I love pure math and ive done lots and lots of Analysis, am currently doing complex and functional analysis, and ive done lots of linear algebra and abstract algebraic structures and am currently doing group theory and Galois theory. So I know loads of technicalities and things, But my question is how do I explain to my non maths friends what analysis is? Usually i say calculus, decribing graphs and finding properties of graphs that can be described by a function like y=x^2 and stuff. For algebraic structures I always mention "imagine working with letters like x and y but you cant just assume that x+y=y+x, for example"
Can anyone describe analysis and algebra in another way that someone with very limited mathematical knowledge can understand? Especially coming up to xmas time, I know all my family will be asking what im doing in my maths course lol. I dont want to start explaining Banach spaces but after a few wines I'm sure I will try
I dived into category theory recently(reading Basic Category Theory by Leisner), although I don't have a strong background in abstract algebra. I learned some basic group theory on my own and I only know the definitions of the rest of important structures. I understand some of the examples from the book on categories, mostly about groups/monoids, but I think I don't really understand the ones involving more complicated structures well enough. My question is whether my approach is fine considering that I learn CT just out of interest, or I will miss really a lot without further knowledge in algebra? If I need algebra, is there any "crash course", containing just enough information for understanding examples from CT, missing some details which are usually covered in standard algebra courses?
So I know this uses Lie groups and Lie symmetries, but honestly, I know nothing about them. My abstract algebra knowledge and skills are mediocre at best as well, but I do like working with differential equations, so there's that.
I'm looking into this subject more on my own, but I'm hoping, before I start, if anyone's taken a course in this or studied this, could they let me know?
And also, if there are any good books for this, or any ideas about any prerequisite knowledge I'd need, could you please let me know that as well?
Thank you!!
For Real Tho, My Ti has really activated hard to understand those goddamned memes. I very desperately want to be able to understand all those subjects. It's not just menes though! I want to learn every subject I have in depth!
Philosophy
Economy and Trade
Logic
Maths
Physics
Alchemy
Literature
Biology
Calculus
Geometry
ALL OF IT!!!!!!!!!!!!!!!!!!
The applied course has around 50% of it dedicated to computations in Python. The abstract class is almost 100% focused on proofs and theory. I’m not sure which course would be more beneficial to me, but I think I would enjoy the applied course more because I haven’t taken a more proof oriented course yet. Which do you guys believe would help me more for a statistics masters and quant research?
Hi everyone! I'm a math PhD with 10+ years of experience tutoring advanced math. Most of my students are undergraduate math majors, but I'm open to working with anyone that has an interest in learning more high-level math.
I'm currently tutoring students in discrete math, abstract algebra, real analysis, complex analysis, and number theory. If you are interested in hiring a tutor for any of those subjects then I hope you consider working with me.
Here's a link to my tutoring website and here's my YouTube channel. You can also contact me directly via email at tutor@herndonmathservices.com. Thanks! I hope to hear from you.
I'm a math major, abstract algebra and algebraic geometry are the fields of study that mostly took my attention, so I'm planning on doing my master degree and my PHD in something related to it. Recently in a discussions with some friends with a degree or a major in computer science, I was told that abstract algebra is useful for game development, but we ended the conversation before they could explain me how. So can someone explain to me where abstract algebra is useful in game development, or at least point me the topics where it's useful, so I can search for myself? Ps: I'm not talking about linear algebra, I'm interested in applications of abstract algebra, group theory, ring theory, galois theory, algebraic geometry... Ps2: Although I'm doing a major in math now, I have a degree in computer science, so it won't be a problem to understand any explanation with technical terms.
|G|= 315=3^2*5*7 with unique Sylow 3 subgroup. The 3-Sylow subgroup T is of order 9, thus abelian. Such a group has no automorphisms of order 5 or 7, so any Sylow 5-subgroup centralizes T, and so does any Sylow 7-subgroup. I understand everything up to the part any Sylow 5-subgroup centralizes T. What do they mean by centralize? And why would that lead to the following :Therefore there is an abelian subgroup H of order 3^2*7?
i'm in my last year of my bachelor's in math, and i've fallen deeply in love with abstract algebra, specifically field theory and galois theory. i would love to pursue an academic career involving these subjects or anything of the sort, but as far as i've seen most research (at least in my university) involving abstract algebra also involves differential geometry (lie groups and lie algebras), which i don't really like, or topology, which i love to study but wouldn't enjoy researching. what are other research topics that could be closer to my interests?
I am an undergraduate mathematics student and I have both courses as part of upcoming semester. Suggest me good books in Abstract and Linear algebra to do exercises from. Thanks in advance.
I have an Abstract Algebra final in four days. We have learned group theory, ring theory and a tiny bit of field theory. All of the problems in the class are proofs or demonstrations. I have consistently done well with the homework, but the assignments have all taken me forever. I find knowing where to start with proofs very difficult, but once I get going I usually do alright.
The exams are another story. I have not done well on the exams, getting about a 50% on both midterms (though many people in my class report the same).
My question is pretty vague, but can any of you recommend some resources, study techniques or other tips to gain a better intuition in abstract algebra? I did well in calculus classes and linear algebra (non-proof based), but that was because I could sort of picture what was going on, and could get an idea of where a problem was going before starting.
I know it's called ABSTRACT algebra for a reason, but are any of you able to visualize abstract algebra problems? Like how should I think about a coset, or a quotient group/ring? I don't understand the significance of these structures, they just seem like things I have to calculate.
For example, I like dihedral groups because there is a polygon I can picture rotating and flipping. I like symmetric groups because I can visualize the combinatorics (marbles in a bag etc.). For most of abstract algebra, though, I can't visualize the structures, don't have an intuition for them, and don't really get how they interact. Anything you all can think of that have helped you gain an intuition for abstract algebra?
TLDR; I wan't to be able to visualize group/ring theory and understand how the structures in groups/rings interact better
In abstract algebra textbooks one often hears of structures (groups, fields etc) with the operations of multiplication and/or addition defined on the elements of the structure, but never division. What I’m trying to figure out is why none of the structures one learns about has division defined on it. The only answers I can think of are that either a structure can’t be closed under division because one can’t divide by 0 or that division is just an inverse to multiplication.
I'm honestly not even sure how to Google this. We can do things like adding random variables, so there's distribution families which are closed under addition (eg binomial for fixed p is closed under addition). Is there a notion of a basis random variables for a family (eg Bernoulli(p) is enough to generate binomial (n,p), but sum(ai xi) for xi iid Bernoulli spans much more-- what I'm not sure).
Is there an area of probability where questions like these fit? An abstract algebra of random variables?
Hi! Sitting in the airport wondering what is the next object in this sequence. If a group is a set equipped with one operation and a ring is a set equipped with two operations, what do we call a set equipped with 3?
More generally, what do we call sets equipped with n operations? (Not looking for a field, which is just a ring where the set is abelian)
Need help!! I'm self-studying abstract algebra as a non-math major all alone. Maybe I'll find a tutor next month. Before that, i wanna clear my query which is important to me. I was told by one of my instructors that I need to be familiar with proofs before getting into advanced mathematics cause he noticed me struggling. So he recommended me a book of logic and proof. "Mathematical proofs: A transition to advanced mathematics" by Albert D. Polimeni, Gary Chartrand, and Ping Zhang.
But the problem is I have very little time(2 months) for my exam. There are many examples for some topics there are 10 to 15 or even 20 examples and questions. I got stuck in a single chapter for 10 days. It is not that I am not understanding. I am understanding and able to solve problems.
Sometimes due to limitations of time, I tried to skip a few examples but I am afraid of further consequences (don't know whether they are real) of not being able to solve problems of abstract algebra. Just like the fear of missing something. This fear caught up in my head witch is the fear of lacking prior exposure which demanded to understand and solve problems in abstract algebra. I help my juniors a lot when I notice then struggle but mine is advanced and literally no one is above to help me.
