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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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3
votes
2answers
62 views

Is there a better/faster way to take anti-derivatives of simple functions than “reversing” the derivative rules?

Update: For what it's worth, I will wait another few hours to see if anyone else has a more comprehensive answer to my question. But if not, I will "accept" one of the two extant answers, both of ...
-2
votes
1answer
49 views

Should I go into a master's program for math? [closed]

I'm currently in my undergrad for math and my school offers an expedited bachelor's to master's program. I liked a lot of my math classes, such as all the calculus ones, a symbolic logic course, ...
0
votes
0answers
60 views

What is Number Theory, and how should one go about studying it? [closed]

I have a bachelor's degree in math, and I'm considering to start a masters degree. I've always been intrigued by "Number Theory" in the most intuitive sense: prime numbers and their behavior, ...
0
votes
0answers
29 views

How to develop abstract thinking and problem solving skills?

I am currently doing post graduation in Industrial Mathematics. During my graduation years, I did not have much trouble in understanding the theorems or I should rather say, the arguments in the ...
3
votes
0answers
88 views

How can I start learning algebraic geometry from an algebraic viewpoint? [closed]

Though there are quite many questions on MSE about how to learn algebraic geometry, personally I still have something not very clear. Actually, I feel good when learning algebra and have studied ...
7
votes
3answers
165 views

How to learn without looking at solutions? (real analysis)

I have 2 weeks to do real analysis HW set, I work on them everyday, but many questions I spend hours on and cannot figure out. In the end, I google them (and feel horrible), read the proofs, and think ...
0
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0answers
20 views

Advice on mathematical and physical sources & dictionaries with the indexes (filters)

Could you recommend some resources or dictionaries on mathematics and physics with terms filtered by thematic indexes, such as the Compendium of Chemistry Terminology (a.k.a. the IUPAC Gold Book) or ...
0
votes
2answers
56 views

Books in these areas [closed]

I need hierarchical book list in these fields: Algebra (I, II), Geometry, Trigonometry, Precalculus, Calculus and Linear Algebra. For example: In Algebra Intro books, then intermediate books then ...
2
votes
1answer
68 views

Is it worth it to understand why math works, even in college? Or because of the pace should I just stick to memorizing steps and formulas.

I will be taking a college pre-calc math class soon and I was wondering if it is worth to try to understand math or just memorize formulas. You know, all the "Why does this work?" questions and math ...
0
votes
0answers
64 views

Suggestion for course taking

(Summary) There will be a reading course using Differential Geometry: Bundles, Connections, Metrics and Curvature by C.Taubes. What is the prerequisite for this book? Is its contents something that ...
0
votes
0answers
22 views

Learning modular form for Riemann surfaces

I am currently learning Riemann surfaces and am wondering if learning modular forms would be helpful (like improving my understand, introducing more useful tools in Riemann surfaces,etc), since books ...
4
votes
1answer
88 views

About (relatively) recent progress in manifold topology and de Rham cohomology

Background: I'm at the end of my BsC and in the next semester I'll start my MsC. I'm already familiar with analysis on manifolds (at the level of Tu's "An Introduction to Manifolds" and Spivak's "A ...
1
vote
0answers
73 views

How to finish my PhD [closed]

I have M.Sc. in Mathematics and I was/am working on a PhD for almost 10 years now, but I haven't published a thing. I have many results (most in a single field) and potential paper drafts, but I never ...
0
votes
1answer
129 views

Where and how should I submit a math paper? [closed]

I've been working on a math paper on and off for years and I think I'm about ready to submit it to some Journal. I recently read that LaTex is preferred but I've already done $15$ pages with many ...
7
votes
2answers
108 views

Learning Math as a Med student (Self-Learning Undergraduate Mathematics).

I'd like to learn mathematics at a (semi-?)professional level. I'm studying Undergrad Medicine in South Asia. I'm looking to build up on my understanding of mathematics from scratch. This is to help ...
4
votes
4answers
190 views

Are proofs always synonymous with explanations?

As I have looked at more and more complicated mathematics I have often found formulas and theorems and so on where I understand the proofs for them but I still don't feel like I understand how they ...
4
votes
1answer
71 views

How to find (research) literature?

