In these pages are the latest information (including sample chapters and errata) for all the various books that I have been an author of:

- T. Tao, Solving mathematical problems: a personal perspective, Deakin University Press, 1992.
- T. Tao, Three regularity results in harmonic analysis, in “Topics in analysis and applications: selected theses”, R. Coifman, ed. World Scientific Publishing, 2000.
- T. Tao, Analysis I, Hindustan Book Agency, 2006.
- T. Tao, Analysis II, Hindustan Book Agency, 2006.
- T. Tao, Solving mathematical problems, second edition, Oxford University Press, 2006.
- T. Tao, V. Vu, Additive Combinatorics, Cambridge University Press, 2006.
- T. Tao, Nonlinear dispersive equations: local and global analysis, CBMS regional series in mathematics, 2006.
- T. Tao, Structure and Randomness: pages from year one of a mathematical blog, American Mathematical Society, 2008.
- T. Tao, Poincaré’s legacies: pages from year two of a mathematical blog, American Mathematical Society, 2009. (Includes graduate texts on ergodic theory and on the proof of the Poincaré conjecture.)
- T. Tao, An epsilon of room, Vol I., Graduate Studies in Mathematics, 117, American Mathematical Society, 2010; and An epsilon of room, Vol II., American Mathematical Society, 2010. (Includes a graduate text on real analysis.)
- T. Tao, An introduction to measure theory, Graduate Studies in Mathematics, 126, American Mathematical Society, 2011.
- T. Tao, Topics in random matrix theory, American Mathematical Society, 2012.
- T. Tao, Higher order Fourier analysis, Graduate Studies in Mathematics, 142, American Mathematical Society, 2012.
- T. Tao, Compactness and contradiction, American Mathematical Society, 2013.
- T. Tao, Hilbert’s fifth problem and related topics, American Mathematical Society. 2014.
- T. Tao, Spending symmetry, in preparation.
- T. Tao, Expansion in groups of Lie type, Graduate Studies in Mathematics Vol. 164, American Mathematical Society, 2015.

I will unfortunately not be able to respond to any requests for full-length copies of these books, beyond the material already linked to in these pages.

I have also been involved with the following books, though not as a primary author:

- The Princeton Companion to Mathematics, edited by Tim Gowers, J. Barrow-Green, I. Leader. Princeton University Press, 2008.
- Mathematicians: an outer view of the inner world, Mariana Cook, Princeton University Press, 2009
- Komplexität und Universalität, Terence Tao and Jochem Berlemann,
*Die weltweit besten mathematischen Artikel im 21. Jahrhundert*, Band 2, 2014. (A translated and illustrated version of this talk of mine.)

## 72 comments

Comments feed for this article

6 July, 2008 at 2:00 am

lovysinghalDear Prof. Tao,

I had tried to write this comment earlier too, but somehow it did not get posted. I just wanted to point out an error that the second and third books listed above are published by Hindustan Book Agency and not Hindustan University Press. To the best of my knowledge, there is no publication such as Hindustan Book Agency!

Regards,

Lovy

24 November, 2010 at 8:49 am

DineshHello Professor Tao,

I would like to know how much you studied each day in your secondary school years.

Thank You

29 June, 2012 at 2:40 am

Dr Owais AhmadU r absolutely wrong there is hindustan book agency in india

6 July, 2008 at 8:11 am

Terence TaoDear Lovy: Thanks for the correction!

28 July, 2015 at 3:18 pm

rajhi terence,

i have a general question.is mathematics something that which already exists in nature and you people are discovering it or is it an invented concept….

6 July, 2008 at 12:43 pm

lovysinghalSorry, I meant “no publication such as Hindustan University Press!”

5 August, 2008 at 3:04 pm

关于近期的学习计划 « Liuxiaochuan’s Weblog[…] 关于近期的学习计划 August 5, 2008 — liuxiaochuan 我打算开始用较长的时间学习非线性偏微分方程，以陶哲轩的两门课程math 251A和251B为主要学习内容。教材为陶哲轩的书： Nonlinear dispersive equations: local and global analysis。 […]

21 February, 2014 at 12:55 am

Anonymous川哥加油！

27 February, 2009 at 12:15 am

milosDear Prof. Tao

Your book Solving mathematical problems: a personal perspective are really graet. It is very inspirational for mathematicians worldwide.

12 March, 2009 at 3:23 pm

AnonymousDear Professor Tao,

I have a stupid question: If you are good at math, then does that mean also, that you must be good at physics? And that if you are not good at physics, then you’re probably not good at math?

thank you for your time.

1 April, 2009 at 6:51 am

Kai.KuHello,Dear Professor Tao.

I am a student from china,a non-famous university.I am studying math.I begin to study math later some years than you. Now in the fourth years in the university.I feeled it is a litte later. I have some interested in real-number,topo,geometry.And I have a bad English!

Thank you!

1 June, 2009 at 11:38 am

world citiesthanks Dear Professor Tao.

23 June, 2009 at 9:47 am

PaymanHi Professor Tao

I just wanted to ask you,what`s your attitude about mathematics?What thing or things makes you to work on math subjects and cunstractions?

Is commutative algebra or Homological algebra your favorite branches of math?

All the best

Payman

9 July, 2009 at 11:49 am

mathematiciansDear All blog visitors,

here is a nice book yet published,

it introduces you to Prof Tao and some other great mathematicians of our time:

Mathematicians:

An Outer View of the Inner World

Mariana Cook

With an introduction by R. C. Gunning

http://press.princeton.edu/titles/8860.html

best,

6 September, 2009 at 1:41 am

AnonymousDear Prof Tao,

I recently bought a copy of your book: Solving mathematical problems a personal perspective. I thank you for helping students interested in maths, to learn how to solve problems. Your generosity to those average in maths , is beyond expectations.

And to answer Anonymous on physics and maths. I think you can do maths without doing physics or any other science subjects.

23 November, 2009 at 12:56 am

PrakashYou are my biggest inspiration when it comes to solving maths..I enjoy the way how you describe maths as a game and play with it…Outside the maths world you are such a humble personality….it really makes me consider you ‘the most beautiful mind ‘on Earth

2 December, 2009 at 4:07 pm

AnonymousDear Prof Tao,

I wish there was a complex analysis book which was written by you.

Your analysis book is one of the most lucid math books I’ve ever seen.

Finally there is a man who is a master of both math and pedagogy. Thank you.

31 January, 2010 at 9:19 pm

Dasapri Setiawan TanDear Terry,

Just now I find you in FB and please called m as Iwan. I know you more less in 1983 in Indonesia I had ever read you little biografy of you in the Indonesian’s local journal. I really more want to know of you and especially about your genious. How old when you pass the elementry? junior high school? Senior High School and the university?

So I really fan to you.

Best Regards from your friend from Indonesia,

Dasapri Setiawan Tan

2 March, 2010 at 5:58 am

UjjwalDear Prof Terence Tao

I have gone through your book Analysis- I and i have found it to be the best book on Real Analysis i have ever come across. The attitude of looking at the fundamentals that is missing from most of the books does indeed place this book far ahead of many others..

I felt that is it not possible to Replace the axiom that 0 is the not the successor of any natural number by the Principle of Mathematical induction ? I mean it is possible to prove it via induction, Is it not ??

The light shed by you on this post is eagerly awaited

Thank you

Ujjwal

2 March, 2010 at 10:52 am

Terence TaoEach of the Peano axioms is independent of the others; there exist number systems which obey all but one of the axioms. For instance, a cyclic group Z/NZ, which “wraps around” N back to 0, will obey the induction axiom, and all the other Peano axioms except for the the one about 0 not being the successor of any element.

14 May, 2010 at 1:34 am

Murvat, BakuDear profesor Tao,

I really admire of your talant! I wish you more successes in math.

