Videos
Vi Hart: “Vi is the creator of math-related videos that have together gathered over 100 million views, including the “Doodling in Math Class” series, “Hexaflexagons”, and “Twelve Tones”.” Her main youtube channel is here.
3Blue1Brown: “3blue1brown, produced by Grant Sanderson, centers around presenting math with a visuals-first approach.” His youtube channel is here.
Numberphile: “Numberphile is produced by video journalist Brady Haran. The stars of the show include mathematicians and other guests from around the world. Topics range from the sublime to the ridiculous… from historic discoveries to latest breakthroughs.” The youtube channel is here.
Blogs and Web Sites
Ask a Mathematician/Ask a Physicist: A Q/A site with lots of very interesting questions and answers written by mathematical physicist Seth Cottrell and mathematician Spencer Greenberg. Cottrell also has a book out, which includes some of the most popular posts at the blog. Greenberg also has a web site here.
Mathematics Stack Exchange: High level question-and-answer site, where experts answer all kinds of questions about mathematics.
mathoverflow: Professional level question-and-answer site, where experts answer all kinds of research-level questions about mathematics.
nRICH: “NRICH is an innovative collaboration between the Faculties of Mathematics and Education at the University of Cambridge which focuses on problem solving and on creating opportunities for students to learn mathematics through exploration and discussion. NRICH provides thousands of free online mathematics resources for ages 3 to 18, covering all stages of early years, primary and secondary school education — completely free and available to all.”
+Plus Magazine: “Plus is an online magazine which aims to introduce readers to the beauty and the practical applications of mathematics. Plus provides articles and podcasts on any aspect of mathematics, covering topics as diverse as art, medicine, cosmology and sport, a news section, showing how recent news stories were often based on some underlying piece of maths that never made it to the newspapers, reviews of popular maths books, and puzzles for you to sharpen your wits. We have a regular interview with someone in a maths-related career, showing the wide range of uses maths gets put to in the real world. And all past content remains available online, which besides making for good browsing is, we hope, a useful resource for maths school students and teachers.”
mathblogging.org: “From research to recreation, from teaching to technology, from visual to virtual, there are hundreds of blogs and web sites writing about mathematics and its many facets. For the longest time there was no good way for math readers to discover math writers, and for math writers to be found. We want to change that. We have collected over 600 blogs and other news sources in one place. That number is steadily growing, and we invite you to submit even more! Meanwhile our editors showcase their favorite articles (home) and sites (featured). Our goal is to be the best place to seek out math-related content on the web.”
Platonic Realms: Mathematics miscellany, including quotes and an encyclopedic collection of mathematics-related articles.
John D. Cook: Solving hard problems in applied mathematics.
Tim Gowers: “Mathematics related discussions” hosted at his blog by a Fields medalist. His web site is here.
Nick Hobson’s Mathematical Miscellany: Contains numerous links to interesting mathematics.
Cathy O’Neil: Author of Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy.
David Richeson: “I am a Professor of Mathematics at Dickinson College. I am passionate about many areas of mathematics, but my research focuses on dynamical systems, topology, the history of mathematics, and recreational mathematics.”
James Tanton: “Joyous approaches to school mathematics … middle school, high school, and beyond.”
Sue VanHattum: “Math Mama is Sue VanHattum, a community college math teacher interested in all levels of math learning, and the mama of a teenage son. I entered the blogging world as I began work on Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers.”
Doron Zeilberger: Combinatorics, experimental mathematics, and provocative opinions.
Math for Love: “We are Dan Finkel and Katherine Cook, a husband and wife team devoted to transforming how math is taught and learned. We develop math games and curriculum, including tons of free lesson plans that we give away here. We train teachers and produce professional learning materials. And we write puzzles, produce math-art shows, and do whatever we can to show people how playful, beautiful, and life-changing mathematics can be.”
Mathologer: Fun mathematics resources developed by professors Burkard Polster and Marty Ross. The youtube channel is here.
Walter Fendt: Applets and more.
Articles and Lecture Notes
arXiv: “arXiv is a free distribution service and an open-access archive for scholarly articles in the fields of physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics.”
MacTutor History of Mathematics Archive: Created and maintained by Edmund Robertson and John O’Connor of the University of St. Andrews.
Museum of Mathematics: “MoMath, the National Museum of Mathematics, is an award-winning museum that highlights the role of mathematics in illuminating the patterns and structures all around us. Its dynamic exhibits, galleries, and programs are designed to stimulate inquiry, spark curiosity, and reveal the wonders of mathematics. The Museum’s innovative exhibits will engage visitors of every age, from 1 to 100!”
John Armstrong: High-level expository content.
Math Pages: Lots of articles on mathematics, physics, and their history by Kevin Brown.
Paul’s Online Notes: Written by Paul Dawkins, Lamar University. Extensive notes in pre-calculus algebra, calculus, and differential equations. Includes lots of practice problems with answers.
Pete L. Clark: Also see his numerous university-level lecture notes here.
Tanya Khovanova: Also see her blog here.
Willard Miller: Graduate-level lecture notes.
Roy Smith: Lots of lecture notes.
Terence Tao: Lots of high-level expository and research content here from a Fields medalist. His blog is here.
Jan Vrbik: Numerous undergraduate-level lecture notes.
Online Courses
MIT Open Courseware: “MIT OpenCourseWare (OCW) is a web-based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity.”
Professional Associations
Fields Institute for Research in Mathematical Sciences: Also see their Centre for Mathematics Education.
Canadian Mathematical Society: Also see their Education section.
Ontario Association of Mathematics Educators:
Notices of the American Mathematical Society: Also see the AMS blog, On Teaching and Learning Mathematics.
Mathematical Association of America:
Vector: Journal of the British Columbia Association of Mathematics Teachers
Humour
Pi is Wrong!: Provocative and humorous criticism of the definition of pi from Bob Palais at the University of Utah.
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