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2
votes
0answers
25 views

Derivative of terminal state w.r.t. the inital conditions.

Let $x\in R^n$ and consider the system $$ \dot{x}=f(t,x) \;\;\mbox{with}\;\; x(0)=x_0 $$ and suppose that we know it's exact or very accurate solution $x(t)$ for the time interval $[0,T]$. I'm ...
3
votes
1answer
41 views

Book Recommendations for Picard Big and Little Theorems

Does anybody have book recommendations for reading about Picard's Little and Big Theorems? Preferably, I am looking for a book that is intended for an undergraduate/first year graduate student who ...
17
votes
11answers
2k views

Gap year to study math

This is a plan in its earliest and thus least concise stage, so either bear with me or don't read the following babble (I bolded some of the important stuff): I am a high school graduate who is about ...
2
votes
0answers
38 views

Researching advice

Hey fellow mathematicians, For the second Semester of my senior year in high school I was able to work on an in depth project on prime counting functions, since I had already completed two years of ...
2
votes
1answer
66 views

How do you use reference books?

Reference books at the research levels often does not include any problem or exercise. While you can't read these books like novels(you normally need to work on other sheet of paper), I'm just ...
8
votes
3answers
766 views

Does writing a bachelor thesis make sense?

I am a math student in my fourth semester. At my university, it is common to write a bachelor-thesis in the end of the bachelor program in almost all subjects while in the math undergraduate program ...
0
votes
1answer
23 views

Approximation Theory: Iterative Methods

Can someone explain to me the general idea of what's going on? I don't get how the functions are being formed, nor do I know why we redefine $h(x)$ to ensure convergence after we defined $g$ ...
0
votes
1answer
48 views

Tools for Undergraduate Research of an Infinite Series?

I am working with an infinite series. I am presenting a presentation on this infinite series at a conference at my university. I have been manipulating the infinite series (power series). I have found ...
1
vote
1answer
67 views

Is Arizona State University known for their applied mathematics REU/PhD program?

I've been accepeted to ASU's NSF REU program for this summer, but I've also been accepted to Mayo as well for their REU (although not technically sponsored by the NSF). Have you guys heard about ...
0
votes
1answer
100 views

Topics on Algebra-Ring Theory for an essay-project on undergraduate level!!

I'm an undergraduate in the mathematics field. So i want to be a little more productive and wanted to do an essay or project on Algebra Ring-Theory (because I got it as a course this semester -Ring ...
10
votes
2answers
328 views

Undergraduate Mathematics Research

I am currently an undergraduate junior. I have taken most of the standard undergraduate math courses and a few introductory graduate courses (measure theory, algebraic topology, complex analysis, ...
0
votes
2answers
64 views

Doing for the first time a mathematical essay! Tips [closed]

I am an undegraduate and i though of doing my first essay on number theory!I kinda have the topic and i started selecting info from different references..but i dont want it to be just a copy paste ...
9
votes
4answers
522 views

Topics on Number theory for undergraduate to do a project

Im an undergraduate in the mathematics field ..So i wanna be alittle more productive and wanted to do an essay or project mostly on number theory or Algebra(Rings or Groups) and i want to ask if you ...
4
votes
6answers
596 views

Applications of Complex Numbers

For my Complex Analysis course, we are to look up applications of Complex Numbers in the real world. The semester has just started and I am still new to the complex field. I want to get a head start ...
0
votes
0answers
46 views

Knot Theory: Conway Skein Relation

I am trying to figure out what exactly is this proposition proving. Is it saying take the trivial link and attach u trivial links to it ( like the borromean rings)? Or are we just taking u copies of ...
2
votes
0answers
37 views

Timelike Loop Spaces as Projective Null Twistor Spaces

I have already asked this question in physics.stackexchange, but have not got any answers, so I have decided to ask it here. Let $\mathcal{M}$ be a spacetime, and let $\Omega\mathcal{M}$ denote the ...
2
votes
0answers
31 views

Is numerical stability preserved under basis transformation for pde

I'm using a Backward Time Central Space method to solve the heat equation in polar coordinates. In Cartesian coordinates, it is easy to show this is unconditionally stable (by assuming solution of the ...
6
votes
3answers
262 views

How to stay academically active during a Mathematics Gap Year?

This year I started at the University of Cambridge to study Maths. I was very unfortunate to contract a serious infection early on in the term, and as a reult it has been mutually decided between ...
4
votes
0answers
429 views

Soft question : First year student and confused

I hope I won't tire the fellow mathematicians with this question but I am very, very confused... I am a first year undergraduate student of Mathematics. I can't say I am a prodigy, maybe having an ...
2
votes
3answers
147 views

What is an awesome book as an introduction to hyper groups

I'm a grad studen and i'm choosing an area to follow on my doctorate (in?) and I've been thinking about extension of topological group theory results to topological hypergroups, but for that i need to ...
1
vote
0answers
36 views

Senior Research Group

I have been elected to participate in a senior research group where each undergrad has the freedom to choose any advanced topic in mathematics. As far as background, I've taken multivariable calculus ...
0
votes
2answers
104 views

Best Line Graph Plotting Software for Display Board

I want to make some line graphs which will be put up on a Display Board in a exhibition So I want to make them eye catching .. Which are the best free available softwares?? Please help.
1
vote
0answers
73 views

Research paper Journal

I am a high school student and want to submit a research paper to a journal. I know that most journals are very hard to be published for the first time. Can anyone suggest me journals which publish ...
0
votes
3answers
138 views

top journals in analysis

as an undergraduate I find analysis as my favorite.I want to read journals regarding that. give me top 5 journals in analysis(real,complex)? top 5 journals in differential geometry? and generally some ...
1
vote
1answer
67 views

I have reached a rut in my understanding of control systems. How do I cross this?

A little background here. I'm an undergrad in the final year. I have decided academia as my career path. My grades are not high but my research caliber is good and I have ongoing projects that are ...
1
vote
1answer
167 views

Operator curl and gradient

Operator curl $\nabla$ x$(\cdot)$ (x is cross product) working on a $ C^1$ vector field and operator gradient $\nabla(\cdot)$ working on scalar fields. And results of these operators is vector ...
6
votes
2answers
175 views

Level of math required to start research? [closed]

How much math does one needs to know to start doing research? Can you start just from an undergraduate understanding? Or do you need graduate level and beyond? How do high school students do math ...
-1
votes
1answer
116 views

Undergraduate research project

How one should approach research as a undergraduate? I am learning analysis from APOSTOL and abstract algebra from HERNSTEIN. Also tell me how doing research is different from problem solving?
1
vote
0answers
76 views

What resources are available for undegraduate research?

I'm reading Landman's Ramsey theory on the integers, from the preface: The student needs not to be intimidated by the words "Ramsey theory", thinking that the subject matter is too deep and ...
1
vote
1answer
85 views

Switching to mathematics

On what areas of mathematics should an electronics and communication engineering student focus on if he wants to go on for mathematics research in areas closely related to electronics and ...
0
votes
2answers
160 views

Interesting research topics in nonlinear dynamics

I have a strong interest in nonlinear dynamics but I was wondering what would be some interesting topics that I could research on at the undergraduate level? So far I am getting acquainted with the ...
2
votes
1answer
33 views

Problem with a summation suffix.

Please can someone tell me why we drop the summation of i here? $S = \sum_{i,j}(y_{ij}-\mu -\alpha_i)^2$ $\frac{dS}{d\alpha_i} = \sum_{j}(y_{ij}-\mu -\alpha_i)$ It's part of a question which is ...
36
votes
5answers
3k views

What is mathematical research like?

I'm planning on applying for a math research program over the summer, but I'm slightly nervous about it just because the name math research sounds strange to me. What does math research entail ...