I just learned (from Emmanuel Kowalski’s blog) that the AMS has just started a repository of open-access mathematics lecture notes. There are only a few such sets of notes there at present, but hopefully it will grow in the future; I just submitted some old lecture notes of mine from an undergraduate linear algebra course I taught in 2002 (with some updating of format and fixing of various typos).

[Update, Dec 22: my own notes are now on the repository.]

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18 December, 2016 at 1:41 pm

AnonymousThat is a nice one.

18 December, 2016 at 5:05 pm

AnonymousIt’d be nice if there were an upvoting system in place, and also a comments section for each set of notes.

18 December, 2016 at 8:26 pm

John SidlesIt may be that existing StackExchanges effectively provide the rating service that you suggest, in the sense that (for example) searching

MathOverflowfor “Kowalski notes” finds the well-rated question “Elementary Aspects of Galois Deformation”, which includes a link to (what are now) Kowalski’s open math notes.A substantial and not-readily-duplicated virtue of the StackExchanges (as it seems to me) is that StackExchange ratings aren’t readily “gamed” (in the all-too-familiar sense that, for example, Amazon product ratings can be gamed).

In summary, if it becomes common practice for StackExchange comments to reference AMS open math notes (when applicable)—perhaps tags could be introduced to facilitate this?—then two systems that individually are very good for mathematics might together be even better.

18 December, 2016 at 9:21 pm

Emmanuel KowalskiThe notes that are on Open Math Notes are _not_ those on Galois deformations! (They couldn’t be, because those were notes I had taken during a course of J. Tunnell, not something that I had written myself).

19 December, 2016 at 6:21 am

John SidlesMy apology is hereby extended, and especially, my appreciation and thanks are extended you and your mathematical collegues for your work in sharing your notes. Perhaps this shows why StackExchange tags for AMS open notes might eventually—as the number and variety of notes increases—prove helpful to the community at large, in that there’s no very obvious (to me) upper bound to the number and variety of open notes that might be posted in the long run.

18 December, 2016 at 8:32 pm

Free Math Notes by AMS | Singapore Maths Tuition[…] learnt from Professor Terence Tao’s blog that there is a new series of free math notes by the American Mathematical […]

19 December, 2016 at 5:56 am

AnonymousThe book “A singular mathematical promenade” by Etienne Ghys is remarkable both by its high mathematical quality and by its many beautiful artistic illustrations.

19 December, 2016 at 6:11 am

Lars EricsonHere’s one not on AMS: https://web.math.princeton.edu/~nelson/books/rept.pdf

In general it would be nice to see a lot more advanced math courses with interactive tests on EdX. Right now EdX, Coursera, Lagunita and the like have many many special interest courses but very few courses that take you from undergrad through graduate mathematics up to say the level of a pure or applied math Masters degree and pre-PhD oral exam.

19 December, 2016 at 6:12 am

Lars EricsonAnother thing that would be great to have somewhere is an interactive skill assessment that probes you on questions throughout college to graduate math and gives you back a picture of where you have been trained.

20 December, 2016 at 5:58 am

victorivriiI am rather disappointed by an implementation. There are two reasons for this

1) The Lecture Notes are 𝘰𝘱𝘦𝘯 but not 𝘰𝘱𝘦𝘯 𝘴𝘰𝘶𝘳𝘤𝘦, and therefore an instructor cannot modify them easily, adjusting to the particular cource. Basically these Notes are free rextbooks.

2) I strongly believe that 𝘱𝘥𝘧 is the most suitable format for scholarly articles and books, but lecture notes and textbooks are rather different. 10 y.a. I believed that 𝘱𝘥𝘧 was the best format for them as well, but 𝘩𝘵𝘮𝘭 has been advancing (html5, MathJax, etc). Sure, 𝘱𝘥𝘧 has been also advanced but its improvement are not that beneficial for math publications, especially because many of the require AA/AR versions 10+, not available for any plutform other than MacOS and Windows, leaving Linux on the cold. Other pdf browsers are not full-featured (no embedded movies/3D-models, no javascript support).

I believe that instead of 𝘩𝘰𝘴𝘵𝘪𝘯𝘨 online LN, AMS would fare better just 𝘤𝘢𝘵𝘢𝘭𝘰𝘨𝘪𝘯𝘨 them.

20 December, 2016 at 6:47 am

Douglas CostaWhoa, great news!

To all readers: Don’t forget to archive those PDF links, for example to archive Terry’s “https://terrytao.files.wordpress.com/2016/12/linear-algebra-notes.pdf” just type it after “https://web.archive.org/save/” like this:

https://web.archive.org/save/https://terrytao.files.wordpress.com/2016/12/linear-algebra-notes.pdf

This to ensure that these collections wont get lost and to ensure that it is there for future generations!

20 December, 2016 at 8:28 am

Merry ChristmasNice but rough implementation. Why course pages show files names like v3(PDF) instead of just giving a link? Some links are broken, e.g. for Étienne Ghys “A Singular Mathematical Promenade”.

