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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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1answer
30 views

Given a graph $G = (V, E),$ prove that if $|E| > \binom{ |V| -1}{2}$ then the graph is connected.

I know that a similar exercice was already posted on this website but I would like to have a piece of advice concerning the method/way of thinking I used to solve this problem. I don't know if I can ...
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0answers
34 views

Advice for teen planning on pursuing career in mathematics [on hold]

I am currently in High school, 16, and currently just curious as what to do as a career and going into Mathematics seems quite interesting. I have done some very math-based things on my own, such as ...
2
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0answers
47 views

Bachelor thesis in mathematical physics.

After 3 years of study of mathematics and physics, I wish to write my bachelor thesis, starting in September, on a mathematical physics subject. I have prior mathematical knowledge of differential ...
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0answers
65 views

What are the best pure mathematics Masters in Europe to prepare for a Phd? [closed]

Now I'm in my forth year of studies at University and I'm looking for a one year master which would prepare me for a Phd in Pure Mathematics. I am looking for master programs that attract the best ...
2
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0answers
41 views

On the choice of your university and how it affects your career [closed]

I am a bachelor student in mathematics in Switzerland, and this question has been on my mind for a while. To begin with, how much does the university you're studying at influence your "mathematical ...
4
votes
1answer
70 views

How do you manage your study time at university? [closed]

I'm studying 3rd year maths at university and havent done that well in my first semester. I'll be starting 2nd semester next week on 4 maths subjects. I want to study through everything in my 3 maths ...
3
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4answers
275 views

How challenging did you find Real Analysis before the penny dropped? [closed]

I've been following 'Understanding Analysis by Stephen Abbot' and have been struggling with exercise questions even after an in depth read of the chapters. I have read numerous statements by authors ...
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0answers
49 views

Background of Commutative Algebra for Cohen-Macaulay orders and bibliography

In this semester, I'm doing a project in Algebra, and I would like take some advices and suggestions. To be more precise, I will study the Cohen-Macaulay Orders and modules in relation to the Krull ...
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2answers
654 views

Graduate School (Can I be a Mathematician?) [closed]

I am posing this question for myself, but many people surely are wondering the same, so I think this is valuable for others as well as myself. There are similar questions on the site but they do not ...
5
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0answers
80 views

How do you stay focused in advanced (pure) mathematics lectures?

Throughout my entire university career, I've found it incredibly difficult to focus during lectures, so much so that I at one point stopped going because I found it easier to just learn it on my own. ...
2
votes
1answer
134 views

Is pursuing a maths degree right for me? [closed]

I'm currently going torough the most humiliating moment of my life and I would really apreciate a honest advice from someone who works in the field of mathematical research. This year was my first ...
1
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1answer
61 views

Maximizing the total number of feasible constraints of a linear program

I have an optimization problem with $N$ linear inequality constraints and $K$ real valued parameters (e.g. $0.2\alpha_1+0.5\alpha_2\geq 0$, $K=2$) and no objective function. Here $N$ is much larger ...
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0answers
66 views

What subjects to study to improve “mathematical maturity/fluency” to learn more efficiently?

tl;dr: What advanced math subjects should I study to be able to learn new material more efficiently? I recently finished undergrad as a computer science major, but in my current work there's a ton of ...
3
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1answer
117 views

Good Proof Problems for a High School Student?

High school student here... So recently, I have accomplished what I am considering the most exciting breakthrough of my mathematical journey so far... I WROTE A PROOF! I proved that the sum of any ...
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2answers
48 views

How to substitute trigonometry intuitively?

