Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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...").

1
vote
1answer
59 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 ...
1
vote
0answers
48 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
votes
1answer
105 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 ...
0
votes
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. ...
1
vote
0answers
95 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
votes
2answers
126 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
vote
0answers
88 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
vote
1answer
38 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
votes
1answer
105 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
votes
6answers
558 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 ...
0
votes
3answers
127 views

How to become really interested in math?

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 ...
1
vote
0answers
90 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 ...
0
votes
2answers
108 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. However, I have had a hard ...
1
vote
1answer
92 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 ...
4
votes
6answers
147 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 ...
2
votes
1answer
51 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.
1
vote
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
44 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. ...
0
votes
0answers
32 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
votes
3answers
90 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
votes
1answer
84 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 ...
2
votes
2answers
102 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 ...
2
votes
0answers
182 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 ...
2
votes
1answer
98 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 ...
1
vote
0answers
54 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
votes
1answer
130 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 ...
2
votes
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
votes
1answer
114 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 ...
0
votes
4answers
256 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 ...
0
votes
1answer
50 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 ...
5
votes
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"....
0
votes
0answers
28 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
votes
3answers
101 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
votes
2answers
189 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 ...
0
votes
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
4
votes
0answers
81 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
votes
2answers
163 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 '...
4
votes
0answers
89 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 ...
0
votes
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?
0
votes
1answer
32 views

Equivalence of quadratic forms and general advice about “Number Theory” (by Borevich-Shafarevich)

At the very beginning of the "Algebraic Supplement" of "Number Theory" (Borevich-Shafarevich) I read: Any quadratic form $f$ can be written as $$\sum_{i,j=1}^{n} a_{i,j}x_i x_j,$$ where $a_{i,j}=a_{...
0
votes
0answers
27 views

What question should I ask about a stochastic matrix?

I am advising a student project on automated music generation. They have analyzed frequency data for note transitions in Jazz music, looking at about 30 different pieces of music. They have ...
2
votes
1answer
1k views

How to use the AOPS books?

I just acquired the art of problem solving prealgebra book. I would like to ask, how does one use the AOPS books, are they meant to be supplementary to a full textbook? Or are they used for ...
0
votes
3answers
94 views

Should one prove all Dedekind-complete ordered fields are isomorphic before using the real numbers in any formal matter?

As mentioned in an early post I spent about nine hours cumulatively trying to construct the reals axiomatically from the bottom up using naive set theory. Though eventually I realized I made an error ...
4
votes
2answers
117 views

What are the mathematical topics most essential for an applied mathematician?

I am an undergraduate student of mathematics. My question regards those mathematical topics which are indispensable to applied mathematicians: what are they? My conception is that real analysis, (...
0
votes
1answer
188 views

Is it impossible to grasp Multivariable Calculus with poor prerequisite from Single variable calculus? [closed]

Would it be possible to keep up or would i be overwhelmed by a hopeless struggle trying to grasp the new material while at the same time looking back at as well as relearning a few core concepts from ...
-1
votes
2answers
126 views

A simple reverse engineering of calculation. [closed]

I have a formula $x=\frac{1}{\frac{Y}{1000}}$ which is the calculation for converting Parallax to Parsec. I need to reverse it but can't remember how to reverse $1/$ . So for a Parallax of $49....
0
votes
1answer
23 views

How do I manipulate a trio of equations for Acceleration / Velocity / Position such that if I change the number of iterations, the result is the same?

This is for a thought experiment I'm programming. Let's say I have 2 cars; 1 in front, 1 in back. I'm adjusting the rear car's acceleration so that it will never be closer than 1 second's worth of ...
0
votes
5answers
134 views

How to understand theorems and their proofs faster? [closed]

I am a PhD student works in group theory. I have did the course work required to do research. I am facing one big problem that my learning speed is very slow. I have spent around 6 months on a single ...
3
votes
1answer
74 views

Standard and/or advanced curriculum preparing for a grad school in Applied Math

I was wondering what would be a list of Applied Math courses (sort of like a road-map for an Applied Math student interested in a Applied Math PhD) which preferably contains absolutely essential ...
6
votes
3answers
227 views

How to explain proofs to audience smoothly?

I have given 5 to 6 presentations till now (on abstract algebra topics ). Many times to me it appears that most of the people in the audience have not understand the most of the part. Some people ask ...