How to do Research in Mathematics
Vložit
- čas přidán 1. 07. 2024
- Unlimited Learning with Coursera Plus: imp.i384100.net/Zd1dn0
(my referral link)
***
So you're not sure about going into #academia, starting #PhD and doing #research for the next couple of years? Don't worry, this guide is for you!
Sign up at DataCamp: datacamp.pxf.io/c/2222728/101...
(my affiliate link)
DataCamp is a great way to learn data science online from scratch. Hands-on approach, online exercises, practical problems, great instructors.
✅ I have prepared a complete course on getting a Data Science Job
datasciencerush.thinkific.com...
✅✅ If you want to learn online, look at top courses here:
datasciencerush.com/top-10-co...
✅✅✅ Math Books you should read:
datasciencerush.com/data-scie...
--------------------
Przemek Chojecki is an AI entrepreneur with a PhD in mathematics and a member of Forbes 30 under 30 list in Poland. He did his PhD in Paris at Universite Pierre et Marie Curie, then became a Research Fellow and a lecturer at the University of Oxford. After returning to Poland, he took up research on artificial intelligence and mathematics, and founded a technological group ulam.ai, where he is the CEO. Within the group he co-founded multiple AI ventures ranging from logistics to the fashion market, and using cutting-edge technologies.
-----------------------
Please subscribe to my channel:
/ @przemekchojeckiai
or support this channel by a PayPal donation
paypal.me/przchojecki
-----------------------
Follow me on other media:
Facebook: / przchojecki
Instagram: / prz.chojecki
Twitter: / prz_chojecki
Medium: / pchojecki
tags: math research, research in mathematics, mathematics research, phd in mathematics, phd mathematics, how to do research, mathematics, research paper, how to make good research in mathematics, math research tools,
If you want to learn online, I highly recommend Coursera with their annual subscription Coursera Plus: coursera.pxf.io/qnLRPL
I can't pay...
I belong to a poor country pakistan.
Please help me to learn advance mathematics. I also want to publish paper in pure mathematics. I have done my mathematics from islamia university of bhawalpur pakistan
Thanks ! I am a freshman in high school and want to do some research of my own especially on the Riemann conjecture. This was very helpful !
I hope you manage to do it
All the best! I will pray for you!
i did research on that
U were in 11 grade or 12 grade
@@farinritu8850freshman is 9th
I'm a PhD student in Electrical Engineering, interested in doing research that's more mathematical, and this video was really helpful, helped me put the process in perspective. Thank you very much !
In which college ??
Wow, you're a example of women in STEM if you're from India (I guess)
All the Best 👍🏻
Informative video. Thank you Sir.
Hello, excuse me sir that I am want to research in mathematics. How can understand and done well in his field. How should we must to select the area in the mathematics which has most valuable in the present time.after vocation inform me sir.
I am intermediate educational student not to mention I am self taught pentester engineer electric engineer Lamp stack developer music producer I got a research upon math so I wanna publish it thanks for reading.
Thank you!
Thanks
hi i am a freshman phd student in computational mathematics. now，i need to pick my phd topic.I don't know how to choose a suitable topic.the topics my supervisor suggested are too big .one of the topics is related to my lab.another one is machine learning which is total new for my lab .
What is your PHD topic sir 😀
Thank you so much sir 🙏❤️❤️❤️
Thanks
What if i am not able to solve the problem ??
Please subscribe to my channel:
czcams.com/channels/Eq0oQsS-voRnSWbcviIDGA.html
Are there research targets you have to hit every year as a university lecturer? Like prove 5 problems every year?
It's more about what research papers you write and where you publish them. The better the papers the higher chance you'll get grants and better position at a university.
Sir, could you, please, also share how to prepare a presentation for a research paper rich in complex mathematics?
If we include complex mathematical equations in the presentation slides, the audience is expected to lose interest in the presentation. If important equations are not included in the presentation slides then important details may be left unadressed and unexplained.
Hello..
I'm an undergraduate in maths in my final year
Any tips for writing a dissertation?
Thank you
Choose something that intersts you. :)
Hi
Can you make a chart for each move in a rubic cube ??
So we found it's all mathematical interpretation which shows it's combination amd permutations and all the possible data output at every level by most advanced methods of matrix induction ???
All the trends of databases which are associated with every move so we found out every desired conditions at given time
So we winning the lottery or any thing at any time like a proven theorem but not as a probability
Or changes of chances
😛😛😛😛
Could you tell me, what is your research topic ?