Given a sequence $\{a_i\}$ such that $a_1=1$ and $a_{n+1}=a_n+\sqrt{1+a_n^2} \;\;\;\;\; \forall{n \in {\mathbb{N}}}$ Calculate $$\lim_{n\to \infty}\frac{a_n}{2^n}$$ I had the answer with me. ...
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0answers
98 views

Fake solution to Navier-Stokes Milennium problem? [closed]

I apologize in advance if this question is in the wrong section. I was looking through the recent published papers in the journal "Applied Mathematics Letters" (Q1 in Scimago, H Index 75) and I found ...
16
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2answers
134 views

Learning math while visually impaired

My eyes are destroyed. I have been unable to learn math beyond decimal division in school due to laziness and unhelpful teachers. I am now trying to mitigate this mistake by learning math from the ...
1
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0answers
92 views

Algebraic Number Theory and Euler's constant

After studying Herstein's books for Algebra (undergraduate and graduate) alongside some books in Analytic Number Theory, I decided to study Algebraic Number Theory as well. I read a recommendation on ...
1
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1answer
39 views

Are there standards for how to structure 4D vector math?

This is a somewhat subjective question, but I am also asking if there are a standards. This question is about the general math but some of it is in the context of computer programming. Some specific ...
2
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1answer
146 views

What should one know before learning galois cohomology

I recently became interested in galois cohomology, but I don't know if I have enough math to learn about it or where to start learning it. What should I know before I start learning about Galois ...
5
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6answers
571 views

What are options after finishing high school mathematics early? [closed]

I am a high school student with two years left until I graduate. I managed to move through my high school math curriculum quicker than expected and am on track to take AP Calculus AB this coming ...
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3answers
147 views

How to become really interested in math? [closed]

I'm a high school senior. What can I do to be really interested in mathematics ? I know some of my batch-mates (from meeting them at several math Olympiads) are like insanely good at math (know lots ...
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0answers
94 views

No math camp for math research students? [closed]

I am a beginning graduate student in Mathematics. When I was in school, there were lots of math programs like summer programs to hone problem solving skills. But at the graduate level, I cannot really ...
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2answers
112 views

Where to go from here (Warning: SOFT QUESTION)

It is now nearing summer time and as consequence, I will have a lot of time on my hands. As such I've been trying to figure out how to spend my time in a productive manner. I need to practice to get ...
1
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1answer
98 views

Having trouble gaining mathematical intuition

I recently started studying advanced mathematics on my own, after taking two classes in college (discrete math and advanced mathematical logic) that spurred my interest in the topic. However, I am ...
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6answers
150 views

Is it OK to be picky about math you find interesting? [closed]

I am a layman interested in mathematics, and I would like to hear mathematicians' views on the following: Is it normal to be picky about mathematical stuff you find interesting? I ask because 80% of ...
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1answer
56 views

A good and comprehensive book on number theory and group theory

I am looking for a comprehensive and introductory (lot of examples, exercises) book that deals with topics like group theory, Dirichlet characters etc. Thanks for the advice.
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0answers
29 views

Computing with large vectors and matrices

I'm working on a project that requires the use of large data sets; vectors and matrices with millions of entries. Normally I've done my projects (small scale stuff) with Matlab and never had an issue. ...
4
votes
1answer
48 views

Good source of measure / integration computation problems to build intuition?

I have taken course in measure theory based from Royden's "Real Analysis" last year and now am reviewing the subject using Folland. However, neither book seems to have many "computational" problems. ...
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0answers
35 views

Is probability heavily related to graph theory?

Can one take a probability elective course without taking any graph theory or advanced combinatorics class before? lets assume that one knows already the basic difference between variation, ...
2
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3answers
96 views

Is there a solution to $y=\ln(x)+x$ which yields an answer in the form $x^2=…$

How could I write $y=\ln(x)+x$ as $x^2=...$ Since there might be another solution to this problem I'll give some background. So I had a math test yesterday where they wanted you to calculate the ...
2
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1answer
86 views

Mathematics book recommendation from High school freshman level to Graduate

I am originally from India and there the mathematical curriculum was all about the formulas and not about the understanding.I used to excel at those exams,but since I have moved to Europe I have been ...
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2answers
128 views

Recommended Books for differential equations?

I am planning to take Differential equations next semester, but due to a timetable issue I want to study most of it this summer in my spare time to make it easier. These are the Topics that will be ...
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0answers
219 views

Suggestions for a reading list in Statistics and intro to machine learning

I have built a reading list based on recommendations and suggestions found on several posts from this community. My intention is to use this reading list to acquire a good understanding about ...
1
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1answer
131 views

Order of Pure Math Topics to Self Study for PhD Admissions Qualifier

I'm an Industrial Engineering graduate looking to make a switch into Pure Math at the Masters Level/PhD. I have undergrad experience in Calculus (upto Differential Equations) and Probability and ...
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0answers
59 views

Confusion about number theory topics

So, my background in Number Theory is - Elementary Number Theory(that I did mainly from David Burton's text) and Serre's A course in Arithmetic(first half on algebraic methods that included p-adic ...
2
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1answer
132 views

Can one study analysis without algebra?

I have completed my B.Sc. in math and will be starting M.Sc. math in a few months. During my undergraduate classes I found the real analysis and general topology courses the most interesting and the ...
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0answers
41 views

Confusing regarding final year modules

My university has released the modules that I am available to take next year in my final year of undergrad. A PDF was also provided grouping the modules into their respective mathematical topics. I'...
0
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1answer
160 views

Preparation for Folland/Royden/Graduate-Level Analysis

I’m trying to prepare for further study in Analysis and was wondering what advice you all would give. I have read (most of) Abbott’s Understanding Analysis and have started Rudin’s Principles of ...
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4answers
314 views

What would you put on a 5 x 8 index card to be used for your Linear Algebra final exam? [closed]

It's the first time in a math class that I am allowed to utilize an index card for a test. I realize this is subjective, but I am not intending to sound naive or insincere. I am genuinely curious as ...
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1answer
51 views

How to get better at simplification?

Related to this question. This problem is the root reason why I was never good at math - I am horrible at all forms of simplification in mathematics, hence I am bad at proofs. The problem is that ...
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2answers
76 views

Suggestion regarding transition to Mathematics

I have studied mathematics upto High school level and also studied Calculus 1 and 2. I also have studied basic ODE. Recently i read a book "The Heart of Mathematics : Invitation to effective thinking"....
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0answers
32 views

Sources to learn about tensor products of modules

I am trying to learn about tensor products of modules in Dummit and Foote, but I am having trouble understanding their exposition. I am looking for suggestions for other texts that have good ...
2
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3answers
115 views

Relearn, improve and filling gaps in Mathematics for University

I know that several similar questions to this one have already been posted, but I can't find an answer that really suits me and my needs and after some research and reading I'm starting to feel quite ...
5
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2answers
194 views

Learning Technique

I'm prepared for the competitive exam like this (a sample question). In order to solve the problems, first to familiarize with the prerequisite for the each concept. It's ok! My problem is: If I'm ...
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2answers
42 views

Either, Or, Both…a question in mathematical writing [closed]

I want to write that "this transformation changes either rank of effective matrix, or norm of effective matrix, or both" I want to avoid repeating "of effective matrix". How can I do this
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0answers
83 views

Is there active research on topological groups?

So I came across something called "Topological Groups". I have just taken a course on topology/and some basic algebraic topology which i really liked. My mind was blown. I said topological groups are ...
4
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2answers
187 views

Can I skip part III in Dummit and Foote?

I am reading Abstract Algebra by Dummit anfd Foote. I have already taken an introductory course in linear algebra, mostly at the level of Strang's MIT OCW Linear Algebra. My question is: Can I skip '...
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0answers
95 views

Can a profoundly gifted high school student directly enter a graduate program? [closed]

I'm a high school math teacher and I've been working with a profoundly gifted student. His case is highly unusual, and I wonder whether it is possible for him to enter a math grad program without ...
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0answers
20 views

When to prove continuity using sequential definition of continuity?

Using the $\epsilon-\delta$ definition, for proving continuity of a function is always a way, but when should I use the sequential definition. Are there any cases where it is more comfortable?