For you Lang fans, note that "Undergraduate Algebra", 3rd edition (1987), was previously published as "Algebraic Structures"(1967). When Lang switched publishers to Springer-Verlag they republished some of his books under different titles. I'm working on a list, will post when I get it all deciphered.
@@TheMathSorcerer whats the hardest book to learn from starting at basic mathematicsto the last math subject ever which is numb er theory? right. all in one
The best TH-cam channel for me. You know I'm 54 and started loving mathematics thanks to you videos. I bought some books to start working on mathematics with my kids. Thanks a lot for sharing.
It was Serge Lang who coined the word "Diophantine Geometry", explicitly making it a branch in modern mathematics. Mordell wrote a review on his 1962 book Diophantine Geometry, heavily criticising the book for being too difficult to read (even for such a prominent mathematician L. J. Mordell!). But Lang responded with no mercy: I write my books as it should be, and nothing else. Both Mordell's review and Lang's response can be found in Lang's Fundamentals of Diophantine Geometry (1983).
I am sure that the soul of late Serge Lang is both delighted and flattered by your video. This is the way to honour the dead by remembering them and talking about them, respectfully. In my belief, most deceased souls pick up fans' thoughts from afar, no matter the distance.
I actually enjoyed A First Course in Calculus. I got an older edition which was brief and focused on the essentials, without flashy artwork/images or uninteresting applications. I think the oldest edition has been re-released under the title "Short Calculus", less than 300 pages and you learn all the calculus covered in a first course at my uni. It skips epsilon-delta stuff but is otherwise rigorous, as I recall it. A great book for a beginner in calculus and a great preparation for more rigorous books like the ones by Spivak or Apostol :)
I was born in 2005, and am now here as a calculus student myself. Even though my school doesn't use Mr. Serge Lang's books for class, this video has persuaded me to get one. Thanks for the recommendation!
I remember Serge Lang from Yale. He was a true-blue, _bona fide,_ one-hundred-percent weirdo. He had more weirdness in his little finger than most people have in their whole personalities.
@@TheMathSorcerer My favorite math professor at Yale was Angus McIntyre. He was always clear, and very nice, and he had one hilarious habit: he would scratch his nose with the same hand that was holding the chalk (this was back in the day when professors still used chalk) and the chalk-dust would get all over his face, so that by the end of the lecture he looked like a mime or a clown.
My advisor was mentored by Serge Lange. In fact, 5 of my favorite math professors all graduated from Yale at around the same time, and all studied under Lang. I don't know much about him, but my professors all thought highly of him.
I have Serge Lang's _A First Course in Calculus,_ 5th edition. It's around 600+ pages long and covers the basics (only single variables). I think it is a great book for beginners. I like it how he covers very important topics from elementary mathematics because students don't know them as a rule. Yeah, I know they all say that they studied precalc and that they don't need such topics, blah-blah-blah... *I think they do need it and they don't really know it!* I also think that most Lang's books are very good. You can hardly go wrong with them. They are indeed a good choice and can also work as additions. Of course, if a student plows through Stewart's _Elementary Algebra and Trigonometry_ which is around 1000 pages and then focuses on Stewart's _Calculus,_ it's even better than doing Lang's _A First Course in Calculus._ I just don't think that's realistic for 99% of students. They would either not have time or will to do that. So, Lang's books are kinda shortcut to get the gist. I guess, Lang's approach is very smart and good for teaching people without crowding them with too much information or tough problems.
Start with Lang’s Introduction to Linear Algebra. The first edition is only 170 pages and a really good way to get a first (geometric) feel for the subject. You can start it before calculus.
I looked at a number of Lang's books, and to me he doesn't seem to be interested in developing computational aspect of a subject, or the student's capabilities thereof, rather he seem to focuse on mathematical ideas and concepts; although that might not be in a very theoretical way. I felt he sought to enable a student to "feel" and to have an understanding of what's going on in the subject, sort of to grasp the subject matter of a book. This was how I thought of his books, generally, and It I found them valuable for that very reason, which make him stand out among math authors.
I appreciate your appreciation for books. It is worrisome that libraries get rid of these old books. Extra copies I can understand if they’re not in demand but I hope they keep at least one… Not just mathematical books but others too.
I'm surprised to hear someone think the exercises in A First Course in Calculus are too easy. There are definitely fewer exercises than in books like Stewart, and whether fewer exercises is a good or bad thing is up for debate I guess. But I found the exercises (and the exposition) to be quite a bit more sophisticated than in most books aimed at the same audiences, with a focus on big ideas and guiding students to derive useful expressions, rather than on drilling. And it does more drilling than any of his other books I have looked at. It *isn't* as hard as Apostol as is, but if you leave out starred stuff in Apostol they are basically the same other than that Apostol includes a chapter on differential equations and some (very) basic complex variables stuff. I have the most recent edition of A First Course in Calculus (5th, published by Springer-Verlag), so maybe this was different in an older editions.
My sister went to Union college. Some of my best memories were my parents driving there from NYC. I was in elementary school so I had to come along. I remember My Mom would pack fried chicken with bread and how it actually tasted good cold. I enjoyed seeing the transition from city to rural country side. Small world.
