Learning Hard Math
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- Опубліковано 22 кві 2024
- In this video I talk about advanced mathematics courses and how to succeed in them. Do you have any advice for people? If so, please leave a comment below.
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Thank you:)
When you don’t have a grasp on the prerequisites you owe it to yourself to go back and master the prerequisites
Yes, very true.
After graduating from college and taking additional undergraduate courses as a college graduate and acquiring extra, used, text books, I am amazed by the variety of ways in which professors and text book authors vary in terms of the selection and presentation of topics. As a result of such variations, as students progress into more advanced courses, they may find themselvea in situations that require a level of mastery of some aspects of prerequisites that is greater in some way than the coverage of those apects was in the prerequisite courses. For example, although I got an A in both semesters of a precalculus level technical mathematics course, Calculus 2 required a level of mastery of trignometric identities that was more advanced that the coverage of such identities in technical mathematics was. Furthermore the technical mathematics course involved very little, if any, work in three dimensions. Consequently, in Calculus 2, and especially in Calculus 3, it was significantly difficult to analyze conic sections and other geometric entities in three dimensions. In addition, the linear algebra that Calculus 3 involved was more comprehensive and more advanced that the linear algebra that was covered in technical mathematics was.
Sometimes its really easy to see the root cause early on and this is an example. Really early on they say they need to do a bunch of simple problems to grasp concepts. That's what they need to do - do lots of those problems. There are no shortcuts in maths. You have to do the foundational work if you want to understand things later on.
The problem come when you dont have time to re see the bases
Where can I get a set of these foundational definitions/theorems? like from Number theory, Set theory, etc..(GCD, Euclid's algorithm, Cardinality, Bijection, etc) ... is there a specific book which covers this? or a website? or I have to search manually and learn it
I feel like the higher up you go in maths, the fewer resources (professors, textbooks, etc) there are which actually understand the entire course, or can explain it. I've done "textbook surfing" my entire academic life. During undergraduate, I'd have to go through 2-3 textbooks to find a chapter topic explained well somewhere. In early grad school it went to 5-7 textbooks to understand a section topic. I've recently started self studying differential geometry and for some of the more subtle concepts/theorems, it's become a treasure hunt to find places they are explained well.
Excellent idea!
I urge you to share what you can find. Totally not on LibGen and such. Wink wink. Fuck big Academia and fuck publishers.
Try Boothby Intro to Differentiable Manifolds and Riemannian Geometry.
@@jessewolf7649 Thanks for the suggestion, will check it out!
Hey bro... I'm an undergrad but still struggling with theorems and how to learn them or solve their proofs and I also want to ask is it necessary to do all practice questions i have three maths in this sem
For stochastic? You need just a little set theory (first few chapters are fine), Calc II, a bit of Diff Eq's, and obviously be very strong in your probability theory. If you get the Sheldon Ross book "Stochastic Processes", Chapter 1 is basically a crash course in probability theory, but the problem is, even that will be quite challenging if your probability game is weak. I would highly recommend "A First Course in Probability" by Sheldon Ross. It's the first book that finally made me understand combinatorics. And of course don't skip the proofs. 😄
I have some suggestions. Gather more books on the subject. Sometimes your assigned textbook doesn't explain a particular subject well. Other books may help make it clear. I had 4 or 5 calculus textbooks on my book shelf. When I didn't understand a paragraph in my assigned text, I'd use the other books for reference. I bought those books dirt cheap, mostly from library book sales. This idea was from my math teacher, who was a Caltech grad.
Another idea...read the assigned chapter well in advance of the lecture. Don't wait until the day before the lecture. Read the chapter one week or more ahead of time. It gives you time to digest the subject material, and to take notes on the parts that you don't understand. That way you can be ready with questions for the instructor. It also makes "getting lost" in a lecture less likely. You will be able to keep up with the instructor during the lecture.
Im not sure if this comment will be seen, but i would love to see a video about the career path of math majors after finishing the university
Yeah I would like that as well
Me too!
Math is = reality, so anything you want. Business, economics, computer science (AI), statistics, etc. you have the tools to open your own business, consult someone else’s, and sell things etc. you can do anything if you understand math. You can project expected growth in the future and position yourself accordingly. It’s a seed in which anything you wish can grow :) this is unique to math, as everything else sprouts from it- even us, and our universe is all mathematical. You can do anything at all, so I don’t think there’s an answer anyone but you can give to yourself :) though I know you would appreciate if he gave you a point in the right direction.
