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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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4
votes
1answer
148 views

How to learn language to read math text? [closed]

I recently discover new mathematical wealth in non-English texts. Sadly, the two language that I speak are not German, Russian, Chinese, French, or languages that belong to the world leading math ...
0
votes
0answers
56 views

How to stay mathematically sharp during a engineering gap year

I am on a gap year due to financial reasons but my question is how to stay active during the gap year. I fear that I would lose all the momentum and fail my first year. I will be studying engineering ...
3
votes
1answer
208 views

Getting an undergraduate research experience in an unfamiliar topic

I am a second-year Computer Science undergraduate. I have been steadily getting into mathematics - after taking the basics in my first year and taking a course in set theory my second year I ...
-1
votes
1answer
100 views

Career path for a CS undergrad who wants to enter into mathematics research

I am a second year compsci undergraduate. My program is a 4 year program, so I have 2 more years left. However, I feel that I am not motivated enough, or not satisfied with the quality of teaching in ...
4
votes
3answers
85 views

Good sources for statistical texts

I was just hired to a new job and some knowledge of statistics is needed. In my mathematics undergraduate studies (which I finished very recently), I studied quite a bit of probability but not at all ...
3
votes
1answer
232 views

Can a normal graduate discover something in mathematics?

When I was in High school, I really developed my interest in mathematics. From that time , I always had an ambition to become mathematician or to discover something in mathematics. Because of some ...
4
votes
1answer
119 views

Intuition: about the construction of a stochastic integral

Problem: I do not understand the step, of how we define the stochastic integral. In my lecture notes we define firstly infite sum then finite. On the page 132 of Karazats, Shreve (BM and Stocastic ...
3
votes
2answers
130 views

Literature suggestions: Stochastic Integration; for intuition; for non-mathematicians.

I would like to get a good feeling of stochastic integration in a more intuitive way (to be able to easily explain it to a first year math student or a physicist). Example of what I want to understand ...
2
votes
0answers
140 views

Game Theory/Optimization: what strategy optimizes my employability? How to pragmatically assess my utility funciton and hence my payoff? [closed]

I would like to receive some very pragmatic answers, and if not, informed opinions. So I have to choose three elements out of list A and 3 elements out of list B and I want to pick them so that I can ...
2
votes
1answer
2k views

where do combinatorics play a role in computer science?

I am graduated from computer science. I need some advice in Combinatorics material related to master fields of computer science. I already know that discrete mathematics have a key role in some ...
0
votes
3answers
54 views

When solving “Prove this” problems, is it wrong to begin by plugging in the given information?

Suppose $Ae^{iax} + Be^{ibx} = Ce^{icx}$ for some nonzero constants $A, B, C, a, b, c$, and for all $x$. Prove that $a = b = c$ and $A + B = C$. When given questions like this, my first instinct is ...
15
votes
1answer
1k views

Combinatorics looks incomprehensible, is it that I lack “mathematical maturity” and what should I do?

I think this soft question may be marked "opinion-based" or "off-topic", but I really do not know where else to get help. So please read my question before it's closed, I am really desperately in need ...
11
votes
6answers
779 views

Autism and math: advice on mathematical thinking and problem-solving

I have Autism. For me, this means that instead of seeing the whole picture, I see the details more than anything else. This means that I from time to time get stuck. Getting stuck in a certain path of ...
0
votes
2answers
147 views

Have PhD students/graduates solved all of their undergraduate textbook problems? [closed]

My friend is telling me that people who get their PhD's in math have solved almost every problem in their undergraduate textbooks. I find this hard to believe. Either every PhD graduate is ...
3
votes
0answers
62 views

Study guide on calculus

I have studied calculus until line integrals and double integrals,and I think i quite understand the ideas and concepts, but im afraid i haven't done as much excercises as i desired , and it has ...
4
votes
1answer
429 views

Graduate Functional Analysis Course : Background Required [closed]

I'm an undergraduate with some measure and integration theory background. The undergrad analysis course I took at my institution covered the equivalent of the first two chapters of Folland's Real ...
0
votes
2answers
275 views

Topics in Algebra - Advice for Seminar

I have a seminar in Algebra next week, and I need to lecture. The professor gave us the freedom to choose a subject and I need suggestions. I have taken a course on group theory and a course on Galois ...
6
votes
2answers
1k views

What are some easy papers in mathematics understood by undergraduates?

