Questions tagged [advice]

Questions asking for advice on various mathematical matters. Be careful that your question is answerable, and also that it is not a polling question (e.g. "What is the best / your favorite way to...").

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67 views

Which class/subject is generally more difficult for someone who is not very good at proofs; Rings and Fields, or General Topology? [closed]

Yes, I have studied real analysis (up until an intro of metric spaces) and group theory. I was average-bad at both (worse at group theory though). But I need a rigorous, proof focused course to show ...
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3answers
211 views

Beginner feedback on real analysis proof

I am a bio student self-studying Abbott's Understanding Analysis and would love some feedback on one of my answers to an exercise. I have no experience writing proofs, and I'm used to plug-n-chug math ...
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1answer
126 views

any math success stories after a failure? [closed]

I am a sophomore who took abstract algebra for the first time. Started out with Bs, just learned that I failed the course, which is to be expected given the fast decline of my mental health. However, ...
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0answers
89 views

How should one study Graduate Mathematics with a weaker background?

My question is: how should one go about studying graduate level mathematics when they have a weaker background? This is probably a weird question since most of the people go in to graduate mathematics ...
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1answer
51 views

Need help/tips/advice from someone who has a degree in Applied Mathematics

As you can see from the title, I require advice from Applied Mathematicians. I currently have a BSC(H) degree in Mathematics. Although I have a BSC(H) mathematics degree, there are certain topics or ...
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70 views

Pathway to learning perfectoid spaces.

If one has as a starting point the "standard knowledge" of IMO and strong notions in algebra, topology and analysis, and if the end of the road is to reach a high level in algebraic geometry ...
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84 views

Payments structure in an increasing-payments perpetuity

I quote Life Insurance Mathematics (Gerber, 1997). A certain type of perpetuities with increasing payments is defined by two parameters, $m$ (the number of payments per year) and $q$ (the number of ...
3
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2answers
459 views

How to get better at Proofs [closed]

I'm still quite early in my Journey of Mathematics and as I have progressed I have found a constant wall; proofs. Every time I try and learn to do simple proofs, I struggle to find an actual strategy, ...
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1answer
58 views

Will naming all theorems and results I go over in a textbook aid in learning? [closed]

Something I have always thought since working with math textbooks is that it is very opaque to refer to a result like "Theorem 8.2" or "Proposition 1.10". When I took my intro to ...
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124 views

Learning modern algebraic geometry

I have read several posts on road maps for learning modern algebraic geometry, but it seems that whenever I open up a book on the subject (Hartshorne or Vakil's notes or Qing Liu) I make no progress ...
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3answers
158 views

Book recommendation for beginner

I understand this question seems to be off-topic and basic to you. But I want to learn about mathematics, I understand that it depends on many factors, but what I really wanted was the recommendation ...
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2answers
132 views

Majoring in Physics vs Mathematics (Pure)

I am a third-year UG student enrolled in a five-year BS-MS dual degree program. I just got the opportunity to personalize my courses and pick a major at the start of this semester. I went with a ...
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50 views

How to define basic open set in infinite product topology excluding a certain Lemma 3.8

Source: A First Course in Topology by Robert Conover 3.3 Definition Let {$(X_\lambda, T_\lambda$):$\lambda \in \Lambda$} be a nonempty collection of nonempty topological spaces. The Product topology ...
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162 views

Apostol's Calculus II vs. Mathematical Analysis books

I'm a second year math undergraduate and I'm looking for a book for the three analysis courses I'm taking this year: Differentiation of Multivariable functions, Integration of Multivariable functions ...
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2answers
99 views

Question about subset of $ \ell^2 $ space

I have some doubts regarding a problem that I found in notes about metric spaces. We have the set A of sequences that satisfy $ \sum_{i=1}^{\infty} ({a}_{i})^2 \lt \infty $. This is the $ \ell^2$ ...
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1answer
62 views

Need examples of different functions for homeomorphism in product topology [closed]

I am looking for a bunch of examples of homeomorphisms in the finite product topology. I need it for a proof Someone mentioned my question was vague . The theorem is: Let n>1 and let $X_1,...,X_n$ ...
2
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1answer
116 views

Higher Level Mathematics & Piecewise [closed]

Apologies if this isn't the right place to enquire about this; I'm really looking for potential connections to what I've been doing as opposed to having a maths question answered. With that being said,...
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0answers
54 views

