Brendan W. Sullivan: Math Links
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Interesting Mathematics Websites
Problems and Puzzles
- r/problemoftheday — Sub-reddit for interesting mind-benders and math challenges of all difficulties and genres
- Open problems in graph theory — Maintained by Doug West
- William Lowell Putnam competition — Problems from 1985-2011 (solutions available 1995-2011)
- Puzzle Toad — Ongoing list of puzzle problems from combinatorics, graph theory, and related topics in computer science. Maintained by CMU Professors Tom Bohman, Po Shen-Loh, Alan Frieze, and Danny Sleator (whence the acronymic name)
- Open problems which anyone can understand — Thread on mathoverflow with a list of not particularly famous problems in math that are as of yet unsolved but still understandable by a math student.
- Search Pi — An applet that searches the known digits of pi for any sequence you want.
History and Human Interest
Fun & Recreation
- Numberphile — Video series devoted to specific numbers and their interesting properties, motivating lots of abstract mathematics for beginning students
- Proofs Without Words — A collection (on mathoverflow) of insightful and "aha!" proofs that consist of just a picture, with little need for explanation
Education and Writing
Interesting and/or Funny Mathematics Videos
Interesting Journals, Papers, Articles, Essays, and Talks
- "How To Write Mathematics" by Paul Halmos — Thorough and informative description of how Halmos writes (he was both prolific and extremely talented!) and how one should approach the process of writing mathematics
- Devlin's Angle: What is mathematical thinking? — From Keith Devlin's blog, a discussion of how mathematicians approach thinking, how non-mathematicians do, and how we can share these thought processes for the benefit of all
- Pi In The Sky Magazine — Run by Pacific Institute of Math Sciences, "aimed primarily at high school students and teachers, with the main goal of providing a cultural context/landscape for mathematics. It has a natural extension to junior high school students and undergraduates, and articles may also put curriculum topics in a different perspective." (their words)
- "What Is Teaching?" by Paul Halmos — Transcription of a talk given at the MAA annual meeting in 1994, advocating for problem-based education, among other recommendations and tips
- A Handbook for Mathematics Teaching Assistants — Written/provided by the MAA, a thorough handbook for TAs, both new and experienced
- Birds and Frogs — Interesting essay from Dyson Freeman about two "types" of mathematicians, birds (who soar above and explore the broad connections) and frogs (who dig in nearby dirt and investigate local beauty), with many examples from the history of math
- Euler Archive — A chronological list with links to Euler's journal articles. Explore the lifelong career of the most prolific mathematician in history!
Great Math Books
I'm most knowledgeable about this particularly area due to my dissertation project, and thus have several suggestions and non-suggestions.
Learning To Write & Read Proofs
For the "layman"
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