Hey there, MS!! I'm among your greatest fans and I love what you're doing. You're a human(e) being!! I LOVE YOUR VIDEOS!!! Whenever I see a new one of yours, I'm like a kid opening up presents on Christmas morning!! YOU'RE AWESOME!!!! :) :) :) :)
I believe that Lang's graduate algebra book, like his other books written at the graduate level (e.g. Differential Geometry, etc.) don't have answers or hints for problems. This is true in general for other authors of graduate books. Although universities may, for grading purposes or to develop the mathematical intuition of their graduate students, encourage this practice, I think it should be left upto the student whether to peek at the answer. I have found that finding the answer can correct a general misunderstanding of a concept or a calculational technique and is an important teaching tool. I wanted to make an unrelated comment on something I just (duh moment) realised. When self studying a math, physics or other topic, it often helps to have an early edition of a textbook. It may have more typos and even occasionally major error, but the presentation is often simpler and briefer and makes the task at hand much less daunting. It's like hiking. If you look too much at the steep trail ahead, it can be very discouraging and make you want to quit. If you can hike with someone else, you can be pleasantly distracted and not think about what you can't do. That's why working with others, in graduate school, but if possible also while self studying, the task of learning is made much easier. Please excuse my worldliness, but its good for me at my advanced age to express myself.
A bit of a late comment, but I think Lang's Algebra is a good reference book. For learning Abstract Algebra in the first course (even a first graduate course), I think Lang would be a nightmare. Dummit and Foote feels written for an introductory course. Lang feels more like a reference book if you already know the stuff but want a quick way to find it rather than looking through Dummit and Foote. I would love to use Lang now that I'm done with Dummit and Foote, but Abstract Algebra isn't my research area!
I agree with the people who say that Lang's "Algebra" is a terrible book to learn from. It is popular among people who already know algebra because it covers so much material, making it a great encyclopaedia of algebraic facts, and the proofs are terse and efficient so that they are pleasing to someone who is simply looking for a refresher. (Bourbakists, rejoice!) But Lang's style is anti-beginner and he completely fails to convey the intuition underlying abstract algebra.
@@colonelfredpuntridge8799 Jacobson is infamous for his non-pedagogical style, much worse than Lang. I know him from his book about Lie algebras, which is probably the most unpleasant book on the subject I can think of. Yet at the same time, it contains a magnificent wealth of unique information and you can learn things there you can hardly find anywhere else if you are willing to put up with the style.
It's a graduate textbook, so that is expected. But it's good for certain things like the structure theory of modules over principal ideal domains for example. Concise, rigorous, elegant presentation. Lang leaves out a lot though - most noncommutative algebra, and there's no development of lattice theory - etc
@@mathvlix Yeah, I tried to take his abstract algebra course. Every class, he would come in with his textbook, open to the relevant page, copy the text onto the chalk-board, read it aloud, and ask "is the picture clear?" If anyone said "no, not really", he would read the text aloud again.
What an egregious error, Sorcerer. I expected better. Yeah right! We all make mistakes. Lol just yesterday I was tutoring someone and mixed up secant lines and tangent lines and got super confused. If you feel bad about this imagine how that made me feel lol
If you find anything of interest or just want to share when going through Serge's Basic Math please do! Currently going through it right now for a rigors course in Pre-Calc.
First hand experience: Serge Lang walks into the library of the mathematical institute and sees his books on the shelf. He goes over to check them and complains "These are all old! Rubbish! You need the new ones." He then pulls them off the shelf to take them away, promising a batch of current, revised versions.
Holy... Serge's books are expensive used on Ebay in England. Must be some "sorcery" going on there. Used books, hardbacks are lovely. I got, think I pinched it from high school (The Lord of the Flies by William Golding). For American viewers most British school kids studied the book at school, along with Harper Lee's To Kill a Mockingbird. Paul Hogarth the illustrator, artist was commissioned to do the covers for Penguin series of Golding's books. So well worth checking out if you like literature and books per se.
I remember cramming Serge Lang books to save myself at high school and university. Lang is comprehensive (or so it seems to me), so I knew if I knew his books thoroughly, I would know enough to pass. I took that loyalty all the way through my life as a postgrad; at work; and; as a mature student (many years). I only recently converted to James Stewart for a (very late in life) BSc in mathematics, and I did so thanks to your channel!
Serge Lang is a French mathematician and french authors write mathematics books differents from english , german or russian ones, i invite you to read all french books the are excelent, the French mathematics have another way to expose and solve the problems and topics.
Yes, I noticed that when my Tunisian professor taught me measure theory using French books. It was a very different approach, but deep and insightful. It actually helped me understand measure theory well. I'm glad I got the opportunity to experience that.
There is a mismatch with your Lang books. The Algebra book is way beyond (in my opinion) the difficulty level of the other books. The better choice would perhaps be his undergraduate algebra book first, then on to his famous Algebra book. The whole reason for using Lang's "A First Course in Calculus" is because it's easier to understand and workout the excercises by yourself. The idea is to move on to "A Second Course in Calculus" and the his Analysis books. "A First Course in Calculus" is now in its 5th Edition and is about 700 pages that includes answers. Anyway, Serge Lang is a great choice.
It's abstract algebra. Sometimes the word _abstract_ is omitted just like with elementary algebra the word _elementary_ is often omitted too. I mean you may have a high school textbook simply called algebra instead of elementary algebra. Specific areas of math require full titles though: algebra Lie, linear algebra, vector algebra, calculus of variations, etc. Here, too, if differential and integral calculus was meant, the words differential and integral would be most likely dropped. But they would not be dropped with vector calculus and stuff like that, i.e. with more specific areas. As to abstract algebra, it is extremely broad. So, it is often called just algebra :)
If I am not mistaken in his forward of the first course in calculus he states that students ~ 15 years old can understand and comprehend his book. Got my old copy in 1986 at Chicago lawn Books sale 25 cents - I prevoiusly withdrew this book earlier - holds history for me. Good video I am glad and ammazed to see other people value such items.
Ya I love these old books! So much history! Your comment is a perfect example of the great history of books like this. It’s so cool that you remember getting this book in 1986 for 25 cents. Great stuff man❤️
I bought Lang's Basic Mathematics based on your recommendation as part of a project to re-learn all the math I did decades ago in high school and college and am really enjoying the book! It's so readable and the exercises are great. Plus, the whole classic simple yellow vibe of the cover is so cool! I will definitely get the Calculus book when I get that far along in my studies! Thanks for the great videos and recommendations!
Have you picked up Lang's Algebraic Number Theory textbook? If you're a fan of Lang, that might be the next one for you to set your sights on. It has no exercises, but it has a thorough overview of the topic, and I think there's some particularly beautiful mathematics that comes out of the field.
He was, I think, at Princeton just a few years before the great Eagle Mathematics group (O'Nan, Tromba and all) all of whom I tremendously admire for the clarity of their thought and writing. Thank goodness we have such generous people or those less fortunate in brain power like myself would maybe give up.
Greetings Mr. Professor, Thanks for the Valuable Concern in admittance of Mistake which clarify the Misconceptions about Mathematician 's Work in every aspects. My Thoughts : I too made a Terrible Mistake of sharing Hyperexpensive, Important Standard Textbooks with Friends, Fellow students at that time and kept in Shrewd Close relatives place which led to Loss of Priceless Books. Lesson Learnt. Moved on and presently Collecting Books one step at a time. Handle with Care. Take Care.. With regards, RanjithJoseph (R.J)
Hey. I'm studying for music theory, and I want to learn mathematics and physics to understand and specialise in tuning systems better. I've taken two years of mathematics in high school (Turkey), and have studied Algebra 1 and some geometry online. I could say that I have some understanding of Algebra 1 and basic geometry. Would you recommend Serge Lang's Basic Mathematics as a way to learn mathematics by myself? If not, what would you recommend someone such as myself to do? If you would, how should I study and what should I do after?
Lang gave a talk in Germany in 2005 and I could have attended it, but I did not. There was no second chance since he died in 2005. Instead I bought his book "Challenges" about the "files" he collected about pseudoscience.
Your videos are great. If you have time then please explain mathematics formula in detail so that new people in mathematics can get the skills of understanding the depth of mathematics formula. Wish you all the best.
I wonder if there are any good deals to be had in having batches of softcover texts library bound into hardcovers? For some of the better texts, even $20 or $30 each might be worth it. I find it bizarre that Lang's Basic Mathematics doesn't have a hardcover edition.
Since you're such a big fan of Lang's, I thought I'd mention that he wrote a book for the General audience: The Beauty of doing Mathematics, 1985; in this small book, the chapters are: What does a Mathematician do and Why? Prime Numbers; A Lively Activity: To do Mathematics; Diophantine Equations; Great problems of geometry and Space. Lang wrote another book for Undergraduates: Math Talks for Undergraduates, 1999. Some of the topics: Approximation Theorems of Analysis; Bruhat-Tits Spaces; Harmonic and Symmetric Polynomials; The abc Conjecture... Lang indicates in the Preface that "I am now presenting a collection of talks for undergraduates as a book. Such talks could be given by faculty, but even better, they may be given by students in seminars run by the students themselves. Such talks have been given at Yale, for instance." I have both books in e-format. He certainly was a lively communicator of mathematics.
Hi, can you make a video about the different areas of mathematics? About how one should go about choosing in which area one should specialize in? (graduate level) Who for example is good in a certain area? How do people think in different areas?
You kinda scared me a lot, you were like: "I made a terrible mistake... And these books arrived the same day Lang died", I was like: "THIS GUY KILLED LANG?????????????" for a while.
The book "Algebraic Structures" he mentions has morphed into "Undergraduate Algebra, 3e", copyright 2005, the year Lang died. Its foreword, by Lang, is dated New Haven 2004, when Lang was 77.
I was reading Black Holes and Baby Universes and Other Essays by Hawking when he passed away. This hit different and even to this day i can't explain it, but it was very personal and i had gained a deeper reverence for him for everything he had achieved and overcame in life. Rest in Peace Hawking.
Not knocking books that have answers at all, there should be a lot more of them with EVERY answer, not just the odd; but very often, having the answer doesn't do much without knowing the 75 steps needed to see how the answer showed up in the first place. In those cases, I think the answers are more for the teachers than the students. I wouldn't worry about not seeing the answers in the back of that particular book, the fault lies more with whoever didn't put that in the table of contents.
More than answers, hints are useful. These are more readable. And of course sometimes the way the exercises are worded themselves give a hint(This is why I still rate Halsey Royden's Real Analysis so highly) Lang's own books are terrible in this regard. The exercise sets have just been cobbled together rather than assembled with loving care with focused themes
@@jamespower5165 I would love an understandable real analysis book, so far with the few works I have on it, it just looks like scams someone pulled out of thin air w/ no way to figure out what they're talking about. open cover? terms so vague it's like madam cleo where her predictions could nearly apply to any random person on the street, or in this case, any random set of numbers.
Is it worth for someone like me to study maths even after finishing school? 🤔 I always sucked at maths and now I feel like I wasted my 12 years of school cause of it.
Think about the man or woman who designed the book covers. Probably with very little budget. Interesting how they are all yellow, the type face they have used, the way they have spaced out the letters. That was once called design and typography. I would urge mathematicians to take a pencil and just draw whatever is in their imaginations. Not matter if you feel embarrassed. That's also a muscle that needs exercising, and it might help you with creative solutions to maths problems.
