Self-Studying Applied Mathematics
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- Опубліковано 20 лип 2024
- In this video I answer a question I received from a viewer. He is wanting to self-study applied mathematics. Do you have any advice? If so, please leave a comment below.
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Linear algebra is a must for applied math.
Why? Can't find obvious application to most engineering except perhaps for computer science
@@hayin2041 To be a little more precise, linear algebra is used in probability, statistics, machine learning, and consequently data science. Methods in data science are so general and powerful that knowing linear algebra will allow you to model and tackle so many problems just because of its utility in data science. Linear algebra has connections to graph theory, which arguably underlies a solid chunk of algorithms. Having linear algebra here, again, this time through algorithms, will let you model and tackle many types of problems. Finally, linear algebra has a lot of applications in pure math too through something called representation theory. So linear algebra underlies many many both pure and applied maths.
Also, if you want to model dynamical systems, which crops up every where from economics to chemistry, you'll want to describe or model the system with linear algebra.
@@Efesus67 thank you
@@hayin2041 linear algebra is important for many optimization techniques, which of course apply to tons of different fields.
Perfect timing, I just declared an applied math major alongside my mechanical engineering BS. This will be a big help, thanks Math Sorcerer.
Not sure if anyone else has mentioned this in the comments, but a text that I must recommend is the Princeton Companion for Applied Mathematics. Just like the one for pure math, it covers loads of topics with readable sections on many areas related to applied math. If you have the question of “what is mathematics used for in real world situations?”, then just flip to a random page in the book and you will get answers to your question pretty quickly. For all levels of mathematical understanding, I think that this book is essential to have for someone interested in applied math. I also highly recommend the pure math version of the book too. They are both unparalleled.
Thank you for the amazing videos you produce, they really help a lot!
God, I really love your UA-cam Channel. This type of guidance would have been invaluable during my tenure in Academia.
The book you recommended looks awesome! Hoping to read some of it between the semesters in the semester break
As always, I love those advice videos ❤
For anyone focusing on APPLIED math or statistics/data science, please consider taking some courses in OPERATIONS RESEARCH.
My recommendation for courses would include courses on statistical theory, regression, machine learning, non-linear optimization, and a course or two in programming. Most jobs coming up for applied mathematicians skew heavily towards data science.
I definitely agree with your advice. Specifically, that all math majors should take abstract algebra, topology, and analysis. This is indeed the "basis" (pun intended?) of modern mathematics. I've had peers who were surprised at the fact that these so-called "applied math" areas made significant use of at least one of these 3 subjects. If there's anything I would add to this video, it is that one shouldn't be too concerned in learning "niche" topics before passing qualifying exams in a PhD program (or during undergrad for that matter). By all means, do step outside your comfort zone, but the priority should be in learning the 3 main core areas (and passing quals). Then, you will choose a PhD advisor which is what really determines whether you fall into "pure" or "applied". I didn't really anticipate before qualifiers what problems I would be ultimately working on. My applied math research made use of further topics in graph theory, convex analysis, and continuum mechanics-all which I didn't learn until after passing quals and learned them "as I go".
In analyzing multiple applied mathematics undergrad programs at various top schools, they seem to be more accurately a program about computational mathematics. Lots of discrete math , stochastic math and analysis.
Strangely topology wasnt common at all at the undergrad level (including MIT and Stanford).
The pure mathematics undergrad specialization at MIT jumps headfirst into analysis, abstract algebra and topology. Then they move onto semi-grad-level stuff like manifolds and fourier analysis. The applied mathematics specialization by contrast is definitely focused toward discrete math, computation and modeling.
In Engineering Physics, a correlated degree to Applied Mathematics, the highest level of math ive seen in undergrad is the math required to study Statistical Thermodynamics-which is more advanced than Quantum Mechanics I & II & sometimes III. The rest was linear algebra, analysis, discrete math and fluid/continuum mechanics.
Thanks for the detailed post btw
@@ultravioletiris6241 Yes, that seems to be the case nowadays. But I think the distinction should really be what your "endgame" is with a BSc and/or MS. That's where you really have to be honest with yourself. If you want to look for a high-paying industry position after completion of said degree, then I think a math major focused on computational math should be more than enough. But, if your focus is to move on to a PhD and do research, then you may want to take algebra/topology/analysis before entering a PhD program. That, or go through the "fire and the flames" (good song by the way) of prelim courses. Also, I should say that "applied math" is a subjective term. But that's a conversation for a later time/post lol
Strang has a book called Introduction to Applied Math which is very good. I also recommend his book Computational Science and Engineering.
About the advance math for engineering book helped me Alot since I'm taking DE this semester when it comes to solving Autonomous DE the concept explains well the school book and more examples about linear and nonlinear DE interesting book 👏👏👏👏👏👏
Thanks for such an amazing book recommendation 👏👏👏👏
you can't go wrong with erwin kreyszig!
The last time I did anything involving more involved mathematics was high school level algebra… I’ve forgotten most of it. Any recommendations for a “beginner” like me?
I always felt like I’d never understand math but, it turns out that I just didn’t have the best instructors. Then in 11th grade, I had the most amazing instructor! She gave us the best notes and I finally had an A average in math for the first time in my life. I’ve recently become interested in learning and using mathematics in my everyday life again just for fun 😅
I’ve been out of high school for a little over a decade now - and I never went to college sadly.
Thanks 🙂
Wish me luck sir, my Ordinary Differential equations exam is in a week. Thanks to you, I studied Laplace very quickly.
What about Fourier analysis?
Take functional analysis as well as all linear algebra, can do some typology as well but no too much
I hope you read my comment.