It was p-adic Langlands program
Hai!priya here from India .I did btech IT. I liked mathematics after my ug .I m doing masters in mathematics coz I fell in love with it . I wanna pursue research in maths in a reputed institution. I really love integral and differential calculus part. Can you please give me some suggestions on how to start research in calculus?what kinda research paper I have to study ? Thanks in advance 😊
Hi, the best way is go to arxiv.org and see what's being done in Analysis - then work backwards looking at references and trying to understand it.
@@PrzemekChojeckiAI thank you very much ♥️🐈
can you suggest me the latest research topic in maths that is usefull now a days as i am undergraduate student
That's too broad a question. Talk with your local professors, especially in applied mathematics department/computer science (probability/statistics/machine learning)
Im 17and I want to do math for my entire life but college sucks....
I am required to have 2 years research experience for a masters program. How do i get this experience?
Probably with a math degree
Words cannot describe how happy I would be to study at Oxford. Their long held internwtional reputation is WELL DESERVED.
Oxford is awesome! :)
What was it like doing a PhD abroad and why did you choose this option?
Great experience definitely, and I chose it because the level of research was higher in France than in Poland in the domain I wanted to do research in.
@@PrzemekChojeckiAI thanks for reply. Did you have to speak french?
@@Anteater23 I didnt have to, but it was nice to have
can I ask you a question? this is really important to me........ I've just created an idea in math. and I want my work to be published in public..... How do i do that? (I'm a grade 10 student) in the Philippines. (i have no idea how can i even start writing anything). i also don't know how to do research. But, i have my solutions and ideas, proofs in my white board. Can you help me? I've been working on these in weeks and I'm not done yet but I'm sure that i will figure it out.
(i have no idea what I'm doin) sorry for my English.
I havent done research myself but i believe keeping a record of your ideas and proofs is extreemly important. We forget much more than we think. Mathematical papers are usually written in latex (special writing program where u can write mathematical symbols, takes a while to learn but definitely worth learning). Keeping record in latex is pretty good (i cant use pen and paper since i justend up losing them and they're un organized). Latex is for free so ye (there's a website for where u can write in. just sign up with ur gmail for free, search latex in google and u'll find it). Dont try to learn it just to learn it, preferably u shud do a project and keep record of your work and you write what u come up with in latex. Then u search up how to do what u need to know to implement certain symbols.
Reading alot of papers on what's been done is important but that's very hard if you cant understand the symbols they use (their are different symbols for every subject so ye pretty hard to read papers but that's for the future.)
Put this in the latex document (it's called packages and the structure of the text. let's u use certain symbols and organize the document with title and name and so on):
%Comments do not appear in the document
%Everything before \begin{document} is preamble so won't appear either.
%Here we state which LaTeX packages we want to activate in the file which aren't the default.
%Some packages like most of the ones below are automatically downloaded with LaTeX.
%Others need to be downloaded separately e.g. from here ctan.org/
%There is a lot of literature online about which packages you may need to do what you want and how to use them e.g. LaTeX Stack Exchange.
\documentclass[11pt, a4paper, draft]{article}
\usepackage{fullpage}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{latexsym}
\usepackage{natbib}
\usepackage{indentfirst}
\usepackage{etoolbox}
\usepackage{accents}
\usepackage{enumitem}
\usepackage{array}
\usepackage{titlesec}
%Can specify the length of paragraph indents:
\setlength{\parindent}{1em}
%Here we make our own commands:
ewcommand{\ud}{\mathrm{d}}
ewcommand{\uD}{\mathrm{D}}
ewcommand{\ue}{\mathrm{e}}
ewcommand{\ui}{\mathrm{i}}
%Here we can make our own format for theorems, lemmas etc:
ewtheoremstyle{italic}{10pt}{0pt}{\itshape}{}{\bfseries}{.}{0.5em}{}
\theoremstyle{italic} %All of the following have our italic style.
ewtheorem{lemma}{Lemma}[section]
ewtheorem{prop}[lemma]{Proposition}
ewtheorem{cor}[lemma]{Corollary}
ewtheorem{claim}[lemma]{Conjecture}
ewtheorem{theorem}[lemma]{Theorem}
\theoremstyle{definition} %All of the following have the default definition style.
ewtheorem*{definition}{Definition}
ewtheorem*{notation}{Notation}
ewtheorem*{remark}{Remark} %remark without numbers
ewtheorem{Remark}[lemma]{Remark} %remark with numbers
ewtheorem*{example}{Example}
ewtheorem{Example}[lemma]{Example}
%Delete this to number equations (1), (2), (3), ... instead of (1.1), (1.2), (1.3), ..., (2.1), ... etc.
umberwithin{equation}{section}
%How far do you want sections, subsections to be numbered?