I prefer books that do not have solutions but rather have hints. Some solutions are okay, but I think having solutions for most problems will not allow your brain to go to that weird place where it forces solutions because in the back of your head you are always thinking, "Well I can just look up the answer."
Indeed. In fact, hints are more readable than solutions. And some books have focused exercise sets with a single theme and the way the exercises are framed themselves constitute a hint(Halsey Royden's book is a good example of this type)
@@jamespower5165 an overly formal solution often gives you no intuition for how it was derived. hints build intuition which is what you primarily hope to gain from exercises
@@brydust Exactly. After reading the proof of the inverse function theorem in Walter Rudin's infamous book, I literally walked away from mathematics for 8 months or so!
Imagine how often people buy books from living authors that pass as the books are in transit. It's probably fairly common. In your case, you knew about the author's death.
Hej! Just found your channel. Great content. I have just started a programme in applied data science and was wondering if you had any recommendations for beginner books/websites on probability and statistics
As far as writing style and clarity of complex math topics, would you have any contrast/comparison between the late Dr. Lang and Dr. Isaac Asimov? I'm a big fan of Dr. Asimov but don't believe he ever wrote a full course book on Algebra. I do have his "Realm of Algebra" and "Realm of Measure". Dr. Asimov is renowned for his ability to explain complex topics so that even "I" -as an idiot- could understand. 😵💫
Courant books are classics and still, there aren’t recent books that are better. If you have a calculus course based on Courant & John it is almost a guarantee that it will be a good one. Writing mathematics as Courant is extremely difficult
@@josantonioalcantara Agree. I still keep a pdf copy, along with his What is Mathematics, Feynman Lectures on Physics, Thorne & Blandford Classical Physics, Knuth TAOCP on the Samsung pad that I am replying now. Now read them just for fun.
@@燕北山前萬梅山莊主人 how come not? Courant is the novelist of mathematics. It’s a pleasure to read him. Arnold and Kai Lai Chung are also very entertaining to read. Green, Brown and probability is highly recommendable. His basic book of probability is a delight. Arnold book on ODEs should be the book for differential equations. The only issue with the latter is that we are not used to develop mathematics in that way.
For you Lang fans, note that "Undergraduate Algebra", 3rd edition (1987), was previously published as "Algebraic Structures"(1967). When Lang switched publishers to Springer-Verlag they republished some of his books under different titles. I'm working on a list, will post when I get it all deciphered.
awesome, if you do please post it, I am very curious!! Thank you!!
@@TheMathSorcerer whats the hardest book to learn from starting at basic mathematicsto the last math subject ever which is numb er theory? right. all in one
What was the point of this video?
The best TH-cam channel for me. You know I'm 54 and started loving mathematics thanks to you videos. I bought some books to start working on mathematics with my kids. Thanks a lot for sharing.
That is awesome!
Starting to love math at 54 is inspiring, thank you for the comment.
It was Serge Lang who coined the word "Diophantine Geometry", explicitly making it a branch in modern mathematics. Mordell wrote a review on his 1962 book Diophantine Geometry, heavily criticising the book for being too difficult to read (even for such a prominent mathematician L. J. Mordell!). But Lang responded with no mercy: I write my books as it should be, and nothing else. Both Mordell's review and Lang's response can be found in Lang's Fundamentals of Diophantine Geometry (1983).
Oh wow Interesting! Thank you!
I am sure that the soul of late Serge Lang is both delighted and flattered by your video. This is the way to honour the dead by remembering them and talking about them, respectfully.
In my belief, most deceased souls pick up fans' thoughts from afar, no matter the distance.
❤️
Your enthusiasm for Maths is infectious. love your videos!!
thank you:)
Exactly. I am also finding myself hunting for math books after watching his videos
I actually enjoyed A First Course in Calculus. I got an older edition which was brief and focused on the essentials, without flashy artwork/images or uninteresting applications. I think the oldest edition has been re-released under the title "Short Calculus", less than 300 pages and you learn all the calculus covered in a first course at my uni.
It skips epsilon-delta stuff but is otherwise rigorous, as I recall it. A great book for a beginner in calculus and a great preparation for more rigorous books like the ones by Spivak or Apostol :)
I was born in 2005, and am now here as a calculus student myself. Even though my school doesn't use Mr. Serge Lang's books for class, this video has persuaded me to get one. Thanks for the recommendation!
That's awesome!
I remember Serge Lang from Yale. He was a true-blue, _bona fide,_ one-hundred-percent weirdo. He had more weirdness in his little finger than most people have in their whole personalities.
hahahahahaah wow
@@TheMathSorcerer My favorite math professor at Yale was Angus McIntyre. He was always clear, and very nice, and he had one hilarious habit: he would scratch his nose with the same hand that was holding the chalk (this was back in the day when professors still used chalk) and the chalk-dust would get all over his face, so that by the end of the lecture he looked like a mime or a clown.
I remember he dated a student in my residential college.
@@wavesAndBerms Lang?
I find his constant fiddling with the book he's talking about really weird.
My advisor was mentored by Serge Lange. In fact, 5 of my favorite math professors all graduated from Yale at around the same time, and all studied under Lang. I don't know much about him, but my professors all thought highly of him.
Don’t worry. I literally embarrassed myself in front of my professor today. You’re a human like everyone else.
