My list is by no means exhaustive, they are just the books that I have encountered. The hardest part of making a video like this is trying to pronounce all the author's names correctly so my apologies in advance for any that I said wrong :P Also in Australia we tend to say 'maths' instead of 'math' and there is very little consistency in which I choose to use.

When I wanted to learn English and practise for my listening exam I was listening to her videos!

"Calculus Made Easy" by Silvanus P. Thompson is one of the best calculus books. Reads like a novel and is over 100 years old and can be downloaded for free now, but its also still in print.

My best math teacher was a mad crazy Englishman who taught me math at a high school in France. His name was Mr. Baugh and he taught us calculus, algebra, analytical geometry, trig and probability. He referred to us as the blockheads - pas douée pour le math . He always said he wanted students who had no mathematics but who were extraordinarily good at Latin (sic loquitur). He spoke in a manner that proved he was completely mad and one girl said it sounds like broken French with an English accent but I can't understand a word he says. Mr. Baugh inspired me to swot - hit the books - so I was totally prepared before the lessons as I knew his language was incomprehensible. It worked until we hit probability. In order to understand probability one needs good clear language so I did not do well in that aspect of math as his musings were gibberish to me. I was not alone, except for Gilbert who seemed to understand him. Later on in life I studied Latin and I understood why Mr. Baugh had loved its precision and exactness - "know the correct ending," After this high school college was a breeze and I shuffled through with middling grades and no effort. Later in life however, when faced with difficult choices and unsolvable problems I reached back across time to the insane muttering of that mad, crazy bastard who came to my aid down the years and in my mind I saw him put the numbers on the board and say " prove to me you lot are not hopeless." He is long dead. When he marched into heaven he read the sign put up by the students - " she was always the fastest of ships (said of a very clever girl in class).

The most important math books for a modern student are Velleman 'How to Prove It' and Bloch 'Proofs and Fundamentals'. Work these books out and you will never have serious issues with math. Bloch has also written 'The Real Numbers and Real Analysis' which is a perfect book on the foundations of real analysis, it's so perfect that I wanna cry.

Not boring in the least! I'm 48 years old and I have just started my studies in math. The things that I once found boring are now all I want to do. I am a self taught and well rounded drummer like Buddy Rich. Not quite as great as Buddy but as close as I could possibly get and am still striving to get there. Drums are all about patterns and once you master a particular pattern it opens up a wormhole to other galaxies of rhythms and syncopations and I will be forever be learning these patterns. It is the same for mathematics for me. Drums and math are two of the same and the list that you just introduced is going to open up a whole other Universe for me to absorb. Thank you for all the videos you post! You are a wealth of knowledge and you speak with such clarity so please keep posting videos and I will keep watching. Thank you!

The key to any good maths textbook is to have a picture on its cover completely unrelated to the subject it's discussing.

"Math Major's Drug Deal" I just wanna take a moment to appreciate that combination of words 😂

There are 30 thorns in that cactus

"Introduction to Manifolds" By Loring Tu is super accessible and absolute GOLD, same with Munkre's "Topology"

just your voice calms me down and your videos reduce my stress. Thanks Tibees!

Thank you for the information you have provided here and the extra references stimulated in the comments. I loved to see and hear you talk about mathematics books. I was not bored at any time listening to you! 🙂

If you are looking for a single book to start with on math that covers the basics of the entire spectrum of subject in math, I can suggest "Mathematics For The Millions: How To Master The Magic Of Numbers" by Lancelot Hogben. It really helped me understand how each area of mathematics is related to solving problems in the real world and the writer assumes the reader has little or no background in the subject matter. First published in 1937, it is the older books and their authors that I believe had a talent for reaching students interested in complex subjects like Math.

Tibees you’re really an inspiration for any student, you just make the school seem, not easy, but worthy. I like your personality and I’m looking forward to be like you. Greetings from Mexico and keep it going 🇲🇽

I love "Measurement" by Paul Lockhart. It gives a great introduction to thinking about geometry and calculus by guiding you to great exercises without giving you the answers. It's like having a great teacher guiding you.

Thank you so much, I finished _Fermat’s last theorem_ today. It was a very good entertaining math book, I really enjoyed it.

This is a great list. The best resource i've seen for understanding linear algebra is the video series The Essence of Linear Algebra by 3blue1brown. Absolutely amazing, intuitive way to get the concepts, rather than just rote-learn. So good.