Being a junior(3rd.year) undergraduate in mathematics, I would like to learn how serious papers of mathematics do the proofs rigorously as opposed to textbooks and proffessors in lectures and I wish ...
9
votes
1answer
341 views

What are the characteristics of a good mathematics “side project”? [closed]

A piece of advice for young graduate students (in mathematics) that I've heard frequently is to find early a "side project" to work on alongside your main research enterprise. An obvious question ...
0
votes
1answer
48 views

Inhomogeneous Equation Advice

How would you approach the following equation $$x^4 f'' - \alpha x^3 f' - \left( \beta x^2 + \gamma x - 1\right) f -1 =0$$ where $\alpha$, $\beta$, and $\gamma$ are positive constants? The solution ...
0
votes
1answer
648 views

How to study vectors and 3D geometry

It may be too broad or also offtopic question but I really want to know how to study vectors and 3D geometry. My interest in these topics is very low thus want to gain some .Any suggestions or names ...
2
votes
0answers
162 views

ENS Paris preparation

Good morning everyone, I'm a french student who wants to pass the contest of ENS Ulm I need specific problems and exercises, I hope someone would help me here... I know there are many french student ...
4
votes
0answers
271 views

Can random function of a random variable provide unbounded probability ratio function?

I have an interesting problem which arises from hypothesis testing. Basically, we have a random variable $X$, which follows a continuous distribution $P_0$ under the hypothesis $H_0$ and follows ...
1
vote
1answer
293 views

Can I solve research problems with only BS in Mathematics or do I need PhD? [closed]

Currently I'm undergrad in Mathematics and confused about getting a Phd. I'm not interested in academia. I'm more interested in startups or jobs in the industry. The only thing that is making me to ...
1
vote
1answer
168 views

Failure of education system [closed]

I think the education system in my country has developed my mindset in a way that has hindered my mathematics education. (My questions are at the end.) I am a senior year highschool student in iran,(...
2
votes
3answers
1k views

Is it necessary that I take Real Analysis 2 & Abstract Algebra 2?

Looking for some advising help (my advisor was not helpful)! I'm a Junior Math major interested in Applied Math/Statistics. I'm currently taking Real Analysis I and have yet to take Abstract Algebra I....
6
votes
8answers
4k views

Programming Languages recommended for work in mathematics and to understand computational complexity [closed]

I am an undergraduate mathematics student and I am managing to stay a semester ahead of my classes. One way in which I want to use my free time is to learn a computer language(s) that will help me in ...
3
votes
1answer
633 views

Applications of Probability Theory to Coding/Cryptography Theory

I'm looking to do a PhD in probability, with my project(s) having applications to for example the following (non-exhaustive). Coding theory: eg algorithms for sending data quickly which can be ...
1
vote
1answer
53 views

Sources/Prerequisites for DG

I'm an graduate level in engineering physics, finishing my 1st year. This is what i have so far in math: Calculus (single and multivariable) Line integrals, green's theorem, vector fields. Linear ...
2
votes
2answers
101 views

Need for a Analysis Book with the following requisites

I am a maths graduate .I have to appear for an entrance exam which has in its syllabus the following. Background: I have Read Analysis from Bartle Sherbert and Understanding Analysis:Abbott. ...
9
votes
7answers
2k views

Basic Geometric intuition, context is undergraduate mathematics

At some point in your life you were explained how to understand the dimensions of a line, a point, a plane, and a n-dimensional object. For me the first instance that comes to memory was in 7th ...
1
vote
2answers
416 views

Alternatives to Dummit and Foote for a text in Algebra

I am reading Abstract Algebra from Dummit Foote. I need to cover the following topics for my upcoming exam: Abstract Algebra: Groups: Groups, homomorphisms, normal subgroups and quotients, ...
2
votes
1answer
276 views

How to clear an entrance exam for a PhD in Maths? [closed]

How to clear an entrance exam for a PhD in Maths? In a 5-6 months time there is a PhD exam coming up for me.It consists of questions from Real Analysis,Abstract Algebra,Linear Algebra,Functional ...
0
votes
1answer
225 views

Some advice on studying math on a graduate level (postgrad)

I studied some math and stats as an Undergraduate (up to Multivariable calc/statistics, Linear Algebra, and Real Analysis) but majored in Economics. Unfortunately, I realised a little too late that ...
2
votes
0answers
169 views

Bertsimas & Tsitsiklis's Linear Optimization book

I just want to ask a question about the "level" of this book. In the book's preface it is written that the only prerequisite is knowledge of Linear Algebra. Is this book good for undergraduate ...
1
vote
2answers
89 views

Is this mathmatically correct?