I have Serge Lang's _A First Course in Calculus,_ 5th edition. It's around 600+ pages long and covers the basics (only single variables). I think it is a great book for beginners. I like it how he covers very important topics from elementary mathematics because students don't know them as a rule. Yeah, I know they all say that they studied precalc and that they don't need such topics, blah-blah-blah... *I think they do need it and they don't really know it!*
I also think that most Lang's books are very good. You can hardly go wrong with them. They are indeed a good choice and can also work as additions. Of course, if a student plows through Stewart's _Elementary Algebra and Trigonometry_ which is around 1000 pages and then focuses on Stewart's _Calculus,_ it's even better than doing Lang's _A First Course in Calculus._ I just don't think that's realistic for 99% of students. They would either not have time or will to do that. So, Lang's books are kinda shortcut to get the gist. I guess, Lang's approach is very smart and good for teaching people without crowding them with too much information or tough problems.
Nice 👍
Start with Lang’s Introduction to Linear Algebra. The first edition is only 170 pages and a really good way to get a first (geometric) feel for the subject. You can start it before calculus.
👍
Thank you very much!
I looked at a number of Lang's books, and to me he doesn't seem to be interested in developing computational aspect of a subject, or the student's capabilities thereof, rather he seem to focuse on mathematical ideas and concepts; although that might not be in a very theoretical way. I felt he sought to enable a student to "feel" and to have an understanding of what's going on in the subject, sort of to grasp the subject matter of a book. This was how I thought of his books, generally, and It I found them valuable for that very reason, which make him stand out among math authors.
De mortuis nihil nisi bonum?
Lang certainly did not care about giving students any intuition or "feel" about the subjects he was writing on.
@@mathvlix what does he care for then?
@@JJ-cn2ud who knows. His writing style corresponds to a way people learnt math in this way long ago.
I appreciate your appreciation for books. It is worrisome that libraries get rid of these old books. Extra copies I can understand if they’re not in demand but I hope they keep at least one… Not just mathematical books but others too.
Well, that's how poor collectors get good deals on used books. If libraries held on to everything, it would not have been easy for us.
I'm surprised to hear someone think the exercises in A First Course in Calculus are too easy. There are definitely fewer exercises than in books like Stewart, and whether fewer exercises is a good or bad thing is up for debate I guess. But I found the exercises (and the exposition) to be quite a bit more sophisticated than in most books aimed at the same audiences, with a focus on big ideas and guiding students to derive useful expressions, rather than on drilling. And it does more drilling than any of his other books I have looked at. It *isn't* as hard as Apostol as is, but if you leave out starred stuff in Apostol they are basically the same other than that Apostol includes a chapter on differential equations and some (very) basic complex variables stuff.
I have the most recent edition of A First Course in Calculus (5th, published by Springer-Verlag), so maybe this was different in an older editions.
I am in awe of the prodigious output of authors like this.
I know me too!!
The 2012 softcover 5th edition of Serge Lang's First Course in Calculus is 746 pages
My sister went to Union college. Some of my best memories were my parents driving there from NYC. I was in elementary school so I had to come along. I remember My Mom would pack fried chicken with bread and how it actually tasted good cold. I enjoyed seeing the transition from city to rural country side. Small world.
ahh that's awesome, that chicken sounds so good!!!
I taught my self calculus as tween to varying degrees from his complete course. I have a ton of his titles lying around.
Hey there, MS!! I'm among your greatest fans and I love what you're doing. You're a human(e) being!! I LOVE YOUR VIDEOS!!! Whenever I see a new one of yours, I'm like a kid opening up presents on Christmas morning!! YOU'RE AWESOME!!!! :) :) :) :)
Thank you Pine!!!
I believe that Lang's graduate algebra book, like his other books written at the graduate level (e.g. Differential Geometry, etc.) don't have answers or hints for problems. This is true in general for other authors of graduate books. Although universities may, for grading purposes or to develop the mathematical intuition of their graduate students, encourage this practice, I think it should be left upto the student whether to peek at the answer. I have found that finding the answer can correct a general misunderstanding of a concept or a calculational technique and is an important teaching tool. I wanted to make an unrelated comment on something I just (duh moment) realised. When self studying a math, physics or other topic, it often helps to have an early edition of a textbook. It may have more typos and even occasionally major error, but the presentation is often simpler and briefer and makes the task at hand much less daunting. It's like hiking. If you look too much at the steep trail ahead, it can be very discouraging and make you want to quit. If you can hike with someone else, you can be pleasantly distracted and not think about what you can't do. That's why working with others, in graduate school, but if possible also while self studying, the task of learning is made much easier. Please excuse my worldliness, but its good for me at my advanced age to express myself.
wonderful comment, thank you so much:)
A bit of a late comment, but I think Lang's Algebra is a good reference book. For learning Abstract Algebra in the first course (even a first graduate course), I think Lang would be a nightmare. Dummit and Foote feels written for an introductory course. Lang feels more like a reference book if you already know the stuff but want a quick way to find it rather than looking through Dummit and Foote. I would love to use Lang now that I'm done with Dummit and Foote, but Abstract Algebra isn't my research area!
I agree with the people who say that Lang's "Algebra" is a terrible book to learn from.
It is popular among people who already know algebra because it covers so much material, making it a great encyclopaedia of algebraic facts, and the proofs are terse and efficient so that they are pleasing to someone who is simply looking for a refresher. (Bourbakists, rejoice!)
But Lang's style is anti-beginner and he completely fails to convey the intuition underlying abstract algebra.
To be fair, nowadays I myself use Lang's "Algebra" as my preferred reference for algebraic facts. But I do remember how gruesome it was for past-me.
The worst algebra book (IMHO) is Nathan Jacobson's BASIC ALGEBRA 1. The only thing worse - maybe - is BASIC ALGEBRA 2.