22 December, 2016 at 3:30 am

AxelOn the Theodorus Spiral, look at the line 0, 3, 24 = n!-1.

16+1=17 [0,1[ Steinhaus problem

25-1=24

5*5=3*3+4*4 5 (G1,G2,G3,G4,G6) + 12 = 17 plane symmetry group

Vitruvian men = 8/5 with (3,4,5) + (1,4,V17) *4

Willes-Fermat = (3,4,5) = AM (3,4)/QM (3,4) = 0,7. V2 = 98,99… %

Lambda incompletness…

———————————–

23 (5, 11, 17, 23, 29) only one (p+6,+12,+18,+24)

23 is factorial, Eisenstein and Gaussian = its a “real” prime.

3,5,7

11,13

17,19

29,31

11, 23 are Gaussian and Eisenstein

Only 23 is factorial and not twice.

23 is regular and 3 class factors (the first)

Cunningham 1 (0 iteration) = 11, 13

22 December, 2016 at 4:03 am

AxelMerry Christmas.

4 January, 2017 at 9:04 pm

Peter GentHi Terry,

Thanks for letting us know about this AMS resource and also a big thanks for putting your linear algebra notes up there. I’m currently reading your Analysis book and loving every page so I really look forward to going through the linear algebra stuff next.

Peter.

5 January, 2017 at 10:27 pm

Nischay ReddyHey Terry,

I am planning to go through these lecture notes and attempt the assignments and examinations, and so, I was wondering, how much time were the students given for the midterm and final?

6 January, 2017 at 5:55 am

Lars EricsonHere is a large list of qualifying exams from UMass. I really wish there was an online program that mapped out skills and training with automatically generated and scored questions. Until then, this will have to do: https://www.math.umass.edu/graduate/sample-qualifying-exams

7 January, 2017 at 9:38 am

RamiroProfessor Tao, thank you very much for taking part in this. From the perspective of a non-mathematics student who is still interested in the field, an open source is a major incentive to carry on studying it. It is too bad that not everyone on your university understands the externalities of such an initiative, not making public their coursenotes.

7 January, 2017 at 9:27 pm

chr0538Dear Terence Tao,I’m a Chinese.Now I want to know that how to be a good mathematician.

Sorry,my English is not good. ,,, A Chinese student

9 January, 2017 at 2:54 am

chr0538Dear Mr. Tao, I am a junior high school student who loves math but my IQ is not high. My dream is to learn math and be a mathematician, but I do not know how to do it. Please teach me how to do it. If so, be grateful. A junior high school student who loves mathematics.

9 January, 2017 at 3:54 pm

Chris Aldrichchr0538, Dr. Tao wrote a great book on

Solving Mathematical Problems. Try starting there and see where it takes you. He’s also written some general math articles here on his blog that you can get something out of. Stick with math if you love it. It gets easier as you go further.9 January, 2017 at 8:13 pm

chr0538Thank you very much.

9 January, 2017 at 3:48 pm

AMS Open Math Notes[…] to Terry Tao for the […]

10 January, 2017 at 12:46 pm

LujanaDear Prof Tao,

Math is my passion and I decided I want to be a mathematician. My love for math started when I noticed patterns with number 9 in different arthimetic operations (It’s my favorite number since ever) when I was in second grade and I still notice new tricks to do mental math quickly. It’s fun but it’s way behind the mathematics of our modern world. I discovered mathematicians are interested in prime numbers. So I kept thinking about them. Last year, I came up with a simple function that generates prime numbers (not consecutive ones though). I wasn’t confident about it though for a few reasons: 1) it doesn’t generate consecutive primes 2) it doesn’t generate primes everytime, most of the outputs are numbers near primes but not actaully primes. So it generates primes and numbers near primes, but as the numbers get bigger the primes that it generates become less, and the numbers near the primes are even becoming more spaced from the primes 3) and to be honest I discovered it accidentally as a result of some mathematical flunks (I didn’t derive it logically, and I have no proof for why it works, I just found it and calculated results and discovered it generates primes). The education where I live is horrible. I can’t afford to buy any math books that I want. Recently I learned about Mills constant amd it encouraged me to try to publish my function. But I couldn’t publish it on arxiv because I’m still a middle school student and I don’t have a university email to be registered author. I just wanted other mathematicans to see it and give me any kind of feedback. My name is Lujana Elwan. I’m currently 15 years old and all I want is to become a mathematician like you and like Guass and Pierre de Fermat and Leonhard Euler. But I still can’t understand advanced mathematics. When I try to read a math paper I fail to understand (the mathematical notation used, the mathematical terms, and overall whta is meant byt it). I can’t study calculus because I can’t buy books and I am forced to study for my school exams as well. I hate school where they make us memorize everything to pass the exams. I am a human not a robot. I want to think intellectually and spend my life doing what I love. Please read this, and give me advice.

6 June, 2018 at 3:57 pm

Anonymous“… the exact substance of an object is not important, only its properties and functions.”

should be

“… the exact substance of an object is not important, only its properties and functions ARE.”?