@@chrismichaud2644 A 1st degree in pure maths there are no jobs where you sit and write proofs. A high performer may be paid to go to grad school. If it is applied maths you have actuary, statistical consultant. These usually require you to move to a specific part of the country. Most college or university jobs require a masters or PhD. Like psychology it is not a degree that is going to get you a job without something else to go with it. Like engineering, science, ROTC, etc...
@@salvopippo2 A 1st degree in pure maths there are no jobs where you sit and write proofs. A high performer may be paid to go to grad school. If it is applied maths you have actuary, statistical consultant. These usually require you to move to a specific part of the country. Most college or university jobs require a masters or PhD. Like psychology it is not a degree that is going to get you a job without something else to go with it. Like engineering, science, ROTC, etc...
11:10
"You would be surprised of what you are able to accomplish with enough time and practice."
Taking real analysis as a comp sci major next semester. Going to look at your course this summer so I can come in prepared because I'm like the person you're responding to with high level math. It's just tough.
probably depends on where you are located but personally i felt pretty well prepared to tackle my real analysis class just from the calculus i had in high school
@@brosisjk3993 good to know. I seem a bit slower with proofs than the more talented students, so I just need to spend more time. My school isn't known for its math but we have professors that set good standards.
Attend the Office Hours of your TA and Professor; show up with some good questions, and attempt the homework first.
Organize "Problem Set Parties" with a few classmates. Discussing lecture material and problem sets with your peers is very helpful, and fun way to socialize while getting work done.
no one wants to socialize outside of class anymore
@@Podzhagitel Wow. That's a tragic loss.
Finally, I bought your course College Algebra. Thanks for your teaching. I love your channel. 🙏
Best way to learn harder math, just self study. Most things I learned as an undergrad never prepared me for graduate study. You need lots of luck and fortune of good mentors. As the sorcerer has suggested, find people better than you to socialize with in your journey.
Well selected question. What you said about self taught an make it your priority is the way to go. In my experience learning by "yourself" is just a question of time until you get the answer you were looking for. Just put yourself on it with out throwing everything you got until now.
Thanks for the advice.
Really appreciate your videos . They are very inspiring. Do make a video on how to study trigonometry. Thanks,
This is Sanvie
I am an autodidact in maths and physics, whenever I look at papers on arxiv, I'm like, WTH are these guys even saying. In maths, it is easier because you can follow the logic, in physics, they take leaps of insight and logic, leaving you scratching your head.
This is me this semester with differential equations. I’m a geospatial science student trying to survive a maths minor (only minor that didn’t have residential schools) on an average maths base built at high school 25 years ago…I’ve done reviews of high school content, but I just haven’t got the capacity to spend enough time to make it really stick. Consequently I am incredibly slow when problem solving and have to rely heavily on looking for videos with examples I can follow. Ok for assignments…not so ok for exams. And when exams are worth 60-70% of my overall mark…I spent the whole time completely stressed out that I can’t just ‘get it’.
you are an inspiration
Maybe you can get in a study group with other students but keep in mind that many math students are paranoid and will be tight lipped about their progress on difficult proofs or problems. I’m guessing some of your test questions are going to be proofs with some similar to what the teacher puts on the board. So ask yourself if this problems looks like anything you’ve seen before. Try not to panic. It’s like playing pick up sticks. Pick up any easy ones you can solve and then work your way up to the next easier and so on. This will help you maximize your score and you won’t spend all your time on one you have little hope of solving. I doubt many students will stay in the class to the end.
Totally normal. I think that Proofs are the essence of the mathematical thinking, it appeals to some logic, sometimes counterintuitive , others lots of algebraic tricks, but always very good knowledge of your foundation maths. Stochastic processes is hard itself, I had an undergraduate and postgraduate course. However, I learnt them better when I had to teach them. 😅😝
Have you done a video on how long to try a problem before getting help? I get into stubborn pursuits and end up giving inappropriate amount of time to problems that limit my ability to keep pace.
Sorcerer is from the universe where Jeff Bezos continue to pursue a math degree.
Self learning is the only way to go if you truly want to understand what you're learning, university doesnt give you everything
Real analysis kicks your butt.
UDEMY and pre study before class, mindmaps and practice tests after class. Finally ask the top student how he studies. Basically you want to hit that higher order learning in blooms taxonomy. Also look at the number of credits and activities you are involved in and trim it off if you are doing too much.