There is a facebook post that says the entire population of the planet could live in 2000 square foot houses just in the state of Alaska. Some research shows that there are roughly 1585682383 ...
2
votes
1answer
70 views

Need advice in regards to Calculus

I've recently begun Calculus 1 and if I'm honest, so far it's been challenging aswell as fun. The biggest problem for me so far has been understanding the content. Instead of attempting dozens of ...
1
vote
1answer
391 views

Real analysis, measure theory after the Calculus

I want to get deeper into the real analysis and measure theory(in order to build good mathematical basis for learning stochastic proceses,probability theory etc.). I want to ask you an advice about ...
25
votes
3answers
3k views

Do I need to cite an old theorem, if I've strengthened it, wrote my own theorem statement, with a different proof?

Let's say I have been studying an older theorem statement and its proof. I feel that it can be improved, e.g., I can make it a stronger double-implication theorem statement, with a different proof. ...
0
votes
1answer
301 views

Problem solving ability [closed]

Have a nice day. Please write serious answer. :) I have a problem and reduce my motivation. problems as follows; I am learning math is really very fast. I can read few books only one day. I understand ...
0
votes
0answers
208 views

Complex analysis,Functional analysis for deeper understanding Machine Learning.

I want to get deeper into the Machine Learning(theory and application in Finance). I want to ask how relevant are complex analysis and functional analysis as a basis for Machine Learning? Do I need to ...
1
vote
1answer
248 views

Is it possible to learn homotopy theory from the perspective of HoTT?

I'm more familiar with computer science than math. I watched 15-819 and was able to understand most of the content , I think I can digest the HoTT (Homotopy Type Theory) book as well. However , now I ...
3
votes
2answers
59 views

Am I inhibiting my progress by essentially training myself to rely so heavily on 2D and 3D illustrations, at my current level?

My math education/experience is at a low enough level that I can construct 2D or 3D figures which illustrate the vast majority of equations I encounter. Such visualizations tremendously help me, ...
1
vote
1answer
96 views

Differential geometry book Ddo Carmo or Barret O neiL

Pros and Cons of these 2 books which to choose for a course in Differential Geometry.https://www.amazon.com/Differential-Geometry-Curves-Surfaces-Manfredo/dp/0132125897. or https://www.amazon.com/...
2
votes
2answers
255 views

Math used in industry positions

Are there are any jobs in industry that involve more mathematics than just what a (good) undergrad program would cover: calculus, differential equations, real and complex analysis, some basic group ...
0
votes
3answers
108 views

What are some branches one is introduced to as undergraduate? [closed]

I just completed my high school and have little knowledge about what an undergraduate math program includes. I wanted to know what are various branches of mathematics one is introduced to as an ...
14
votes
1answer
664 views

Mathematical research outside academia

My goal up through grad school had been to spend my life doing academic, research mathematics. I got screwed by my advisor and department, though, so that hasn't worked out. I would nevertheless still ...
1
vote
2answers
91 views

Smart way to deal with factoring quadratics?

For some quadratics such as: $$10x^2+89x-9$$ I factoring by making the observations $10=(1)(10)=(5)(2)$ and $9=(3)(3)=9(1)$, then I try: $$(10x ? 1)(x ? 9)$$ $$(10x ? 9)(x ? 1)$$ $$(10 x ? 3)(x ? 3)...
3
votes
0answers
130 views

Efficient way to rigorously learn AI prerequisites

Question: My formal goal is to be able to rigorously understand the mathematical basis for modern statistical learning methods (ML, deep learning). I am told by math people that this involves: linear ...
3
votes
3answers
126 views

Material to learn some basic combinatorics?

I realize that I'm pretty weak when It comes to basic combinatorics, even with simple things like n choose k I don't feel confident. Furthermore, I've viewed some combinatorics books and the reasoning ...