Mar 18


A Comprehensive And Up-To-Date Link

Library of University Mathematics Lecture

Notes, Webpages and Free Online

Math Texts From Grade 9 To Doctoral Level


The union of the mathematician with the poet, fervor with measure, passion with correctness,this surely is the ideal.

--William James, Collected Essays

  • Ok, we’ve now reached the part of the website I’m most proud of.

  • The part that really is its raison d'etre: The Library.  

  • Remember, the site's overriding philosophy/stated purpose is to provide a public educational resource and forum for financially challenged individuals. 

  • That resource is for self-education in mathematics. 
  • There are a legion of websites that post links to online course materials today. Some of them are listed here.

  • So saying you're linking lecture notes at your website is a little like telling them someone's reading their emails in the USA.

  • It's not exactly earth shaking or original information.

  • But I doubt you've ever seen a site like this, dear hearts.

  • Trust me on this.

  • This is an actual library that tries to compile all currently available free mathematics lecture notes and texts-and will make some attempt to keep it updated.

  • Some backstory first-because this library is really the skeleton that supports the living organism of entire website. 

  • I began composing this webpage in January 2013. The virtual library component, back then, was the webpage.

  • My original purpose for this virtual library, back then, was colossally ambitious indeed.

  • I had the foolish notion in my head of unearthing, cataloging and reviewing a complete list of lecture notes, exercises, course materials and e-books in all the hard sciences.

  • I mean, a totally complete one. 

  • With on-time updates.

  • Total.

  • All subjects in the hard sciences.

  • Mathematics,biology, organic and inorganic chemistry,biochemistry, physics, physical chemistry, geology.

  • All the lecture notes available online at any given moment, completely updated so none escapes the list.

  • You get the idea.

  • To say this was completely unrealistic is a little like saying most lawyers are somewhat ethically challenged.

  • It took me nearly 2 years to assemble, collate and update as far as possible just what I have here.

  • But that being said, I've worked like a dog to create the most complete and informative online mathematics library that currently exists.

  • There are over 5000 sources here!

  • There are a bare handful of sites that have this many free sources linked through it. 2 things in particular make the lecture notes compilation of my website different from all others.

  • Firstly, at this library, there are detailed reviews by me of as many lecture notes and books as I could manage.

  • Yes,you read that correctly.

  • I've personally selected and attempted to carefully read and work through as many of the lecture notes and books as I could.

  • When I and others deemed my brain sufficiently mushy, I had to stop and watch Pacific Rim. 

  •  I'd damaged my thinking capacity sufficiently to be able to enjoy this mindless spectacle.

  • Fortunately, it wasn't sufficiently mushy enough to watch Fox News................

  • All kidding aside, the task simply became too arduous and time consuming. I wanted to have an active website before I went back to my studies-that wouldn't happen for several more years if I was stubborn enough to actually work through every set here.

  • However, this is still very much a work in progress and I do plan to review as many as is humanly possible eventually. But in the meantime, I wanted to begin to build a powerful online presence and I deemed there were sufficient components in place already to create a more then useful online mathematics resource. So I made the difficult choice to concentrate on finishing the undergraduate-level text links, as it seemed to me these would

  • a) Generate the most traffic to this library-and by extension, the rest of the site-as undergraduates would need the most guidance in looking for free study aids

  •                 and

  • b) The users of graduate level texts would not only have sufficient mathematical maturity to judge for themselves whether or not a source was what they were looking for and if it would be helpful to them, but most of them would prefer to do so themselves.

  • So this seemed like the best solution to my corundum.

  • Before getting to the actual library, it’s important to lay a few ground-rules for everyone-including me-to follow. Yeah, I know, I’m not thrilled either. I’d love to just post it and let the material freely fly over the WWW.
  • But that’d be stupidly irresponsible at best and illegal at worst. Most of the sources aren’t mine, of course-and was a result, questions about usage and proprietorship of material come into play.
  • Which brings me to the second unique quality of this online library that sets it apart from all the other pretenders out there. The difficulties outlined above are further complicated by the fact I intend this to be a fully interactive website, especially the library, where everyone who uses it will have input for further revisions, commentary and additions. As a result, I’ll need to lay out in some detail how the website is assembled and this is going to work in the future.
  • Bear with me. It’s like getting your inoculation vaccines as child-despite what the current idiot trend of not getting your kids vaccinated says, it’s better to just do what most of the experts say since it’ll save not only you and your family a lot of pain and suffering later, but the rest of us as well.

The Rules For All Users of The Library

1) Unless otherwise noted, all lecture notes and online textbook links in this library are those that are freely available.

 I define freely available as any source that can be obtaining through an exhaustive search of the conventional search engines such as Google or Dogpile.

For example, all the sources in the “Basic Calculus” section were obtained by simply searching the keywords “calculus AND lecture notes” , "calculus AND online textbooks" or “calculus AND course homepages” and then sorting them by quality and level of difficulty after a careful evaluation by me.

None-repeat, none-of the listed sources were obtained illegally.

No cracking-or to use popular, if strictly speaking incorrect, terminology, hacking-was used to obtain any of these sources. The goal here was to obtain a comprehensive library of sources that could in principle be obtained by people spending months at a keyboard collecting and categorizing links.

