. I'm glad I took it though since it actually proved the Fundamental Theorem of Calculus for me, which I found fascinating. Although I always had a problem with some of the stuff they taught about Cantor. Yes the reals are bigger than the naturals. But I never accepted that the interval from 0 to 1 had the exact same number of elements from 0 to 2. You can put them in a 1 to 1 mapping of course, but you can also put them in a 2 to 1 mapping. And probably other maps as well.

This sounds like an area Australia excels at. We learn basic basic proof idea in High School senior math (Advanced, Extension 1 Math) (From NSW). In Extension 2 math we even learn formal proof techniques like proof by contradiction, induction, proof by contraposition, inequality proofs, number proofs, geometric proofs involving vectors. I think High School math really prepares me for university math in the future due to the focus on higher order thinking earlier on in my mathematics journey (topics learned by Year 12 Math if you take the top level courses for context: Sequences and Series, Trigonometry, Functions, Differentiation, Integration, Vectors, motion, differential equations, statistical graphs, binomial statistics, probability distributions, formal proof techniques, complex numbers (goes to De moivre’s theorem, roots of unity and exponential form), integral techniques (integration by substitution, integration by parts, general integration rules for repeated integration, integration by partial fraction decomposition), mechanics, 3D vectors. This is also reinforced in first year university math courses (like in Discrete Mathematics which is often mandatory for math majors has a part of the course look into formal mathematical proofs).