Make a video about IIT jee exams, that exam is really something solving such tough questions in just 3 minutes is really something to be appreciated.
Hi,I hope you are doing fine.I have been trying to study for the MAT test at Oxford but I can't seem to find the right material,do you have qny recommendations?
All higher level mathematics classes should focus on problem solving during the lecture. If the textbook is decent, it should be up to the student to master the definitions, theorems, proofs with occasional guidance from the professor as need be. There are thousands of advanced undergraduate and graduate programs all reinventing the same wheel by spending the majority of class time proving theorems. The only exception to this would be a grad or post grad level seminar discussing the frontiers of research. J Wolf, PhD, Mathematics
ill just state my problem here... i am an english speaker who has to take analysis 2 and algebra 2 in french as i had to move to a french speaking country and i find it difficult to understand any tips for how i can go by?
Maybe take online courses of the same subjects in English
This is exactly why I'm learning math myself in my tempo and take all the time I need to fully understand things. Formal education is highly overrated and most of the times have no sense.
You run through the material not understanding why and how this works just to pass the exam and moreover - you are also constantly stressed out about it.
My personal opinion is: classes have no sense, only you can teach yourself properly. At least it was the case for me.
i'm on the same boat, although some professors are worth the experience, and the exams are a good challenge too, but i agree with you, the system rushes you through it, and it's very exam centred instead of being centred in understanding. I remember diving deeper in one of my classes and the prof was like, okay but have you started with the next subject? when i said no she said, then get on to it, you are already good in this one and the exam is in a couple of weeks, and i was loving that topic and had to move on because she was technically right, but i was good enough for the exam, i could dive a lot deeper.. that was discouraging to me
same, i considered to study physics or math, but i felt the same
Thanks You Professor Sir! I am a 65 Years Old ,I am from ROMANIA and I like Calculus invented by the genius polymath LEIBNIZ!
Close only counts in horseshoes and hand gernades
Sir, any suggestion for engineers who are learning engineering mathematics at University. Where should we start ? Because it seems alien to us sometimes.
Right 👍👍
Please explain how to master the maths to understand Dirac.
If I sign up for a course...can we text you as the course goes on?
Is there a website that offers mathematical proofs for advanced level courses?
Try ProofWiki?
Try wikiproof
Don't let your dreams be dreams!
No math lab past calc. We would group together. Don't know how social you are but 2, 3 ,4 of us would sit together and work out the problems.
Every new class/course/topic is a challenge, so no sweat there. Just keep in mind that in math (and physics) the latter is usually built on the former....so, if you don't know the topics of before, you will struggle with the current! IME and IMHO.
👍🏼👍🏼
I have autism and I’m having math anxiety. And I don’t know how to prepare for computer engineering technology. My understanding of math is weak, I am struggling In calculus, algebra and trigonometry, and logarithms . I fear that I might fail because of my disability
Don’t put yourself down, bud. Keep working hard and doing practice problems until it becomes more natural. Perhaps start at Precalc review (algebra and trig) before overwhelming yourself with calculus. You got this 🤙🏻
Im autistic and I am failing lol. My advice would be to speak to your doctor, because you may have symptoms that mimic ADHD and they can help you through that, using conscious effort. Also find a learning routine that works for you. I hope you can succeed.
Thought I was alone 😔
somewhat my reasons as well for watching this video 😅
Chatgpt wolfram and those classes will no longer be a proble. Its not the math itsbhard its how so many instructions are so badn
If a student can afford to, they might consider paying a grad student say $20, $30/ hr. or as a flat fee for an occasional 1 - 2 hour tutoring session, over coffee, in the park, or whatever. 🙂
that's a great idea
@@5678plm
I was lucky enough to smoke weed and talk math with my grad student neighbour. He just graduated and I miss him so much.
@@MrAdamo I bet that was fun. Sorry he's
moved away.
I just realised, you look like jeff bezos except with lots of hair 😂
Hanen't watched it yet, But....
2 Things...
1- It's really important and great to Learn How To Learn
2- No such thing as, Oh, I am bad at math or My brain is not for math .... asking for Proof?
Check professor barbra okley's story and the neuroscience behind this
Learning How To Learn from Coursera
from both, neuroscience and cognitive psychology's perspectives,
so it's not just tips and tricks of how to study
Check the next comment
Almost first!
First comment let’s gooooo!
Let's gooooooooooooo!
I don't know about learning hard MATH, I think you should be more worried about learning hard MATHS.
how can i send you an email i need some math tips as well