17 October, 2010 at 3:12 am

maryam alrashedHi,

I am looking for your lecture notes on Riemannian manifolds?? it seems that they are off the page!!!!

Thanks

M

17 October, 2010 at 11:32 am

Terence TaoThe “Poincare’s legacies” book (Vol II) contains a section reviewing Riemannian geometry that was based on this blog post.

10 November, 2010 at 8:14 pm

pocketbikeprideI admire your intelligence. Math is a very hard subject. I’m much more proficient in English.

14 December, 2010 at 8:52 pm

sutrisno wijayai like this blog, inspire me to learn mathematics morely…

thanks to mr terence tao,

2 January, 2011 at 2:47 am

science and mathNice.

Thanks for sharing.

And if there is any ebook version of books then please post the link in this post.

4 January, 2011 at 6:21 am

与非Dear Professor Tao,

First of all, Happy New year!

I’m a student of EE,UESTC in China. Last term I learnt your Analysis(Chinese edition)and I must say it’s a refreshing textbook for me~Thank you!

And now I’m going to study the introductory knowledge of CS. Honestly, it’s a little bit difficult to me, but I’ll stick to the end!

Again,happy 2011 with my best wishes!

Sincerely,

Terence Gao

3 June, 2011 at 8:15 am

Press4wardI am beginning to read Analysis II, which i need to find a good and relatively easy to read book on Lebegue measure and integration for a graduate level course, I really like the way Dr. Tao’s putting together the concept and the key idea.

I wish there will be more higher level analysis book coming from Dr.Tao.

4 June, 2011 at 8:02 am

oliverDear Professor Tao

l am a chinese student.Long years ago,l am heard of you.And,l begin to read your book(real analysis).But l feel very dificult to make sense all words.So l really want to know how l should study.How can l study real analysis well? How should l use many theorems?

thank you

oliver

7 June, 2011 at 4:54 am

werawut changinDear Prof. Tao I am a thailand student . I ‘m studying undergraduate in mathematics . I want to know how to good in mathematics .

I hope to study graduate with you at UCLA .

Respect and Faith

werawut changin

9 November, 2015 at 8:15 am

nicholasgrabillIt’s probably not a good idea to go to a university for a single professor as that professor might leave or change fields of study. It’s usually best to look over the smaller details of a course such as Location, Time, Course, Workload Focus, And such.

1 July, 2011 at 10:49 am

Compactness and contradiction « What’s new[…] Books […]

4 July, 2011 at 8:11 am

Vorlesung Analysis 1 (Wintersemester 2011/12) « UGroh's Weblog[…] Terence Tao, Analysis I / II (Hindustan Verlag; AMS), […]

19 July, 2011 at 8:26 am

ChrisDear Professor Tao,

Can you provide the errata to your books (especially Analysis 1 and 2) in the form of PDF?

[Your browser should have a “Print to PDF” feature (or something similar) that should do this. The CSS is set up to strip out the header and sidebar from web pages printed off of this blog. -T]19 July, 2011 at 10:14 pm

ChrisDear Professor Tao

No, my browser don’t have “print to PDF” feature. I print directly using the print function on the web browser and from the printout, all the mathematicial typings blurred out except the wordings in text. So I am requesting if possible can you upload the errata in the form of PDF as by doing such the mathematical typings will not be blurred out as compared when printed from web browser.

It is difficult to see the blurred out mathematical typings.

27 August, 2011 at 2:07 pm

ardent studentHi prof

I want to say that given the lucidity of your book, one can only imagine how much better your teaching must be.

I therefore request on behalf of all inspired students who would never have the opportunity to attend your lectures that you should give a set of maths lectures (not just on analysis) that may be available for download by these students. Very much like what feynmann and susskind did in physics. Thanks

29 August, 2011 at 2:26 am

Topics in Random Matrix Theory « Francesco Tudisco Homepage[…] I kindly suggest the book, it can be downloaded for free from the T. Tao’s blog […]

12 February, 2012 at 11:00 am

davideProf. Tao,

do You think there will be an Italian version of Your books?