@@colonelfredpuntridge8799 Jacobson is infamous for his non-pedagogical style, much worse than Lang. I know him from his book about Lie algebras, which is probably the most unpleasant book on the subject I can think of. Yet at the same time, it contains a magnificent wealth of unique information and you can learn things there you can hardly find anywhere else if you are willing to put up with the style.
It's a graduate textbook, so that is expected. But it's good for certain things like the structure theory of modules over principal ideal domains for example. Concise, rigorous, elegant presentation. Lang leaves out a lot though - most noncommutative algebra, and there's no development of lattice theory - etc
@@mathvlix Yeah, I tried to take his abstract algebra course. Every class, he would come in with his textbook, open to the relevant page, copy the text onto the chalk-board, read it aloud, and ask "is the picture clear?" If anyone said "no, not really", he would read the text aloud again.
What an egregious error, Sorcerer. I expected better.
Yeah right! We all make mistakes. Lol just yesterday I was tutoring someone and mixed up secant lines and tangent lines and got super confused. If you feel bad about this imagine how that made me feel lol
I cannot express how much hearing the words "Dummit & Foote" bodily catapulted me back to grad school 😵💫
For those whose college/university have access agreements with Springer, all the Serge Lang books are available at no cost for download as PDF.
If you find anything of interest or just want to share when going through Serge's Basic Math please do! Currently going through it right now for a rigors course in Pre-Calc.
will do!
Thanks for clarifying the solutions at the back of the book thing. I am enjoying Basic Math. I find the exercises include easy and hard problems.
First hand experience: Serge Lang walks into the library of the mathematical institute and sees his books on the shelf. He goes over to check them and complains "These are all old! Rubbish! You need the new ones." He then pulls them off the shelf to take them away, promising a batch of current, revised versions.
Holy... Serge's books are expensive used on Ebay in England. Must be some "sorcery" going on there. Used books, hardbacks are lovely. I got, think I pinched it from high school (The Lord of the Flies by William Golding). For American viewers most British school kids studied the book at school, along with Harper Lee's To Kill a Mockingbird. Paul Hogarth the illustrator, artist was commissioned to do the covers for Penguin series of Golding's books. So well worth checking out if you like literature and books per se.
I remember cramming Serge Lang books to save myself at high school and university. Lang is comprehensive (or so it seems to me), so I knew if I knew his books thoroughly, I would know enough to pass. I took that loyalty all the way through my life as a postgrad; at work; and; as a mature student (many years). I only recently converted to James Stewart for a (very late in life) BSc in mathematics, and I did so thanks to your channel!
Serge Lang is a French mathematician and french authors write mathematics books differents from english , german or russian ones, i invite you to read all french books the are excelent, the French mathematics have another way to expose and solve the problems and topics.
Yes, I noticed that when my Tunisian professor taught me measure theory using French books. It was a very different approach, but deep and insightful. It actually helped me understand measure theory well. I'm glad I got the opportunity to experience that.
There is a mismatch with your Lang books. The Algebra book is way beyond (in my opinion) the difficulty level of the other books.
The better choice would perhaps be his undergraduate algebra book first, then on to his famous Algebra book.
The whole reason for using Lang's "A First Course in Calculus" is because it's easier to understand and workout the excercises by yourself.
The idea is to move on to "A Second Course in Calculus" and the his Analysis books.
"A First Course in Calculus" is now in its 5th Edition and is about 700 pages that includes answers.
Anyway, Serge Lang is a great choice.
Why is teh Algebra book published in a series titled "Graduate Texts in Mathematics"?
It's abstract algebra. Sometimes the word _abstract_ is omitted just like with elementary algebra the word _elementary_ is often omitted too. I mean you may have a high school textbook simply called algebra instead of elementary algebra. Specific areas of math require full titles though: algebra Lie, linear algebra, vector algebra, calculus of variations, etc. Here, too, if differential and integral calculus was meant, the words differential and integral would be most likely dropped. But they would not be dropped with vector calculus and stuff like that, i.e. with more specific areas. As to abstract algebra, it is extremely broad. So, it is often called just algebra :)
@@billmorrigan386 but the sorcerer introduced it as an undergraduate textbook, not a graduate one
Springer is currently running a 50% off sale including Lang Algebra code B2S22 (until August 29th) also eBooks
Nice
@@TheMathSorcerer alas I’m too late but thank you
I love your channel! Thanks from São Paulo/Brazil.
Hello Sorcerer, how do those compare to modern books for someone interested to read the whole Lang's series?
Every book is different. Modern books are also very very good:) I don't think I can make any big generalizations since each book is so different.
I'd say old is gold. That's a rule of thumb. However, I can't say anything about these books vs other books. Haven't read any of them.
If I am not mistaken in his forward of the first course in calculus he states that students ~ 15 years old can understand and comprehend his book. Got my old copy in 1986 at Chicago lawn Books sale 25 cents - I prevoiusly withdrew this book earlier - holds history for me. Good video I am glad and ammazed to see other people value such items.
Ya I love these old books! So much history! Your comment is a perfect example of the great history of books like this. It’s so cool that you remember getting this book in 1986 for 25 cents. Great stuff man❤️
Hi math sorcerer, what do you think about Thomas calculus? I mean your opinion on it.
Amazing book!!!!
I bought Lang's Basic Mathematics based on your recommendation as part of a project to re-learn all the math I did decades ago in high school and college and am really enjoying the book! It's so readable and the exercises are great. Plus, the whole classic simple yellow vibe of the cover is so cool! I will definitely get the Calculus book when I get that far along in my studies! Thanks for the great videos and recommendations!