In other words, to paraphrase an old familiar detergent commercial- I worked hard so you don’t have to.

2) For the authors, professors and students who are the creators of all these sources, if you don’t want these works freely accessible in this library for whatever reason-it’s against your politics/religion to have free information available to peasants who can’t afford it, you’re under contract to a publishing company or university to produce this text exclusively for their company or students, the voices in your head tell you it’s important to screw me over to save all life in the United Galaxies from Cthulhu in the year 87,342 A.D.-whatever the reason- send me an email:

[email protected]

Prove you’re the author-then tell me the title and subject of the material you want removed and why. If it checks out, I’ll remove the link. Let’s be clear about something, though. I’m doing this purely as a courtesy to all of you for 2 reasons.

Firstly, it’s out of respect for the immense labor involved in producing a substantial set of lecture notes or an online textbook.

Secondly, if I was writing such a text and had specific intentions for it for my students or as a for-profit work and couldn’t afford to let it be posted for free download , I sure wouldn’t want someone telling me to go f*** myself and posting it anyway.

But make no mistake-I’ve broken no internet access or copyright laws posting any of this material at my site.

If I do remove any posted links by request, it will be strictly a courtesy.

Which is why I’m asking in return that you don’t demand I take it down just because you can.

I’m hoping you’ll ask because of a legitimate copyright concern or because of other plans you have for the material I wasn’t aware of.

If it’s for any other reason-political, ethical, etc.-I reserve the right to deny any of these requests.

I’m trying to create a significant resource for impoverished, debt-riddled students. I’m hoping that as educators, you’d be happy to let them become part of the body of information I’m building here.

If you don’t want them posted at this site for any purely personal reason and you feel that strongly about it-then I suggest you immediately put them behind a firewall or some other manner of restricted access.

We clear on this?

3) In this library, I tend to use the term “text” interchangeably for both lecture notes and actual online textbooks. But this interchangeability is somewhat misleading. Remember-lecture notes, while they have the gargantuan advantages of being freely available and being as inventive, personal and creative as they can be, are not formal textbooks. Therefore they have the huge drawback of lacking all the objective minimum quality standards of proofreading and multiple revisions that official textbooks have. Although with the birth of the internet and the posting of lecture notes as TeX, PostScript or PDF files have forced faculty to be far more careful then in past generations with their lecture notes, they are still nowhere near as polished as actual published textbooks.

I'm a gigantic fan of lecture notes. Indeed, one of my purposes with this library is to make a huge number of notes on various mathematics topic freely available so students can come to love and appreciate them as I do. I think their positive qualities-personal style of the lecturer, free accessibility, etc. -far outweigh their drawbacks for experienced students. Working through such notes, locating and correcting errors not only improves the notes for future class versions, but provides important “brain training” to mathematics students. Of course, for any but the most brilliant students, such corrections are best made either with the assistance of a teacher or in group study with peers.

But for students trying to learn a subject for the first time, when faced with a choice between lecture notes and an actual polished online textbook, should always choose the latter since they're not experienced enough or have the time to be able to work through errors. Even if there's only a handful in the notes, these can be damaging to the beginner. Therefore, my advice to beginning students approaching my site and library for the first time and may not be familiar with the somewhat informal nature of lecture notes-be vigilant for errors and never use a single set of notes as your sole textbook unless you have the help of a teacher.

A good way to avoid this problem is to use several sets of notes on the same topic at once. It’s virtually impossible for 3 sets of notes to have exactly the same errors and it’ll expose you to multiple perspectives on the same topic. To me, this is really the best recommended path-besides, all the notes are free, so why not use more then one?

4) My current plan is to update the library every 6 months to a year. This brings us to the other major difference between lecture notes and actual books and why this may be problematic: Lecture notes are as ephemeral and transitory as the blackboard chalk notes they’re descended from. They are dramatically revised, deleted and reposted in a completely different form all the time. The body of lecture notes on any one subject is as fluid as the ocean. One of the reasons it took so long to compile this library was this constant morphing. Several dozen listings I had when I began the website construction now no longer exist and several dozen more have been created since then. The listings that have been present through all drafts of the site have undergone at least some revision since then.

Which is why TULOOMATH's Library  is intended to be far more then a passive collection of texts; it’s intended to be an active community of users where the users will play an active role in not only the revision of the site, but the individual lecture notes scattered across cyberspace. I’d like all users at this site to freely submit errata, comments, questions, jokes regarding each of the texts that I can then pass on to the authors. If any of these links are dead or no longer accessible, please let me know. Conversely, if there are any freely accessible sources not listed here, please let me know with a link of where to find them and I’ll add them in a future revision. Either post your comment at the message board here or email me at:

[email protected]


All right, I forget anything? Oh, right, one last itty-bitty thing before we get to the library itself: 





All science requires mathematics. The knowledge of mathematical

things is almost innate in us. This is the easiest of sciences, a fact

which is obvious in that no one's brain rejects it; for laymen and people

who are utterly illiterate know how to count and reckon.

-Roger Bacon

Philosophy [nature] is written in that great book which ever is before our eyes --I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.- Galileo Galilei

It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem  must be true.- Herbert S. Gaskill, Foundations of Analysis: The Theory of Limits