What I expect from you is What's really important? am I overthinking? Is it ok to skip until or unless I understood how it works? What kind of topics are specifically more important that I could concentrate on ? Is there any resource in the web which answers my question you can definitely share it to me.. You can also share me the resources how to read a textbook. PLEASE DO REMEMBER THAT THIS IS JUST A PREREQUISITE.
I'm planning to take Math 452 next semester and was wondering who the best professor to take it with. Who do you recommend, and who should I stay away from?
Please recommend me an abstract algebra book which has questions with solutions because I'm facing difficulty in solving problems and proofs and exams are not too far.
Those post is gonna be long so please have patience 🙏🏻🙏🏻 I'll kinda vent now. I don't think it's appropriate here and now to vent but I don't know where to express my fear of this subject other than this group. I'm currently preparing for my abstract algebra exam as a physics major as a person who's not good at maths but managing to understand the concepts somehow. I'm kind of afraid, worried at times and feels like a nightmare that and feel discouraged that I can't clear how hard I try like a giant never ending infinite battle. I can't find any math major around me. The problem is I'm preparing all alone because I work(Basically mine is distance education from a reputed university). I'm comfortable preparing all other physics, chemestry subjects by myself except math and that too abstract math. And here so over the internet many are telling and over-exaggerating everywhere about how hard the subject is and that is almost killing me. Enough of vent! And for the next two months i even don't have a chance to attend tuitions.
What I'm doing to help myself is
- I am following and completely active in all of math related reddit groups, and stack exchange.
- I am using discord mathematics server to clear my doubts and fortunately there are a lots of people and they are literally helping me.
- I'm following this playlist which is very helpful especially to get the big picture of abstract algebra.
https://youtube.com/playlist?list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6
MY BASIC QUESTIONS ARE
- Since i don't know from where to start struggling to find out WHERE TO START?
- Is the above playlist helpful?
If anyone wants to help me personally of have empathy you can help me two possible ways which are very much simple.
-
I have PDF of my textbook. If you are experienced enough you can you can gauge the difficulty level and tell me.
-
And I have few model papers you can tell me going through 2-3 modal papers and I think you'll know what kind of questions appearing like weather they are proofs, theorems or example problems. Awareness of me knowing what kind of questions are gonna appear makes me concentrate on areas which are most important thereby increasing effectivity and efficiency in my preperation. And that's it!
Any advices Sir/ma'am ?
You can also advice me like softwares, websites, which helps me.
Please redirect me if I've posted this in the wrong sub!
I'm in an 8 week Abstract Algebra course and the fast pace has me completely overwhelmed already in week 2. I'm looking for someone who could help/tutor me probably 2x weekly for the next 6 weeks (ideally). I want to actually understand what I'm doing, not just brute force get through it, you know? I don't hate proofs, but it normally takes me a while to think through them and I don't have the luxury of time.
In terms of compensation, I don't have much to offer money-wise, but I'm happy to barter - I'm an artist and Christmas is coming, so I'd be more than happy to do custom work (or lessons) in exchange. DM me if you think we could work something out and I'll send examples of my art and jewelry.
I’m teaching myself abstract algebra using the Gallian book ninth edition. I intend to do only a portion of the exercises though and am wondering which of these I should do.
If you have taken modern algebra/abstract algebra using the Gallian books (regardless of editions) and had a suite of exercise problems you did for the course, I would greatly appreciate that. Thank you in advance!
So I am having trouble finding a sure method on how to find subgroups for Zm x Zn with m,n in Real numbers. The actual question is to find all the subgroups of Z3 x Z3, but I would like to know the method more than the solution so I can find Z2 X Z4 and really any any Zn x Zm. Would anyone be able to help me with this?
Thank you for any help
I am curious what applications for abstract algebra exist in computer science. I have read about group theory and ring theory being used in cryptography. Functional programmers seem to use monoids and semigroups as library design inspirations - although this blurs into category theory? And I would imagine (though I don't know) that coding theory intersects with algebra - is this so?