\setcounter{secnumdepth}{3}
%What do we want included in the table of contents (if we want one)? Put 1 for sections only, 2 to include subsections, etc.
\setcounter{tocdepth}{1}
%The document begins here:
\begin{document}
%Search online for different ways of making title pages, e.g.
\begin{center}
\mbox{}\\[0.5cm]
ule{\linewidth}{0.8mm}\\[0.4cm]
{ \Large \bfseries Title of document \\ \large Subtitle? \\[0.3cm] }
{\large\textsc{NAME}}\\
{Institution}\\[0.3cm]
ule{\linewidth}{0.9mm}
\end{center}
%If you want:
\tableofcontents
\begin{center}
ule{\linewidth}{0.9mm}
\end{center}
%Section, subsection, subsubsection
%Numbering is automatic
\section{Section title}
\subsection{Subsection title}
\subsection{Text formatting}
Words words words. Swedish letters won't work. Get them like this:
{a}, \"a, \"o. (May need to disable `Smart Quotes' under `Format' to make " work here.
Single line breaks don't start a new line. %More line breaks make it easier to locate errors.
Double ones do. \\ Double backslash also starts a new paragraph, but not indented.
oindent Alternatively this. \\ \indent Also this.
Put word in \emph{italics}. Or \textit{italics}, \textbf{bold}.\\
Dollar signs activate maths mode: $a\times(b\times c)=(a\times b)\times c$. \\
Comprehensive lists of symbols can be found online. Here are some: $\times$, $\cdot$, $\dots$, $\cdots$, $\equiv$, $\approx$, $\sim$, $\propto$, $
ightarrow$, $\Rightarrow$, $\mapsto$, etc. Greek letters: $\alpha,\beta,\gamma,\Gamma$ etc. \\
Some functions/operations have their own commands: e.g. $\sin x$, $\cos x$, $\exp x$, $\exp(x^2+y^2)$, etc. Others you must write yourself, e.g. $\text{csc}\,x$.\\ %Writing \, inserts a small space in maths mode
Here we use some of our own commands from the preamble: $\ud x$, $\ue^{\ui x}\equiv\cos x+\ui\sin x$.\\
Fractions: $\frac{1}{2}$, $\frac{\ud y}{\ud x}$.\\
Mathematical text styles: $\mathbb{Z}$, $\mathbb{R}$, $\mathbf{x}$, $\mathbf{A}$, $\mathbb{RP}^2$, etc.
Doesn't work for symbols, Greek letters etc. Use: $\boldsymbol{\alpha}$, etc.
\subsection{Equations}
Display style for equations.
%Equation environment
Equation with a number:
\begin{equation}
-\frac{\ud^2\psi}{\ud^2x}=\lambda\psi
\end{equation}
Equation without a number: %Use * to remove numbers. Also works for sections, subsections etc.
\begin{equation*}
f'(x):=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}.
\end{equation*}
Add labels to numbered equations to refer to equations later:
\begin{equation} \label{whatever}
\iiint_V\ud\omega=\iint_{\partial V}\omega.
\end{equation}
Here we refer to equation \eqref{whatever}. Numbering is automatic. Can do the same for sections:
\subsection{Subsection for the purpose of adding a reference} \label{another}
Refer to Section
ef{another}. %Run file twice for references to display. Otherwise will just show ??.
\subsection{More with equations}
Brackets to fit the size of the text:
\begin{equation}
a\left(\frac{b}{c}+\frac{d}{e}
ight)=\frac{a(be-dc)}{ce}.
\end{equation}
Works for $[$ and $\{$ also.\\
Align environment without numbers:
\begin{align*}
x^2+px+q & = x^2+px+\tfrac{p^2}{4}-\tfrac{p^2}{4}+q\\
& = \left(x+\tfrac{p}{2}
ight)^2-\tfrac{p^2}{4}+q
\end{align*}
Align environment with some numbers:
\begin{align}
(\mathbb{A}(k)-\ui\mathbb{B}(k))(\mathbb{A}(k)-\ui\mathbb{B}(k))^*&=(\mathbb{A}(k)+\ui\mathbb{B}(k))(\mathbb{A}(k)+\ui\mathbb{B}(k))^*\label{akbk}\\
&=\mathbb{A}(k)\mathbb{A}(k)^*+\mathbb{B}(k)\mathbb{B}(k)^*
onumber\\ %no number here
&=\left(\mathbb{A}(k)\middle|\mathbb{B}(k)
ight)\left(\mathbb{A}(k)\middle|\mathbb{B}(k)
ight)^*\label{akbkrank}.
\end{align}
Refer to \eqref{akbk}.\\
Cases:
\begin{equation*}
\partial^r\xi_{l,j}^k(x_j)=
\begin{cases}
k^r\delta^r_l,&\text{if $r=0,1,\dots,n-1$,}\\
\ui(-1)^{r-n}k^r\delta^r_{2n-1-l},&\text{if $r=n,n+1,\dots,2n-1$,}
\end{cases}
\end{equation*}
\section{Theorem environments}
\begin{theorem} \label{firsttheorem}
Statement of theorem. Automatically in italics. \emph{Not in italics}.
\begin{equation}
\int_a^bf'(t)\,\ud t=f(b)-f(a).
\end{equation}
More words.
\end{theorem}
\begin{proof}
Proof goes here. %The QED symbol appears automatically at the end of the proof.
\end{proof}
\begin{cor}
Statement of corollary.
\end{cor}
\begin{proof}
Follows from Theorem
ef{firsttheorem}
\end{proof}
Definition style environments e.g.
\begin{definition}
Not in italics
\end{definition}
\begin{example}
Example
\end{example}
\begin{Example}
Example
\end{Example}
%The package \usepackage{showlabels} is useful whilst writing for displaying your label names in the output document
% so you don't have to search for them in the TeX file. Remove the package when done.
\end{document}
@@theseal126 thank you for everything you deserve a manyvsubscribers
@@sheldoncooper891 hehe, no problem :)
Hi thanks for this video. I don’t know whether to become a lecturer or just a teacher.
Both choices are good, depending on what you prefer (more or less research)
@@PrzemekChojeckiAI Thanks. When I said teacher I meant a school teacher. I think that would be fulfilling but maybe it would be more exciting trying to discover new things. I learnt Galois Theory last year and it amazes me how someone discovered that.
@@Anteater23 You can try becoming a lecturer and see if you like it, and if not become a teacher. :)
@@PrzemekChojeckiAI I suppose it’s easier to do it that way than to go from teacher to lecturer
@@Anteater23 yes, definitely
What is the I.Q. required to become a researcher?
IQ doesn't matter, your problem solving skills do + perseverance.
Sir is PhD necessary for a resacher in math
Yes
Can you tell me how can I do research at mathematics at age of 18
Age doesnt matter, you should try to read papers on arxiv from a domain that interests you and work your way backwards
Hi, Sir! Can you please comment on this idea: Math research now is so hyperfocused that only at most 5 people can understand what you are doing. Instead of looking at math as a whole (e.g., looking for huge connections between seemingly disparate ideas, solving an intractable problem in subfield A by using a tool from subfield B), we are producing results for the sake of producing results (usually so that we don't get fired by our employer). Math now is so filled with minor results that nobody cares about them aside from the publisher and his/her adviser. Thanks!
hi, mostly it's true, 95% of maths is like that, but then there are also huge conjectures people are working on, and ideas bridging various fields. But you can't have this 5% without the minor results being published.
@@PrzemekChojeckiAI Thanks for the insight, Sir. Have a blessed day!
Hey....I m ur new subscriber from India
I also want to do PhD mathematics...🙏🙏
I hope ur vedios are helpfull for me🙏🙏🙏🙏👍👍👍
Good luck :)
Hi sir
I want to write research paper
Can you help me for writing research papers
Hey
Did you get help?
I need help too🙏
I have masters degree in computer science .i want to do phd in mathematics out side the college or external student as i am tooold to study with youngsters
Hi sir
Can you please guide me how to start research which topic is best?
How one can start his research from zero
There's no the best topic. Start by learning what domains of maths there are and learn more about what you would find the most interesting
I want to do PhD in mathematics.
May you help me by suggesting some topics
It's too broad, please talk with one of the professors from your local university
Please can you help me select mathematics topic for my research work as undergraduate education student.
You should ask your university professors for help - in the end they should guide you on the process.
please no chemistry
which is better we read article or books and how we can get it easy
Hi, I am from Pakistan I want to do PhD in mathematics. Give me idea about research proposal and scholarship
Sir how to contact you...?
Find me on Twitter ;)
Let me summarise.
Be brilliant.
With all due respect (and I have much respect for any mathematician), you look like young Mark Zuckerberg
:D :D :D
Machine learning is not mathematics!
It really is, its a bunch of linear algebra.
Thank you!
Thanks