Thank You so much.

Best regards

1 March, 2012 at 11:14 am

AnonymousI would like to apologize prof.Terry Tao where I can purchase saver books online analysis, I am Peruvian.

23 March, 2012 at 9:56 am

Nat Whilk“I will unfortunately not be able to respond to any requests for full-length copies of these books, beyond the material already linked to in these pages.”

I assume that requests for copies of your book don’t literally leave you unable to speak or type. I assume you mean that you choose not to distribute your books freely. How do you reconcile that choice with your proclamation (in regard to the Elsevier boycott) that all mathematicians should make the papers they write freely available? Our papers should be free but your books shouldn’t?

23 March, 2012 at 10:58 am

Terence TaoThat disclaimer is mostly applicable to the books I published up to 2006, for which the copyright is held by the publisher without an explicit agreement to make a full online version available (though I do have sample chapters for most of these books on this site). I obtained such an agreement for the books I published after 2006, and full online versions of these books are available on this web site.

23 March, 2012 at 11:31 am

Nat WhilkWhy did you make such agreements prior to 2006? If it’s wrong for other mathematicians not to make their papers freely available now, why wasn’t it wrong for you to make agreements prior to 2006 that made your books not freely available?

23 March, 2012 at 1:37 pm

Terence TaoPrior to 2006, I was not aware that publishers were willing to enter into publishing contracts while also permitting the author to post full versions of the text online. (There are a few precedents for this, but until recently it was quite rare, in contrast with papers in which online repositories such as the arXiv are well established.)

27 March, 2012 at 11:00 am

Hilbert’s fifth problem and related topics « What’s new[…] Books […]

23 July, 2012 at 11:02 pm

ArminHi Professor. I just started my two-year college. I want to transfer to UCLA for my undergraduate pure mathematics program. The degree my college offers is an “Associates of Arts”. Would it be fine to transfer with this degree?

Thanks,

18 November, 2012 at 10:16 am

Spending symmetry « What’s new[…] Books […]

18 January, 2013 at 4:47 pm

vishwajeet singhHello Dr Tao,

I’ve just started my studies in Random Matrices. Could you please tell me what foundations do I need to have before I can delve into the advanced theory of Random Matrix. Do I need to have foundation in Analysis, Measure Theory, Probability, Algebra or I can exclude Analysis??

Thanks.

11 April, 2013 at 7:16 pm

tramadol causes Acid refluxVery good write-up. I absolutely appreciate this site. Thanks!

16 July, 2013 at 11:55 pm

AnonymousDear Prof Terence Tao,

When i read “Set theory”, i get confused. Fox example, when you talk about intersections of families of sets, you used the word “for all a belongs to I”. I dont know what the exactly meaning of “all” here. Is it mean “every”? for a set, can we always choose or point out “every element” of it ? is it another assumption?

Thanks for your great work, and sorry for my poor English.

and by the way, is there a solution to your exercise? Thanks for your time.

27 September, 2013 at 9:38 am

Venkateswara Reddy KunduruRespected Professor Terence Tao, I liked Analysis I&II very much.The style is very simple and most beautiful. Prof Tao, I request you to post on your blog some of the finest books – which you like much – for senior undergraduate and fresh graduate students on the following branches – Analysis , Abstract Algebra , Topology, Combinatorics ,Graph Theory.

1 November, 2013 at 12:37 am

Books | hrbatanu[…] Books. […]

30 December, 2013 at 4:14 am

krisbaker1994Hello, an open question to all

I remember reading a comment/article where Mr. Tao stated a book or books that he used when he was a child that presented math in a fun way; numbers/primes were imagined as small creatures or something like that; I just need someone to point me to that article/ comment. And if there are any

other comments/articles where Mr.Tao states the different “fun” books he

read so that I can find them for my son . Thank you. Be forever grateful if someone replies. Kristoffer Baker

18 January, 2014 at 2:35 pm

ADear Terrence Tao,

I find it amazing that you have written all these books considering you are a Fields Medalist and do so much research. How do you complete the books without it interfering with your research? Or is it just that you don’t see yourself as being on the clock to produce your life’s work? I noticed some of these were produced before you got the award, so it doesn’t seem like a “going soft”. Do you feel these projects have somehow helped your research?