List of important axioms & definitions & theorems and formulae in several branches of mathematics

Your answers and comments would be really appreciated as they will help me for self-studying. I graduated form the college with BSc in chemical engineering. I had the following maths classes: Zeroth (...
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0answers
146 views

Recommendations and advices for self study and rigorous but in-depth high school math textbooks? [closed]

I apologize in advance for the long text, but I feel that I won't get a proper response without explaining my situation and my level of knowledge. There are similar questions here but none of which ...
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1answer
42 views

Distribution of points and Pigeon-Hole Principle

I found this practice problem in a textbook... "Ten points are given within a square of unit size. Then there are two of them that are closer to each other than 0.48, and there are three of them ...
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3answers
264 views

On formalising logic

Recently, I became fascinated with Set Theory and I am willing to learn more. Although, there are some aspects that I would like to understand before doing it. A lot of questions concerning the ...
2
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2answers
85 views

Struggling with long computations. Any advice?

Sorry for the somewhat strange question but I have been struggling with this for some time now. I am currently in undergraduate Electrical Engineering taking classes on Linear Algebra, Calculus and ...
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0answers
64 views

What should you know before you study "Galois Groups and Fundamental Groups" by Tamás Szamuely?

I am interested in the book "Galois Groups and Fundamental Groups" by Tamás Szamuely. I would have to learn some basics, and refresh stuff here and there. The point of this question is to ...
5
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1answer
107 views

What are resources for filling in the gaps in math understanding? [duplicate]

First, let me apologize if this question has already been answered. I'm new here (first post!) and while I've been searching for similar questions, I haven't found any that match my problem. I also ...
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1answer
73 views

I love maths but I am lazy to read maths undergraduate textbooks in the least [closed]

I started developing passion for mathematics back in 2013 when my Visual Basic Programming language tutor asked me and two other students to write a program to compute the factorial of any positive ...
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1answer
132 views

Will I learn most from reading proofs, proof outlines, or solving problems? [closed]

I have been self studying some topics in theoretical statistics for a bit over a year but still do not have a good balance between reading proofs in detail, reading proofs to get a general idea and ...
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61 views

Rating and advice about topology books by Mendelson, Conover, and Croom

I am 58. I graduated in 1993 from Concordia. I have two hard cover books on topology: Mendelson, Introduction to Topology; and A First Course in Topology, by Robert Conover. So browsing MSE. the ...
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2answers
79 views

Calculus I help - any useful resources, for seemingly "Advanced Calc I" [closed]

Disclaimer: I am not looking for anyone to provide in depth solutions (or any solutions for that matter) to any of the questions. The sample worksheets have just been posted to give an idea of what ...
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1answer
70 views

Questions on ordinals

(Edited) Background The following question comes from the order topology chapter from A First Course in Topology by Conover Theorem 4.1 A subset A of R is open in the Metric topology induced by the ...
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1answer
32 views

Analytic complex functions

The question at hand is: Let $f(z)$ be an analytic function on a connected open set $D$. If there are two constants $c_1$, $c_2$ $∈C$, not all zero,such that $c_1 f(z)+c_2\overline{f(z)}=0 $, $\forall ...
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3answers
58 views

$(V, ||.||)$ normed space and define $d(x,y) = ||x|| + ||y|| $ if $ x \neq y$ and as $0$ if $x=y$. Convergent sequences in $(V,d)$? Complete?

Let $(V, ||.||)$ be a normed space and define $d(x,y) = ||x|| + ||y|| $ if $ x \neq y$ and as $0$ if $x=y$. Describe all convergent sequences in $(V,d)$. I'm sure that all eventually sequences are ...
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1answer
38 views

Finding counterexamples to prove: $f_n \to f$ uniformly on $(0,\infty)$ does not imply $1/f_n \to 1/f$ uniformly on $(0,\infty)$

If $f_n \to f$ uniformly, where $(f_n)$ and $f$ are positive functions on $(0,\infty)$, then is it true that $1/f_n \to 1/f$ uniformly on $(0,\infty)$? Solution: This was shown to be false by using ...
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1answer
20 views

Advice on constructing a sequence of functions when proving a set is not closed.