I noticed that if one wants to get into a new branch of mathematics it is really hard to find good literature to start with. Of course, if one googles the name of the subject one will find a 1000 ...
1
vote
0answers
43 views

Prerequisites for the complex analysis part of Rudin RCA

What are the prerequisites for the complex analysis part of Rudin Real and Complex analysis book? Is it possible to start studying the complex analysis part with the knowledge acquired from the first ...
1
vote
0answers
58 views

Are there huge differences between textbooks?

I am about to start my first year in college. I am not a class type student. I like going deep while studying myself and understanding the reasons, beauty behind these ideas. I have been looking for ...
5
votes
1answer
100 views

Is doing Olympiad problems in Undergrad,worth it?

I am about to enter in second year as a math major, due to some reasons I have never been into amc and imo like stuffs, but as I am gaining interest in math, it is the regret which is hurting me again ...
0
votes
1answer
51 views

What to learn after elementary geometry? [closed]

I'm in love with Euclidian geometry. It seem I mastered elementary geometry, the one that schoolchildren learn throughout school. But I want to proceed to learn it. Could you advice me something? As a ...
0
votes
2answers
80 views

What should I study to prepare for College Algebra?

I'm taking College Algebra this fall (Math 111 at my school.) Math has never been my strong point and it's something that I've always struggled with a lot. School starts on September 25th, and I ...
4
votes
2answers
126 views

I need a little help with real analysis. [closed]

I once decided that I want to understand real analysis. It's looks exciting, construction of sets of numbers and something else, I forgot already. I learned some logic, propositional logic and ...
1
vote
0answers
68 views

Topics for Masters thesis around Birch-Swinnerton-Dyer conjecture [closed]

I am currently looking for a Masters thesis subject in number theory. My favourite subjects are algebraic number theory and cohomologies (I only studied De Rham cohomology). I've been lately reading ...
0
votes
1answer
26 views

To what extent are metric spaces involved in Topology

I am new to both subject areas and am currently choosing modules to take next year. I'm pretty certain I want to take topology but metric spaces is currently not on my list. Would it be recommended to ...
5
votes
0answers
93 views

Elementary Differential Geometry before Manifolds?

Many courses called Differential Geometry (at least in Germany; at least as far as I know!) solely deal with manifolds and not classical/elementary Differential Geometry (curves, curvature, ...
0
votes
0answers
15 views

Is semi-lagrangian 1D advection identical to upwind Euler, when $|u|<\Delta x/\Delta t$?

This looked true to me, I worked through the algebra for 1D and confirmed it. But no one seems to mention it, so maybe I'm missing something... I'm using Bridson's SIGGRAPH 2007 course notes. [5MB ...
0
votes
2answers
53 views

How can I succeed in a college Trigonometry class? [closed]

I'm currently a physics major and I'm taking trigonometry for my fall semester. What are some tips towards succeeding, in order to get into "calculus"?
1
vote
0answers
38 views

Optimization vs numerical methods [closed]

DETAILS: I work as a programmer. After finishing my Bachelors in Statistics I have to choose a Masters. AIM: I want to boost my Math knowledge, both theoretical(I enjoy numerical methods, ...
-2
votes
2answers
47 views

Question about taking an exam in mathematics [closed]

When I attend to lectures I can gasp the ideas very quickly. When lecturer explaining something I can even think what is he going to teach next. Actually, in the class, I am faster than the student ...
3
votes
3answers
55 views

Proving that $I+A$ is invertable when $A$ is nilpotent: What intuition leads to a particular approach?

In an answer to this question, it has been suggested to consider the following: $$(I+A)(\sum_{j=0}^n(-A)^j)$$ Through a series of algebraic operations, it can be shown that $\sum_{j=0}^n(-A)^j$ is in ...
7
votes
1answer
116 views

Staying interested in less tangible math [closed]

I've graduated high school and I am joining college soon. The problem with me is that I'm not finding less tangible math interesting at all. Some people find abstract math to be very beautiful, and I'...
0
votes
0answers
33 views

Tips on studying and becoming proficient at vector calculus

I am a computer science undergrad. I am pursuing my second year open university BS mathematics course. I am currently taking a course on Vector calculus. I am using two text-books - Vector analysis by ...
1
vote
0answers
94 views

After Spivak - Multivariable or Linear Algebra? [closed]

I start UChicago in the fall and would like to test into their Honors Analysis sequence (the test being in late September). I’m about midway through Spivak and I really enjoy it. I hope to finish the ...
1
vote
0answers
62 views