I was planning to write u an email but sadly I didn't get around to doing so. I'm a 26 year-old, former college dropout, I used to study applied mathematics, but now 7 years later I'm back to universiry, back with ambition and love towards math this time as opposed to the first time, not studying it to get a job, I already work as a translator and got my own projects going on, so money is not a problem, except the problem is, I don't like to be told what to study, I don't like to be forced to study specific material, I don't like the idea of studying just to pass an exam and I want the math i study to stick with me for life, regardless whether I'll need it, I just wanna study math because I'm interested in it, and then when it's time for exams, I will go and try my luck, even if I don't do well, I would be okay, since I haven't prepared specifically for them. The reason I'm telling u this is because of the fact that I noticed throughout the years that when I'm forced to stick to certain material and study for exams, the material barely engages me and that's the opposite of what I want. Do you think my plan is doable? I'm at my last bachelor's year by the way
Thank you🙏👍
YES! YES! KREYSZIG’s ADVANCED ENGINEERING MATHEMATICS!!!!!!!! THE ABSOLUTE BEST!!! I am retired and still have a copy next to my KJV Bible.
Follow golden rule "try to derive not to memorise".
is there a reason some of us get addicted to doing reciprocal math 1/137 in search of extra math practice Rinmanns 1859 hypothethis? turn energy to matter at the speed of light or faster
Hi! Can you please give me advice on buying a good Calculus book? In my university we had only one year of Calculus but I think it's not enough for me and I want to explore it further.What book would you recommend to me?(Larson,Seward,Spivak?)
Your advice would be highly appreciated.(I already bought tons of books by your advice and never regretted it). Thanks!
Partial Differential Equations
road to 1 mil 🙏
My advice to anyone is a complete Binge Spree Buying of Math and Physics Books... it's a total Thrill 😀😀 Then , and only then, you should take the recommended Math classes/courses 😀 ... just saying ...
Now to the subject ... "applied Math" can be So So many things it is even hard to describe. In essence every single Scientific field is also Applied Math ... and then there is finance, Operational Research ... I mean ... I could go on for a year talking about books on "Applied Math". Since the person that wrote the email said he works on Physics then a good book for Physics that I do not think The Sorcerer has talked about if Arfken, Harris and Weber book Mathematical Methods for Physicists. But Kreyzsig Book is indeed a Great Reference no doubt, I have one copy for a long long time and I strongly recommend that book.
I did a maths degree a long time ago but never did any topology. Given that I haven't opened any kind of maths book for decades, can you recommend me a starter book on topology?
What best finite mathematics and applied calculus textbooks together
Warner and costenoble
Berresford and Rockett
Wilson
Thank you
❤
Can you give a few talks on math that Community colleges and trades would be taking?
yes great idea! thank you!
I'm really confused about that Is mathematics the branch science or not! What's your opinion regarding this ?
I'm an intensivist, i'm studying real analysis, but the "language" of math is really confuse me, i'm not talking about the notation because right now i want to learn about math reasoning, writing proof, rational behind math,... I really need some point that i can center around, a rigorous center, can you guys recommend me a learning pathway, books,... TY !
First view from my side
Hey Sorcerer i know that the topic that You love the most (regarding maths) is abstract algebra. So the book that im impress that you have not talked about is Aluffi's Algebra: Chapter 0. Pls check it out, is THE BEST abstract algebra book written ever, i promise you that you will love it!
Whats the complete author's name, I wanna check it out, am a collector of math books too
@@gflixes Paolo Aluffi
Linear algebra - yes. But abstract algebra... that one is really hard to connect to applied math. In my view abstract algebra is actually a good example to give if one asks you "which math is not applied?"
Groups theory has many applications in physics.
Point taken, although there are application areas like error-correcting codes and cryptography that draw on abstract algebra.
your hairstyle is like that of Sir Isaac Newton..
Any advice on how someone with a geoscience background can get into applied mathematics
What is specialization apllied mathematics
I have a question and please don't take this up as an offence, but I wondered if you, besides maths, are interested in another science or non-science subject.
It's just that we get to see this all mathematical side, but maybe there is another too.
Yeah I have tons of interests:) I usually don't post too much stuff about them here, but I will try to!! THANK YOU!!!!!!!!
Bench press "Morse & Feshbach".
Ive seen that Abstract Algebra is being used by Chemists, though.
Yeah!! I have an abstract algebra book that covers the stuff that chemists use!!
@@TheMathSorcerer glad to hear it! While my math teachers meant well in Highschool,I would have wished tjat they would communicate math apllications better. I didn't even hear about Discrete math till years after leaving Highschool. So I will admit that one of my life goals is to make these things known, whether I end up in teaching/tutoring or another path.
What are your favorite toppings for hotdogs?
Oh now I'm hungry LOL!!!!!!! Everything!
@@TheMathSorcerer LOL!
hi how do you find pratice problems for math?
textbooks that have worked solutions, probably. You can find a number of textbooks for free and legally online, but I don't know the specifics
REA Problem Solver series, Calculas, Differential equations, Physics Chemistry, Electromagnetics and more. Good luck
@@vcv6560 I have not heard of this series before ,So i will take a deep dive look into it ,Thanks (:
@@johnketema8880 i will try to do that thanks (:
@@fnarmusiccomposition3418 I 1st found them in the early 80s obviously pre-Internet I was shocked at their depth...weight, and even today still a good value
Let him start with Stroud's(advanced) engineering mathematics. He won't regret it.
Hello sir
Applied Mathematics gets only one class in St Finians College Mullingar Co Westmeath Ireland
There's Physics in Applied Mathematics which is handy for atheists from St Finians College Secondary School Mullingar Co Westmeath Ireland who want to study Theoretical Physics