Awesome ✌🏽no need to apologise 🙌🏽 Have to get the abstract algebra book.
Hello, I recently bought Marshall Hall Jr's group theory book, how good a choice did I make?
I don’t have that one yet I should check it out !
Have you picked up Lang's Algebraic Number Theory textbook? If you're a fan of Lang, that might be the next one for you to set your sights on. It has no exercises, but it has a thorough overview of the topic, and I think there's some particularly beautiful mathematics that comes out of the field.
You don't have Lang's Complex Analysis? Is his best book personally
Yeah I have that, it's great:)
And the solutions are available in a separate book by Rami Shakarchi. So it's a terrific package!
Hi professor, thanks for another great video!
He was, I think, at Princeton just a few years before the great Eagle Mathematics group (O'Nan, Tromba and all) all of whom I tremendously admire for the clarity of their thought and writing. Thank goodness we have such generous people or those less fortunate in brain power like myself would maybe give up.
Greetings Mr. Professor,
Thanks for the Valuable Concern in admittance of Mistake which clarify the Misconceptions about Mathematician 's Work in every aspects.
My Thoughts :
I too made a Terrible Mistake of sharing Hyperexpensive, Important Standard Textbooks with Friends, Fellow students at that time and kept in Shrewd Close relatives place which led to Loss of Priceless Books. Lesson Learnt. Moved on and presently Collecting Books one step at a time. Handle with Care. Take Care..
With regards,
RanjithJoseph (R.J)
Always enjoy your content.
Unfortunately, his books made me feel like I didn't understand mathematics. The only book that felt readable was his complex analysis book.
Hey. I'm studying for music theory, and I want to learn mathematics and physics to understand and specialise in tuning systems better. I've taken two years of mathematics in high school (Turkey), and have studied Algebra 1 and some geometry online. I could say that I have some understanding of Algebra 1 and basic geometry. Would you recommend Serge Lang's Basic Mathematics as a way to learn mathematics by myself? If not, what would you recommend someone such as myself to do? If you would, how should I study and what should I do after?
Lang gave a talk in Germany in 2005 and I could have attended it, but I did not. There was no second chance since he died in 2005. Instead I bought his book "Challenges" about the "files" he collected about pseudoscience.
What an honest response, thanks for showing us these great books. Can you please continue to solve example problems from these books.
That's the plan!
The “Algebraic Structures” is revised and updated and retitled as “Undergraduate Algebra”.
Ahh yes, that's what I thought but I wasn't 100% sure. Thank you!!
Your videos are great. If you have time then please explain mathematics formula in detail so that new people in mathematics can get the skills of understanding the depth of mathematics formula. Wish you all the best.
yes, I will do that, thank you:)
@@TheMathSorcerer Really really really thank you.
I wonder if there are any good deals to be had in having batches of softcover texts library bound into hardcovers? For some of the better texts, even $20 or $30 each might be worth it.
I find it bizarre that Lang's Basic Mathematics doesn't have a hardcover edition.
Someone else commented they have a hardcover version. I think it
Might exist and just be extremely rare!
Since you're such a big fan of Lang's, I thought I'd mention that he wrote a book for the General audience: The Beauty of doing Mathematics, 1985; in this small book, the chapters are: What does a Mathematician do and Why? Prime Numbers; A Lively Activity: To do Mathematics; Diophantine Equations; Great problems of geometry and Space.
Lang wrote another book for Undergraduates: Math Talks for Undergraduates, 1999. Some of the topics: Approximation Theorems of Analysis; Bruhat-Tits Spaces; Harmonic and Symmetric Polynomials; The abc Conjecture... Lang indicates in the Preface that "I am now presenting a collection of talks for undergraduates as a book. Such talks could be given by faculty, but even better, they may be given by students in seminars run by the students themselves. Such talks have been given at Yale, for instance."
I have both books in e-format. He certainly was a lively communicator of mathematics.
Thank you for this comment!!!!!!!! Thank you❤️
Your "terrible mistake" is nothing compared to Serge Lang's persistent denial that HIV causes AIDS. I appreciate your videos.
And yet another good video about books
Just in case it wasn't clear- it's okay that you made a mistake. I had a question, I need to learn Geometry, what is your number one recommended book?
Hi, can you make a video about the different areas of mathematics? About how one should go about choosing in which area one should specialize in? (graduate level) Who for example is good in a certain area? How do people think in different areas?
You kinda scared me a lot, you were like: "I made a terrible mistake... And these books arrived the same day Lang died", I was like: "THIS GUY KILLED LANG?????????????" for a while.
The book "Algebraic Structures" he mentions has morphed into "Undergraduate Algebra, 3e", copyright 2005, the year Lang died. Its foreword, by Lang, is dated New Haven 2004, when Lang was 77.
nobody lives forever, for now
Is Silverman's calculus a better choise then?
Hey just wanted to add that the book "Algebraic Structures" is now called "Undergraduate Algebra"
👍👍👍
Everybody makes mistakes. Thank you for your videos and help.
Does the last book have solutions?
So, does Lang really use the Yoneda Lemma to prove that multiplication distributes over addition?
Can you please draw a crisp comparison between Freidberg and Hoffman Kunze
Yea great idea thank you!
prof your honesty is refreshing
i like your videos they are invigorating
keep them coming
👍
wow i just rented the algebra book from the university library an hour ago
Wow nice
Coincidental
I was reading Black Holes and Baby Universes and Other Essays by Hawking when he passed away. This hit different and even to this day i can't explain it, but it was very personal and i had gained a deeper reverence for him for everything he had achieved and overcame in life. Rest in Peace Hawking.