When proving a set, A, is not closed in (C[0,1], ||.||) how does one go about constructing a useful sequence of functions in A that you know will not converge to a point in A. Whenever I look at ...
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0answers
49 views

graduate degrees in Applied Mathematics.

I always thought of the general preliminary for a graduate program in applied math as Calculus, Real analysis, Complex variables, DE, introductory Linear algebra, probability and statistics etc. But I ...
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1answer
39 views

Need condition which will make functions both true

Let $f:X\mapsto Y$ Let $A \subset X, B \subset Y$ What condition on $f$ can make $A=f^{-1}(f[A])$. and $B=f(f^{-1}[B])$ both true? For the first ,its $f$ being 1-1, the second it’s $f$ being onto. ...
2
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1answer
33 views

Trying to clarify my argument in an automata proof

The question: Let $\Sigma$ be an alphabet and $L\subseteq \Sigma^*$ be a non-empty language over that alphabet. Prove that if $L=L^2$ then $e \in L$ (where $e$ represents the empty string). My ...
7
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3answers
323 views

How can I improve creative thinking in Math?

I'm a fourteen year old in the USA, who is currently in 8th grade, about to graduate in about 1 month. Currently I'm learning algebra. I have enjoyed math and recently I realized that math is not all ...
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95 views

Prerequisites for Complex Analysis by Serge Lang

In Serge Lang’s Complex Analysis, he says that a prerequisite is 2 years if calculus. But I’m not sure exactly what he means by this. In regards to calculus related courses, I’ve done 3 semesters of ...
3
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1answer
66 views

Presentation on game theory and determinacy

I have to write a short paper(about 20 pages) and prepare a presentation (about 1 hour) for an exam on Game Theory (it is a general, introductory course). I've looked up some things on the internet ...
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0answers
73 views

Prerequisites for Sullivan's 1970 notes

What are the mathematical prerequisites to start reading Sullivan's MIT lecture notes of 1970: Geometric Topology: Localization, Periodicity, and Galois Symmetry? I have already learnt some algebra (...
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1answer
24 views

A topological subspace question about sets

I am self studying topology. This is not homework I am using Topology For Beginners by Steve Warner I am on Chapter 9 I am having trouble understanding an example Let T be standard topology on $\...
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0answers
71 views

Prioritising what to study over summer [closed]

After this semester is finished, I plan on studying some more maths over the summer. I’m currently a second year student and my summer is 3 months long. Since this is about the length of 1 full ...
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0answers
100 views

I'm 27 years old with an Economics BA, is it too late for me to switch to Mathematics? [closed]

The last 2 years have been very difficult for me, finishing with a very late BA in an area that I really don't like. I found a decent job in clinical trials as a data coordinator, but I was always ...
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0answers
29 views

Addition to previously asked question on Generalized Carmichael Numbers

I had previously asked a question on mathstack exchange (Conjecture on The Generalized Carmichael Numbers) concerning with a conjecture I had discovered. I worked on the problem for a long time and ...
2
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1answer
250 views

Possible Masters' Thesis Topics in Algebraic Geometry and Number Theory [closed]

I am a graduate student at African Institute for Mathematical Sciences (AIMS) in a one-year structured masters program. I am currently looking for possible topics for my master's thesis in the area of ...
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1answer
89 views

Information about Home Primes

I will be doing some research on Home Primes and the lack of resources online baffled me. I would be grateful and thankful to those who contribute to this post adding their prior knowledge , links, ...
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0answers
103 views

Advice for a physics undergrad student [closed]

I am currently a first year student studying Theoretical Physics. This summer I had a mind to try and become well versed on the topics of multivariable/single variable calculus and linear algebra, as ...
0
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1answer
38 views

If I define one or more binary operations that form group(s) over a set, is it correct to call it an algebra?

More specifically, I defined the operations multiplication (non-Abelian, composition of permutations) and addition (Abelian, modulo addition of bounded naturals) over the same set, that can be seen as ...
4
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2answers
844 views

Self Learning Stochastic Process By Sheldon Ross

I have just started self-learning Stochastic Processes by Sheldon Ross (2nd Edition). I am finding the exercises really tough and time-consuming. I even tried searching for a solution manual but ...
2
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0answers
83 views

Soft question-What is a good path to learning pure math? [closed]

So I just got accepted to college and I am going to pursue a double major in math and physics with the intention to eventually become a professor in theoretical physics. I am very interested in pure ...

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