16 August, 2014 at 4:36 am

IshreetHi Terrance Tao,

My name is Ishreet and I study in Sydney in Australia.I am in grade 3.Do you have any grade 3 books for me?Can you please advice?

Thanks

14 October, 2014 at 1:50 pm

esvenDear Master Tao, in your Analysis I Book:

Exercise 2.2.2.

Lemma 2.2.10. Let “a” be a positive number. Then there

exists exactly one natural number b such that b++ = a.

I am an autodidact person , but i can’t solve this exercise. please help.

27 November, 2014 at 4:04 am

Zouhair haddedIn the Proof of the Lemma 2.3.1 of your Book topics on random matrices i didn’t Understand how to get the Constant C from C^n Or Could we replace in the Claim C by C^n

[One can use some portion of the factor to eliminate if is large enough. (One could also eliminate the factor in this fashion, if desired.) -T.]29 March, 2015 at 9:46 am

Alexey VolobuevI believe on p310, 8.1.2, last line, you should have blue-white instead of red-white

[Which book are you referring to? – T.]17 April, 2015 at 3:10 am

AnalysisDear Professor Tao,

In Analysis I, Definition 6.4.1, a limit point is continually ε-adherent to the sequence mentioned for every ε>0.

Then using the observation under the remark 5.4.11, that the preposition 4.3.7 holds for reals, from 4.3.7 (a) and Definition 6.4.1 can we conclude that there exists a N >= m for which each n >= N the limit point is always equal to each member of the sequence for n>= N?

(In high school we were told that the sequence approaches infinitely the limit point but never “touch” it).

Thanks in advance.

(Undergraduate student)

17 April, 2015 at 3:27 am

AnalysisIf the above conclusion is true, then in example 6.4.3, for the sequence mentioned can we say that there for some N >=m each member of the sequence, for n >= N, is equal to 1?

17 April, 2015 at 8:09 am

Terence TaoNo; a counterexample is for instance given by setting and , which is a limit point of the sequence but not equal to any member of the sequence. The reason why Proposition 4.3.7(a) does not immediately apply here is because “-adherent” is not the same as “-close”. For instance, the sequence is -adherent to , because

at least oneof the is -close to , but the first few members of the sequence arenot-adherent to . See also Exercise 6.4.3.17 April, 2015 at 4:01 am

AnalysisCan we say that preposition 4.3.7 (a) holds for two real numbers, but not for one real number and one integer, in order 4.3.7 (a) to be consistent? If so, then can we prove that ε-closeness is consistent for one real and one integer as it concerns inequality but not equality?

25 September, 2015 at 8:41 pm

Peter YangProfessor Tao,

Have you ever made a book which consists of a collection of the posts from this blog? If not, is there any way to download all your posts on this blog?

Thanks!

Peter Yang

[All books published from 2008 onward were initially posts on this blog. -T.]29 September, 2015 at 2:56 am

lin yibinHello,terrence professor.this is my first time to take a comment in your blog.I feel so excited as if you were in front of me。you are my idol.i love math.my dream is to be a best mathematician.but i think it`s difficulty .i want to understand the article in your blog.how could i do?

3 November, 2015 at 10:21 am

Colin RustIn “Spending Symmetry”, p.11 you use the older-style terms “direct limit” and “inverse limit”, for which as you know the newer-style terms are, respectively (and confusingly!), “colimit” and “limit”. A suggestion: maybe indicate both (pairs of) alternatives. It might be a bit awkward, but this is a very common point of confusion.