I'm currently a junior high school student that has exhausted all the high school maths curriculum that my school teaches so now I bought the book Mathematical methods for physics and engineering by Riley, Hobson, and Bence. The book was recommended to me by a great KZfaqr called Simon Clark. Absolutely love it, I've already bought it since and study maths with the book and with free online lectures. I'll soon start Calc 3 (multivariate calculus), then linear algebra and after that differential equations. Thank you very much +Tibees for inspiring me to study maths and physics. Love you!

Talking about math is never boring, thank you for sharing your experience with us

I know I’m late to the party, but I wanted to thank you for this awesome books list. Started _Fermat’s last theorem_ yesterday and it’s very good. Hope I’ll find inspiration for digging more in depth in the fascinating world of maths! Again, thank you.

The absolute boss book I found for Math learning was KA Stroud-Engineering Mathematics. I still use it today when I need a refresher.

An amazing introduction textbook for calculus is "Introductory Mathematical Analysis" by Haeussler, Paul & Wood. I did not enjoy Math at all until I started studying from this book but its comprehensive explanations made me understand all the topics and I started enjoying it after a while. Definitely would recommend!

I'm so happy that you mentioned Needham's Visual Complex Analysis :)

Thank you that you devoted some time to collect this list. I like it.

I recently drove across the country, and stopped by every used bookstore that I saw in order to check the mathematics section. I really enjoy taking a look at the way that different books expose mathematics differently, and I'm also always looking to expand my collection. Based upon this, as well as my experience as a math major, I have several comments on what books should be used to learn mathematics. The key point is this: the right book to use is highly dependent upon what you want to learn, what parts of it you want to learn, and what interests you. Several of the books that are mentioned in the video are what I would call "applied textbooks", which will give good methods for solving individual problems, or classes of techniques for applying mathematical tools to real world problems. "elementary linear algebra" and "early transcendentals" would fall into this category. These have almost nothing in common with some of the books here, like "principles of mathematical analysis", Dummit and Foote, or, to some degree, spivak's "calculus", which I would call "pure mathematics texts". These texts are based upon developing mathematical techniques through proving things. Most of so-called "pure math" is based around making mathematical statements and proving them. Spivak's calculus covers similar material to "early transcendentals", but each topic that is introduced will be rigorously defined (to some degree) and proved. The latter will teach you how to find the integral of e^2x, while the former will teach you how to show that taking that integral is possible, and examine the properties of integration (e.g. how do I know that the antiderivative of a continuous function is continuous, let alone differentiable). "principles of mathematical analysis" goes beyond this, wherein the backbone of the book is theorems, and its main goal is developing techniques for proving other things. Dummit and Foote probably wouldn't look very much like mathematics to the high-school reader, because it presumes that the reader is already very well versed in mathematical arguments. However, there is a third group of books, which aren't talked about all that frequently. These apply rigorous mathematical techniques to applied fields. Most of these books become accessible once someone has a background in linear algebra and multivariate calculus. For example, many books on optimization are fairly proof-based, however they have tangible examples that help to keep the exposition grounded. The book that convinced me to be a math major wasn't an abstract algebra textbook, it wasn't number theory, or non-euclidean geometry. The book is called "optimization in function spaces" by Amol Sasane, and it is accessible to anyone with a good grasp of linear algebra and abstract vector spaces, and multivariate calculus. Finite element analysis textbooks (a common method of dealing with PDEs in engineering) often have these properties as well, but a thorough understanding of these books requires a good understanding of differential equations first. Game theory, mathematical biology, and many other fields have books like these, which delicately introduce a new reader to the idea of rigorous proof without scaring them half to death. What I have discovered is that I really do love rigorous proof, I just find most of mathematics endlessly dry until I find something to apply it to. For me, the third category of books is perfect. For some people (like my roommate), the math is enough in and of itself, so the second "pure math" category is for them. Others will never catch the "rigorous proof" bug, and that's fine. There will always be books in the first category, and the math you'll learn from them will be tremendously useful in whatever field has driven you to learn math.

Nice job, Tibees. One of my favorite books is "e: The Story of a Number". I read it in 2008 and loved it. Will read it again.

I would like to thank you but not for the content of the video this time but for your, I don't know, "energy" in it. You look positive, smily, nice, honest. It is simply contagious looking you giving the recommendation book. Thank you!

Thanks, I appreciate the recommendations. I'm keen to go back to Maths and Physics as an older student. I value this list as a really great guide.

You're an inspiration. I can't thank KZfaq's recommender system enough for introducing me to your videos. Growing up I loved physics and maths but life had other plans for me and I ended up majoring in Computer Science . I want to go into Statistics and Machine Leaning and am currently teaching myself some mathematics using following books Calculus 1 and 2 by Tom Apostle. Linear Algebra by Kenneth Hoffman and Ray Kunze A first course in probability by Sheldon Ross.

Oh I look fondly on that Stewart book, we used the 7th edition back at my university. Genuinely fun times.

Thanks for including Elementary Linear Algebra - Howard Anton This is very great

Love the videos! Keep on making them! Grew up in the following sequence: Counting, Grouping, Addition, Subtraction, Multiplication, Division, Powers, Basic Roots, Algebra I + Geometry, Algebra II + Trig, Pre-Calc, Calc I, Calc II, Calc III, Diff Eq, Linear Algebra + Logic, Prob & Stat + Combinatorics, Graph Theory + Analysis, ...

Top intro stuff (IMhO): 1. Ian Stewart "Concepts of modern mathematics" - issued in 1980, now a bit forgotten. 2. Courant/Robbins "What is mathematics" - absolute classics. 3. "Infinitely large napkin" - google it. 4. "Concrete mathematics" by Knuth & gang - more toward discrete math.

Thanks for the video! You inspire me :)

Thankyou so much ma'am,this video is damn really very useful! It has benefited me a lot ! Please keep making more videos like this ! Thanks again 🙏🙏🙏

Thank you so much from the bottom of my heart for your effort.

Your videos are very nutritive for advanced students in high schools or students in first year of mathematics and surely they have changed the live of many of them. I congratulate you. I wanted to attach my list because I think that for mathematicians and physicists your list is necessary but not enough: 1.- Elementary Classical Analysis by J. Marsden or Mathematical Analysis by L. Kudriavstev or Calculus by D. Zill. 4:43 2.- Linear Algebra by S. Friedberg A. Insel L. Spence or Linear Algebra by V. Voevodin or Foundations of Linear algebra by A. Maltsev or Linear Algebra by S. Lang. 5:36 3.- Ordinary Differential Equations by V. Arnold or Differential Equations with Applications and Historical Notes by G. Simmons. 6:51 4.- Introductory Complex Analysis by R. Silverman or The Theory of Analytical Functions: A brief course by A. Markushevich. I would like to add that T. Needham has covered of glory!! 7:40 5.- Introductory Real Analysis by A. Kolmogorov and S. Fomin or Mathematical Analysis by T. Apostol or Hilbert Spaces with Applications by L. Debnath and P. Mikusinski. 8:54 6.- Abstract Algebra by I. Herstein or Introduction to Algebra by A. Kostrikin. 9:21 7.- Reason in Revolt by Ted Grant and A. Woods. 9:32 Your work about science diffusion will be rewarded by many students of science in the future because your work is love, and, as López Obrador says “The love is paid with love”.

1st... You talk so calm and low, yet I'm so captivated when I listen to you.

Thank you so much for covering these topics.

@Tibees Thank you so much for this video. You have earned my admiration as I can see you truly love Math

Terence Tao is soooo brilliant. Looking forward to reading his book. Of course it's been a while I've passed Analysis I but... true love never fades!

The two texts that got me through my engineering degree and are keepers for me are... Erwin Kreyszig's Advanced Engineering Mathematics, and... Howard Anton's Calculus. Other keepers are Engineering Thermodynamics by William Reynolds and Henry Perkins (my professor :-) ), and for psych Henry Gleitman's Psychology.

OMM! Thank you. Good to see book recommendations to learn

Thank you so much for these videos and information therein. I am seriously considering returning to school in order to begin a career in mathematics.

you've got my like because of spivaks calculus :) (also for fun check out logicomix and uncle petros and the goldbach conjecture)

i got lost in her eyes. any books on how to get out

Bit of a random point, but I love the way your videos start IMMEDIATELY, without intro or other nonsense.

You’ve grown to be one of my favorite youtubers.

Thank you for the lovely video! As an old physics major myself (emphasis on the word 'old'), may I make a couple of other recommendations? For another person's look back at his life as a mathematician (in addition to the famous book by Hardy you mentioned), I highly recommend "Adventures of a Mathematician," by Stanislaw Ulam. Born in Poland but later an emigrant to the United States, Ulam does an incredible job recalling the flavor of intellectual life in the old European capitals during the period between the two world wars. I especially like the scenes, which are particularly well drawn, of mathematicians sitting in cafes for hours talking and doing mathematics. If there was ever a romantic period (and place!) of mathematics, this was it. Ulam became a very close and lifelong friend of John von Neumann and many other of the 20th century's most famous mathematicians and physicists; he was also involved in the work at Los Alamos for the Manhattan Project. He had an incredible sense of humor - something not typically associated with the stereotypical mathematician. Just one example, from his widow (who clearly shared a good sense of humor), who added a postscript to the book in a later edition published after Ulam's death: "He [Ulam] used to say 'the best way to die is of a sudden heart attack or to be shot by a jealous husband.' He had the good fortune of succumbing to the first, though I believe he might have preferred the second.' (Ulam's widow, Francoise Ulam) My second recommendation is "Infinity' by Lillian Lieber. (Giving you a 2nd woman for your list!). Lieber was the head of the mathematics department of Long Island University in New York (U.S.) back in the 1930s I believe. She wrote a series of books on mathematics for the layman that are not at all dumbed down. They are actually quite sophisticated, but presented in an easygoing and entertaining manner. I first ran across them when I was in high school in the 1970s and was amazed. "Infinity" carefully goes through Cantor's discovery of transfinite numbers. It's an amazing book. She also wrote a book called "The Einstein Theory of Relativity" where she discusses both the special and general theories. (She goes into detail on tensor calculus in developing the apparatus needed to properly explain the latter.) All of her "popular" math books are charmingly illustrated by her husband, Hugh Lieber, who I believe was head of the art department at the same university. Anyway, that's my two cents worth! I hope someone finds these recommendations useful. Cheers!

Some more fun books: _Fantasia Mathematica_ and _The Mathematical Magpie_ are collections of mostly literary pieces (short stories and poems) on mathematical topics, including the story "The Devil and Simon Flagg", in which a man offers to sell his soul to the devil if the devil can prove Fermat's Last Theorem by a deadline (this was written long before Wiles). _Sphereland_ is an expansion on the ideas in _Flatland._ _Stress Analysis of a Strapless Evening Gown_ is a collection of humorous mathematical pieces, including a proof that Alexander the Great's horse did not exist, and had an infinite number of legs. Of course, everyone should be aware of the many collections of Martin Gardner's "Mathematical Games" columns. I'll also mention Hofstadter's _Gödel, Escher, Bach._ Lastly, don't forget Lewis Carroll. In addition to the two Alice books, which anyone interested in math or physics must read (especially Gardner's _Annotated Alice_ ), he also did some books of puzzles, which are still available.

Can't wait to get into these next summer!!

It was really useful list for passing my calculus exams. Especially the one recommended by Cambridge, I love maths, so I'm planning to read all of them. Thanks!

needhams book is great! Also, I'm reading "Higher Arithmetic" by H.Davenport. It's a number theory book recommended by Andrew Wiles. It's rather short at ~200 pages but dense.

Visual Complex Analysis is a wonderful book that really opened my eyes on the topic. Before reading it I thought complex numbers had no real meaning and were just arbitrary filler. Prime Obsession is another wonderful book and does a really clear explanation of the Riemann Hypothesis and the breakdown of the various areas of mathematical study in general.

Again! You are soooo helpful to me once again! Thank u! U keep saving me!😱

A very good effort to educate the people who wants to take interest in mathematics.....keep up the good work

This is a great list.But personally I would suggest people to try out Mathematical methods in Physics by Boas. It is written in a way that mathematics seems too easy. Particularly for people interested more in Physics than Maths.

Good recommendation re Simon Singh - He's amazing :-) I have his Cryptography and Simpson's Maths books, not yet the Fermat's Last Theorem one (it's defo on my list though :-) ). BTW have you seen what he did to reform UK libel law? - He called out Chiropractic as mostly bunk, paid heavily for it - but won out in the end. Huge respect from me! :-)

Starting a computer science degree next fall. Thank You for taking the time to make this video. 😀

Such a great content, I'm very grateful.

Currently working through Boas at UC Berkeley!

Abbott's Understanding Analysis is a very nice alternative to Rudin's. It is also probably a better book than Rudin for self learning, or for desperate students (it worked for me).

So glad Mary Boas is on your list. I just sent it (yesterday) to my grandson in Australia. My dad had it on his bookshelf and when he died my cousin’s husband asked to have it. (He worked at GCHQ!) That was thirty years ago. So I found a second hand copy for my grandson who loves maths. He is 16 in May, so it’s in his birthday parcel. KZfaq is so clever!

I dont need mathematics to see how wonderful You are. Thank You for spreading knowledge.

and here comes me who only studies from notes.

Hi Tibees! I really wanna recommend the book "Math, Better Explained" by Kalid Azad because, although by no means a college level textbook, it acts like an introductory guide to some very basic math concepts, and explores those concepts in fun and intuitive ways which makes for some convenient quick learning. Btw I really admire and like your content!

10:24 not for passionate people like everyone else here liking and commenting this video. The more we read the more we crave ! You convinced me, I subscribe ! Greetings from Canada !

Thank you very much for all your presentations.

I study bioengineering and when I was on 3rd semester I took multivariable calculus as an optional subject (everybody in bioengineering is afraid of taking it despite the fact that multivariable calculus is fundamental to understand nature), reading Calculus by James Stewart was the best thing I could do, the book was so clear and explains very well the idea of parcial derivatives and multiple integrals that I felt in love with it. In the other hand, Differential Equations by Dennis Zill is a good book that covers multiple ways to solve an ordinary differential equation (e.g. Laplace transform). I found Introducción al Algebra Lineal by Howard Anton in a sort of recycle paper can, I think someone threw it away and I took it, the book was basically new, but the book I use for algebra is Elementary Linear Algebra by Grossman. By the way, I think that talking about math books is very interesting because I always want to know which book is the best about explaining complicated math ideas.

A recommendation for a good leisure-type math book that is really easy to read is "Alex's adventures in numberland" by Alex Bellos, it explains various mathematical concepts like logarithms, higher dimensions, how they arrived at pi, euler's number and how they discovered them. Really good read :)

I liked the list as much as the video. Thanks for making the video on the title.

Thanks for the book reviews and lists!

Might I add Stein & Shakarchi's four-part analysis series?

"The man who counted" from Malba Tahan is way too basic but very interesting

Thank you for the inspiration and information!

You are an inspiration to many. Keep it up! My best wishes! 👍

For linear algebra I also recommend “Linear Algebra Done Right” by Sheldon Axler, for me is the best linear algebra book ever

What about "In a mind for Numbers" ? It teaches how to be good at math and science..

Thank you so much for your recommendations.

Interesting! Might look into some of these, as I would need to refresh my math. I had a fairly good relationship with math in high school, but sort of lost a lot of it in the years, but then became an applied statistician in epidemiology (hence a math refresher would be good)

Mathematical methods for physics and engineering is good for anyone doing maths as well.

It's late night in Buenos Aires right now to think in maths but I wanted to mention these books. I lovehate them A First Course in Calculus by Serge Lang Calculus by Michael Spivak Vector Calculus by Jerrold E. Marsden&Anthony Tromba Notas de Algebra by Enzo Gentile Linear Algebra by Kunze&Hoffman Complex Variables and Applications by Churchill&Brown Probability & Statistics by Seymour Lipschutz An Introduction to Wavelet Analysis by David Walnut Statistical and Computational Methods in Data Analysis by Siegmund Brandt Love your channel

She is good human from our planet to help those who seek to ease mathematics learning, Thank you.

Definitely NOT boring at all.... :-) Getting the right books (and teachers!) is critical IMO... ...In the past one was stuck with whatever was in the reading list, at the school/public/Uni library, on display at Technical Books et al., or if you were smart and not too shy (I was only half-qualified :'( ) to ask Librarians or bookstore people for suggestions or publishers' catalogues... so pretty much Pot Luck (especially in smallish-town New Zealand). Having someone like you (and collecting opinion from your viewers) list some good ones could save people lots of grief and time. Thanks for doing this one! :-)

*Mathematics: Its Content, Methods and Meaning* by: A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent'ev

You are so beautiful. And thank u for this video. It's really useful.

Thank you, this really helped!

I must thank you for these precious books, lam an Engineering student in mansoura university and you helped me so much :-)

"Talking about Maths books is one of the most boring things you can do." I couldn't disagree with you more.

What’s a good book on Algebra ? Honestly I never paid attention in school I really want to learn Algebra.

Howard Anton's textbook on "Calculus" is excellent...35 years ago when I was a freshman in engineering school and now when I need to brush up. It is for a solid three-semester course, with plenty of special topics.

Thanks for the recommendation for Linear Algebra, there is a lot of good books out there but even just reading about changing basis section was very helpful.

What's your accent from

omg i fall in love with her

Thanks for showing a direction in mathematics

Thanks for the list, The book I liked on your list was Visual Complex Analysis. I haven't read it but I am looking for additional math books to study on my own. Gilbert Strang's books on Linear Algebra and his MIT Open Courseware class are also really good.

You remind me of Pam from ‘The Office’

Hi. I recommend "Proofs and Fundamentals" by Ethan Bloch, its lecture is very clear and "eye-opening" for a first semester student. And for Linear Algebra, Gilbert Strang's MIT OCW lectures are excellent, so I bet its book on the subject is worth reading.

thanks Miss you are so clever and so kind thank , those books are uplifting :D

Thanks for sharing-great list, really like your smile.