What other areas of CS, applied or theoretical, make use of abstract algebra?
I'm self-studying advanced maths as a non-math major all alone. Maybe I'll find a tutor next month. Before that, i wanna clear my query which is important to me. I was told by one of my instructors that I need to be familiar with proofs before getting into advanced mathematics cause he noticed me struggling. So he recommended me a book of logic and proof. "Mathematical proofs: A transition to advanced mathematics" by Albert D. Polimeni, Gary Chartrand, and Ping Zhang.
But the problem is I have very little time(2 months) for my exam. There are many examples for some topics there are 10 to 15 or even 20 examples and questions. I got stuck in a single chapter for 10 days. It is not that I am not understanding. I am understanding and able to solve problems.
Sometimes due to limitations of time, I tried to skip a few examples but I am afraid of further consequences (don't know whether they are real) of not being able to solve problems of abstract algebra. Just like the fear of missing something. This fear caught up in my head witch is the fear of lacking prior exposure which demanded to understand and solve problems in abstract algebra. I help my juniors a lot when I notice then struggle but mine is advanced and literally no one is above to help me.
What I expect from you is What's really important? am I overthinking? Is it ok to skip until or unless I understood how it works? What kind of topics are specifically more important that I could concentrate on ? Is there any resource in the web which answers my question you can definitely share it to me.. You can also share me the resources how to read a textbook. PLEASE DO REMEMBER THAT I THIS IS JUST A PREREQUISITE.
I'm self-studying abstract maths as a non-math major all alone. Maybe I'll find a tutor next month. Before that, i wanna clear my query which is important to me. I was told by one of my instructors that I need to be familiar with proofs before getting into advanced mathematics cause he noticed me struggling. So he recommended me a book of logic and proof. "Mathematical proofs: A transition to advanced mathematics" by Albert D. Polimeni, Gary Chartrand, and Ping Zhang.
But the problem is I have very little time(2 months) for my exam. There are many examples for some topics there are 10 to 15 or even 20 examples and questions. I got stuck in a single chapter for 10 days. It is not that I am not understanding. I am understanding and able to solve problems.
Sometimes due to limitations of time, I tried to skip a few examples but I am afraid of further consequences (don't know whether they are real) of not being able to solve problems of abstract algebra. Just like the fear of missing something. This fear caught up in my head witch is the fear of lacking prior exposure which demanded to understand and solve problems in abstract algebra. I help my juniors a lot when I notice then struggle but mine is advanced and literally no one is above to help me.
What I expect from you is What's really important? am I overthinking? Is it ok to skip until or unless I understood how it works? What kind of topics are specifically more important that I could concentrate on ? Is there any resource in the web which answers my question you can definitely share it to me.. You can also share me the resources how to read a textbook. PLEASE DO REMEMBER THAT I THIS IS JUST A PREREQUISITE.
Please redirect me if I've posted this in the wrong sub!
I'm in an 8 week Abstract Algebra course and the fast pace has me completely overwhelmed already in week 2. I'm looking for someone who could help/tutor me probably 2x weekly for the next 6 weeks (ideally). I want to actually understand what I'm doing, not just brute force get through it, you know? I don't hate proofs, but it normally takes me a while to think through them and I don't have the luxury of time.
In terms of compensation, I don't have much to offer money-wise, but I'm happy to barter - I'm an artist and Christmas is coming, so I'd be more than happy to do custom work (or lessons) in exchange. DM me if you think we could work something out and I'll send examples of my art and jewelry.
Please recommend me an abstract algebra book which has questions with solutions because I'm facing difficulty in solving problems and proofs and exams are not too far.
Hi. I'm a math PhD with over nine years of experience tutoring advanced math. I tutor undergraduate math majors, graduate students, and anyone else with an interest in learning more high-level math. I like working closely with students to create personalized lessons and study plans that are based around their goals.
You can learn more about my tutoring services on my website or watch a few sample lessons on my YouTube channel. If you are interested in scheduling an intro meeting please email me at tutor@herndonmathservices.com. Thanks and happy studies!