If you made it through school without making friends with BOB (back of book), I don't know how you ever finished homework haha
Not knocking books that have answers at all, there should be a lot more of them with EVERY answer, not just the odd; but very often, having the answer doesn't do much without knowing the 75 steps needed to see how the answer showed up in the first place. In those cases, I think the answers are more for the teachers than the students. I wouldn't worry about not seeing the answers in the back of that particular book, the fault lies more with whoever didn't put that in the table of contents.
yeah and very few books have answers to the proofs, it's super rare!
More than answers, hints are useful. These are more readable. And of course sometimes the way the exercises are worded themselves give a hint(This is why I still rate Halsey Royden's Real Analysis so highly) Lang's own books are terrible in this regard. The exercise sets have just been cobbled together rather than assembled with loving care with focused themes
@@jamespower5165 I would love an understandable real analysis book, so far with the few works I have on it, it just looks like scams someone pulled out of thin air w/ no way to figure out what they're talking about. open cover? terms so vague it's like madam cleo where her predictions could nearly apply to any random person on the street, or in this case, any random set of numbers.
How about a video on Series Solutions of Differential Equations ... thanks
Actually I dont understand anything in the book 'Basic Mathematicas'
Is it worth for someone like me to study maths even after finishing school? 🤔 I always sucked at maths and now I feel like I wasted my 12 years of school cause of it.
I always think it’s worth it❤️
It'll change your mind in unimaginable ways. Give it a second chance, and start slowly!
@@ILoveMaths07 okay I will. Thank you. 😊
@@TheMathSorcerer okay, I will. 🙂 I guess the first book is a good introduction into maths for noobs?
Creepy things happen: my son received his bank card with a default 4-digit pin which was the same as mine. What are the 'odds' of that happening :)
Wow lol
1 in 10,000 if the bank's PIN selection algorithm is truly random.
100% if the program was written by a lazy programmer:
#define PIN 1234
Introduction to linear algebra by serge lang is easy to read. Please do the review of that book
Think about the man or woman who designed the book covers. Probably with very little budget. Interesting how they are all yellow, the type face they have used, the way they have spaced out the letters. That was once called design and typography. I would urge mathematicians to take a pencil and just draw whatever is in their imaginations. Not matter if you feel embarrassed. That's also a muscle that needs exercising, and it might help you with creative solutions to maths problems.
If you want to make studying calculus and linear algebra easy, you should master geometry
I prefer books that do not have solutions but rather have hints. Some solutions are okay, but I think having solutions for most problems will not allow your brain to go to that weird place where it forces solutions because in the back of your head you are always thinking, "Well I can just look up the answer."
Indeed. In fact, hints are more readable than solutions. And some books have focused exercise sets with a single theme and the way the exercises are framed themselves constitute a hint(Halsey Royden's book is a good example of this type)
@@jamespower5165 an overly formal solution often gives you no intuition for how it was derived. hints build intuition which is what you primarily hope to gain from exercises
@@brydust Exactly. After reading the proof of the inverse function theorem in Walter Rudin's infamous book, I literally walked away from mathematics for 8 months or so!
Got 2 of the 4 Lang Books. I found Lang's Calculus book to be easy. And Lang's Algebra book to be much harder than Dummit and Foote.
you obviously are responsible for his death... I see no other possibility.
Imagine how often people buy books from living authors that pass as the books are in transit. It's probably fairly common. In your case, you knew about the author's death.
His AIDS denialism was super-weird.
Omg yes it was so weird!!!
That's very interesting! Thanks! I wasn't aware of that.
Awesome ✌🏽no need to apologise 🙌🏽
do you think about creating a discord server
I have I just don't know if I can keep up with it lol. I can't keep up with the comments currently hehe.
Hej! Just found your channel. Great content. I have just started a programme in applied data science and was wondering if you had any recommendations for beginner books/websites on probability and statistics
Hello math Socerer
can you review Proofs by Jay cummings?
He was killed by Ivan Drago in Rocky IV, but the follow-up book by R. Balboa was excellent
How to study math ob english as a foreign language?
I too love Serge Lang's books. He gets right to the point.
As far as writing style and clarity of complex math topics, would you have any contrast/comparison between the late Dr. Lang and Dr. Isaac Asimov? I'm a big fan of Dr. Asimov but don't believe he ever wrote a full course book on Algebra. I do have his "Realm of Algebra" and "Realm of Measure". Dr. Asimov is renowned for his ability to explain complex topics so that even "I" -as an idiot- could understand. 😵💫
How old are you sir ?
I like Courant & John books on Calculus better.
Courant books are classics and still, there aren’t recent books that are better. If you have a calculus course based on Courant & John it is almost a guarantee that it will be a good one.
Writing mathematics as Courant is extremely difficult
👍👍
@@josantonioalcantara Agree. I still keep a pdf copy, along with his What is Mathematics, Feynman Lectures on Physics, Thorne & Blandford Classical Physics, Knuth TAOCP on the Samsung pad that I am replying now. Now read them just for fun.
@@TheMathSorcerer 🙏🙏
@@燕北山前萬梅山莊主人 how come not? Courant is the novelist of mathematics. It’s a pleasure to read him. Arnold and Kai Lai Chung are also very entertaining to read. Green, Brown and probability is highly recommendable. His basic book of probability is a delight. Arnold book on ODEs should be the book for differential equations. The only issue with the latter is that we are not used to develop mathematics in that way.
Hi, i have a differential equation book by rainville, i didn't understand anything. I only learn from your video s
I love Serge Lang's Books
Sadly it is too late for him to cancel your order.
Great vid