5 November, 2015 at 6:41 pm

nicholasgrabillBesides those listed, would you recommend any other books as nice mathematical reads?

17 February, 2016 at 2:40 pm

naveedDear Professor Tao,

In chapter 2 of Analysis I, the object n++ is never defined. Assuming it is a function, it is not stated until lemma 2.2.10 that every positive natural number has a unique pre-image. However, before that, when considering Definition 2.2.1 (definition of addition), the question does come to mind whether a preimage (any, not necessarily unique) can always be obtained from n++. The questions I have are:

1. Does definition of addition (2.1.1) assume that given a number not equal to zero, one can always work out the (unique) “predecessor” to it?

2. In attempting the proof of lemma 2.2.10 (Let a be a positive number. Then there exists exactly one natural number b such that b++ = a), how do I perform induction on a when, by statement of the axiom of induction, the property should be true for 0 but clearly here is true for all a except zero. I have always taken the first element available ( in this case 1) when doing induction. However, here I am trying to work from first principles, hence this question.

3. is “n++” a function? If so, it seems to have been implicitly defined through its characterisation by axioms of natural numbers. Is that a valid way of defining functions?

Many Thanks for your time,

Naveed

17 February, 2016 at 7:14 pm

Terence TaoThe definition of addition is recursive, and relies on Proposition 2.1.16, which in turn uses pretty much all of the Peano axioms. Strictly speaking, one does not directly use Lemma 2.2.10 in the proof of Proposition 2.1.16, but the two statements are certainly very consistent with each other (as you say, if there were a non-zero number with no predecessor, then it should not be possible to uniquely specify a value to that number from a recursive definition, although formalising this intuition rigorously requires a bit of work.)

For your second question, you can perform induction on a statement such as “Either is zero, or there exists exactly one number such that .”

For the third question, strictly speaking is an operation rather than a function, but it can be made into a function once one has a little bit of set theory available: see Example 3.3.2.

23 July, 2016 at 2:24 am

AnonymousDear Professor Tao,

I dont know if you know the beautiful blue Danube walz composed by Johann Strauß. The spark for the music was provided to him by a dream containing the words ” Viana be glad oh oh why why”. So dreams often contain some hidden dormant breakthrough. Stepping out of the mist into the dawn of a new beauty.

Now my dream : 1+1= 2 or 1.

1+2= 3 or 1 or 2

1+3= 4 or 1 or 2 or 3.

2+2= 4 or 1 or 2 or 3.

2+3= 5 or 1 or 2 or 3 or 4.

5+7= 12 or 1 or 2 or………………..or 11.

It has to do with groups and circles and the fact that any chess piece can be replaced by a musical instrument and any chess game can thus be turned into a musical composition of some sort, and waves combining up to form larger waves, or breaking up into many individual smaller waves.

Thanks for a great website and your time ( youtube lectures etc…)

William.

5 September, 2016 at 6:02 pm

plmDear Terence, when do you plan to AMS publish your multiplicative analytic number theory notes?

By the way I feel they are your most impressive lecture notes, displaying the broadest array of skills and originality in their combination, do you see some other set of notes you are more proud of? (I suppose you will include related posts like that on the Montgomery uncertainty principle.)

One more question: do you feel you could easily rework out all the results you have presented at least in lecture notes? I mean given the title of the notes, give the main results with proofs? Which would give you the hardest time?

Congratulations and thanks for all the work.

2 October, 2016 at 3:49 am

Repository AlphaFor those who are not aware Analysis I & II have been published in their third edition at Springer, https://www.springer.com/gb/book/9789811017896

@Terry What are all the differences between this edition and the second one? Thanks!

18 January, 2017 at 4:38 am

AnonymousRespected Tao sir I have a general doubt on whether harmonic series of natural numbers have any direct asymptotical formula with the p nth prime.

5 April, 2017 at 8:55 pm

sport6011I find it amazing that you have written all these books considering you are a Fields Medalist and do so much researce.there are different types of books this is great work so far.