(soft question) Summer Math Project for Undergrad

I’m an undergraduate math major and am currently a rising sophomore. In my first year, I had a fair bit of experience with real analysis and linear algebra (but nothing fancy). I have some free time ...
0
votes
2answers
92 views

Publishing material on own website

Im working on an open famous problem (i.e. a conjecture in mathematics), but i am having a hard time figuring out if i can or should publish any of the material im working on, on my website. I don't ...
0
votes
3answers
55 views

Will an introduction to number theory help clear concepts of base conversion [duplicate]

I am having a hard time understanding why the division algorithm works during base conversion even after reading some of the answers given on this site. Obviously I am missing a formal introduction ...
3
votes
1answer
68 views

How hard should one try proving textbook theorems? [closed]

It’s often said that, when you see a new theorem in a textbook, you should first try to prove it. And Bellman said that, if you can solve a problem, it’s an exercise; if you can’t, it’s a research ...
0
votes
0answers
67 views

Mathematics without coordinate systems

Suppose that a) I understand mathematics to the level of e.g. Rudin's "Principles of mathematical analysis" b) I want to completely expel "coordinate systems" and the resulting "analytic geometry" ...
1
vote
0answers
33 views

Poincare's Inequality

Assume $\Omega \subset L_d$, for some $d > 0$. Then, for all $u \in W^{1,q}_0(\Omega)$ $1 \leq q \leq \infty$ , $\left \|u \right \|_p \leq (d/2)\left \| \nabla u \right \|_p$. Prove that the ...
0
votes
0answers
85 views

Any good alternatives to Inverse Symbolic Calculator?

Inverse Symbolic Calculator (ISC for short) is down https://isc.carma.newcastle.edu.au/ :-( What would you use instead of this resource now? Wolfram alpha can give answers in simple cases, but from ...
0
votes
0answers
16 views

Information about circular sections of an oblique cone with conical base.

I'm looking for information in English about the topic of circular sections of an oblique cone with conical base since almost all the information on this topic is in French and there is little ...
4
votes
0answers
64 views

advice on PhD proposal [closed]

I am a PhD student in pure mathematics, and I want to work in the field of $C^*$-algebras and operator algebras I am looking for a relatively comprehensive view of this subject. For example, what ...
7
votes
1answer
169 views

What is the best way to study graduate level mathematics?

I am studying a 400/500 level measure theory math book on my own. Right now, when I read it I try to read the proposition then the following proof. And then try to do the exercises on my own. I ...
0
votes
0answers
13 views

Q: How much overlap is there between pure and applied graduate courses, in the UK?

I am a final year BSc Mathematics student and I am seriously considering taking a Master's sometime soon. Some institutions have two separate courses for pure and applied maths. My question is, if I ...
2
votes
0answers
47 views

Research topic- Evolutionary Graph Theory

I read Evolutionary Dynamics by Martin A. Nowak and became fascinated with evolutionary graph theory. I'm mentoring an undergraduate student in the subject and would like to give him a research ...
2
votes
2answers
117 views

Is graph theory considered to be easy, or remarkably elementary? [closed]

I'd just like an opinion from someone more experienced. I'd like to study exciting and complex fields, and I'm wondering whether or not I should leave graph theory behind. I have somewhere between 2 ...
2
votes
0answers
57 views

Career Advice: Where to apply Analysis in Industry?

$\textbf{Background:}$ I am a fourth-year undergraduate at a major university in the US, and I will be staying for a fifth year before proceeding to pursue a masters degree. I have taken courses in ...
1
vote
1answer
25 views

How do I determine the interval over which my error calculation should be conducted?

I've been instructed to find the values of x for which the function $f(x) = e^{-2x}$ may be approximated by the Maclaurin series $1-2x+2x^2-\frac{4}{3}x^3$ with an error of less than 0.001, but no ...
0
votes
1answer
28 views

Determining the values for which a Maclaurin Polynomial approximates $f(x)=\cos(x)$ within an error of 0.001

I'm tasked with determining the values of $x$ for which $f(x)=\cos{x}\approx 1-\frac{x^2}{2!}+\frac{x^4}{4!}$ has an error no greater than 0.001. Using the error for Taylor polynomials $E = |R_n(x)| =...