(Always) Under Construction

There are many tricks of the trade that make certain common tasks in mathematics easier. I will try to detail some of them here, providing links and some explanations.

For math majors and graduate students

Tips with TeX and figures:

• Detexify LaTeX handwritten symbol recognition: quick-find the symbol command you are looking for!
  or you could just search through The Comprehensive LaTeX Symbol List -- see page 172!
• Inkscape: Draw using a nice GUI, then output as TikZ!
• For Beamer (presentation program), TikZ, and BibTeX (bibliography), see a presentation prepared with Fei Ye: either in PDF form or in TEX form
• For more details about TikZ (a recursive acronym standing for "TikZ ist kein Zeichenprogramm," German for "TikZ is no drawing program"), check out the pgf manual and TikZ and PGF examples
  
• Possibly useful packages include "ToDoNotes" and "Changes"
• Possibly useful external programs include the LatexDiff program and websites ShareLatex.com or Overleaf.
  
• TikZposter: Create posters with this TeX package designed by Rick Barnard and a colleague
  
• On writing mathematics: How to write mathematics badly, a talk by Jean-Pierre Serre; How to write mathematics by Halmos; ... (more to come)

For resilience:

• Living Proof: Stories of Resilience Along the Mathematical Journey

For effective communication of data:

• Technically Speaking series of videos on making good presentations
• The creator of the website Junk Charts refers to this as The Trifecta Checkup: What is the question? What does the data say? What does the visual say?

Professional materials:

• Make a professional website! Find one you like and imitate it!
  (People who took my advice include: Kyle Istvan, Austin Scirratt)
• Start building your CV as you go.
• Make contacts with professors in your subject area... they might one day be colleagues

For teaching:

• When you answer a student's email, make the question and answer available on your website so that you don't have to answer it again.
• Make sure your students know How to Email a Professor (also here)
• Share this with students who ask: "Did I Miss Anything?"

For going to graduate school:

• My biggest advice is to establish a social support system, either with other students in the department or with (local) undergraduates that you might have something in common with, like a hobby or a sport. When things start to get difficult, and if you are far from friends and family at home, you will be glad you had one in place already.
• In 2007, I helped to start a program for incoming graduate students that helped bond the group of us. It is still running to this day. You don't necessarily need support from your department like we had. Prior to 2007, I kept it simple: I invited people to lunch midweek, to hang out the weekend before the semester begun, or to join us for a game of ultimate frisbee.
• What advice did you wish you had before undertaking a PhD in science? Answer by Tom Mcneill
• Advice from Ada Morse
• An article discussing "imposter syndrome," anxiety, depression, and suicide among the mental health challenges of graduate students.
• Ph.D. students face significant mental health challenges
• What is Imposter Syndrome and how can you combat it?

For finding a job in industry:

• Jesse Johnson's post on the Low Dimensional Topology blog entitled Dispatches from the Dark Side
• Evelyn Lamb's post on the AMS Blog on Math Blogs on What Are You Going to Do with That?

On the job search in academia:

• Advice you won't hear about location

On mathematics for all:

• AMS Blog inclusion/exclusion
• National Association of Mathematicians, open to all persons interested in promoting excellence in the mathematical sciences and promoting the mathematical development of all underrepresented minorities
• Spectra, the Association for LGBT Mathematicians
• 500 Queer Scientists
• Mathematically Gifted & Black
• Mathematicians of the African Diaspora
• Latinxs and Hispanics in Mathematical Sciences
• Math for Equality buttons etc on Zazzle

AMS Blogs:

• Graduate Student Blog
• PhD + Epsilon
• All AMS Blogs

For knot theorists

Useful tools in knot theory:

• https://github.com/joshuahhh/knot-identification-tool (used to be http://web.mit.edu/joshuah/www/projects/kit/) lets you identify a knot you draw (and change its crossings)
• http://katlas.math.toronto.edu/wiki/Main_Page The Knot Atlas contains tables of knots and their invariants
• http://www.indiana.edu/~knotinfo/ Knot Info allows you to compare invariants across many knots
• http://homepages.math.uic.edu/~culler/gridlink/ The GridLink program can be used to compute Knot Floer Homology
• SnapPea
• Globular
• Knoto-ID to identify knotoids

Some knot-related "links":

• Vi Hart's video on knots called "Doodling in Math Class: Snakes + Graphs", November 2010, showcasing the "Tait checkerboard graph" from my research
• Dan Silver's History of Knot Theory talk at the X-Math conference at LSU, Summer 2009
• Numberphile's two videos with Mariel Vazquez from UC Davis on applications of knot theory to DNA in The Shape of DNA and How DNA unties its own knots
• Dave Auckly's Crunched Charms, an introduction to knot theory in the New York Times' NumberPlay, May 2014
• Henry Segerman's Triangulating the figure 8 knot complement, October 2014, showing why 3-manifold theorists and hyperbolic geometers care about knots
• William Thurston's Knots to Narnia at UC Berkeley, March 1992, explaining why cyclic branched coverings are interesting
• Some cool visualizations posted on YouTube by my math younger brother Mustafa Hajij

Some articles from the Concise Encyclopedia of Knot Theory:

• Alternating Knots by William W. Menasco
• What is a Singular Knot? by Zsuzsanna Dancso
• Invariants of Spatial Graphs by Blake Mellor
• Diagrammatic representations of knots and links as closed braids by Sofia Lambropoulou
• State Surfaces of Links by Efstratia Kalfagianni
• Turaev Surfaces by Seungwon Kim and Ilya Kofman
• Linking number and Milnor invariants by Jean-Baptiste Meilhan
• Quantum invariants via Hopf algebras and solutions to the Yang-Baxter equation by Leandro Vendramin

Conference announcements:

• Low Dimensional Topology blog's list of upcoming conferences

Math blogs:

• Low Dimensional Topology blog
• The Electric Handle Slide blog, started by Peter Lambert-Cole, who was also a graduate student at LSU, and Laura Starkston while we were at a summer school in Budapest in 2012
• Terry Tao's blog (with a section on Career Advice)
• John Baez's blog

For the general public

Other fun stuff:

• Vi Hart's great website
• Tom Lehrer's "Lobachevsky" (jokingly)
• The History of Mathematics, a four-part BBC documentary
• How to Turn a Sphere Inside Out
• Fermat's Last Theorem
• Donald Duck in MathMagic Land from 1959

Some great fun and educational YouTube channels:

• Vi Hart
• NumberPhile
• Steve Mould
• Veritasium (science)
• Minute Physics
• Minute Earth
• Physics Girl / Woman
• A Capella Science
• Vsauce
• Dara O Briain: School of Hard Sums, a BBC show hosted by a comedian trained in mathematics that features some fun problems.

Webcomics:

• XKCD and what if?
• Saturday Morning Breakfast Cereal

Games:

• Euclid the Game: Compass and straight-edge constructions
• Planarity.net, the problem of embedding a planar graph, designed by John Tantalo and Mary Radcliffe -- who was an REU student at LSU!
• Simon Tatham's Portable Puzzle Collection, a collection of many math-minded games -- shown to me by Cody Armond
• A list of some games that was floating around the internet.

Math-related TV shows for kids:

• Square One TV: on PBS from 1987 to 1992
• CyberChase: on PBS from 2002 to present
• The Doozers: kids solve problems with engineering, on Hulu from 2014 to present

Education:

• Resources from Scott Baldridge, author of "Elementary Mathematics for Teachers" and "Elementary Geometry for Teachers" and the lead writer and lead mathematician for the Eureka Math/EngageNY mathematics PK-12 curriculum.
• Bedtime Math, including stories that end with short math problems that you can read to your kids!