A great way to keep up-to-date with the current directions in your field is by skimming (abstracts of) papers uploaded to Arxiv. This is where the most recent pieces of research appear, months and even years before their actual publication in a refereed journal.
To subscribe to subject classes, or delete existing subscriptions, send an email containing 'add' or 'del' commands. For example,
To: math@arxiv.org
Subject: subscribe [Your Name]
add Algebraic Geometry
del Symplectic Geometry
will add AG and delete SG from your daily feed. The subject classes can be abbreviated (AG=Algebraic Geometry). To get a list of the valid subject classes, send an empty message 'To: math@arxiv.org' with 'Subject: subscribe'.
Comments:
You will receive an email every weekday containing titles and abstracts (plus titles of old ones that have been revised).
You will receive ONE email no matter how many subject classes you have subscribed to. They will be separated by subsections.
Once you find an abstract interesting you can click on the link provided to go to the full paper on Arxiv.
A great way to keep up-to-date with the current directions in your field is by skimming (abstracts of) papers uploaded to Arxiv. This is where the most recent pieces of research appear, months and even years before their actual publication in a refereed journal.
To subscribe to subject classes, or delete existing subscriptions, send an email containing 'add' or 'del' commands. For example,
To: math@arxiv.org
Subject: subscribe [Your Name]
add Algebraic Geometry
del Symplectic Geometry
will add AG and delete SG from your daily feed. The subject classes can be abbreviated (AG=Algebraic Geometry). To get a list of the valid subject classes, send an empty message 'To: math@arxiv.org' with 'Subject: subscribe'.
Comments:
You will receive an email every weekday containing titles and abstracts (plus titles of old ones that have been revised).
You will receive ONE email no matter how many subject classes you have subscribed to. They will be separated by subsections.
Once you find an abstract interesting you can click on the link provided to go to the full paper on Arxiv.
Stackexchange is a great place to ask questions and practice writing math. See my profile there.
See my collection of problems in advanced calculus if you preparing for a Preliminary Exams/Qualifying Exam in advanced calculus, or analysis.
Only interested in multivariable differential calculus? Click here!
Do not dismiss any piece of math as "easy, trivial, undergrad, etc." You can find deeper meaning in any math!
Immerse your mind in your problem. Keep your mind working on it all the time. There will be a "wait a second, can't I just..." moment, but you should constantly engage your brain in the problem for that to happen!
Never give up too early. Follow that approach again and again and again...
Trust your advisor. With their years of experience they often have the right intuition from the beginning.
Do not trust your advisor! Yes, I know I just contradicted myself, but... Everyone can go wrong. Verify for yourself. Convince yourself by your own research and not because your advisor said something was doable or not.
Find your place in the community. Brand yourself and sell your skills whether they are in teaching, in graphics, in coding, or something even more unique. Let themm know you!
Do not run from any chance to give talks, write math, or just spread your knowledge.
TBC.
Are you new to teaching/TA'ing? These notes might be helpful.
If you would like the Word file templates of these teaching related material please email me: Sample course outline and weekly schedule that I send my students before day 1. You can find sample worksheets, exams and midterms in my Teaching.
Teaching in a Nutshell!
An inspiring talk on mathematical education: