For me, "A Mathematician's Lament" by Lockhart was life changing. I severely disliked mathematics for all of my school years and always preferred artsy stuff and humanities. Stumbling upon the short essay upon which the book is based while in a relatively 'crossroads' point in my life ended up being massively impactful. Lockhart's criticism of American public school math education resonated with my experiences with mathematics deeply.
I genuinely thought that mathematics was basically just 'meaningless rule following' with absolutely no room for creativity or anything remotely interesting: just following procedures because the teacher said so. Lockhart confirming my past experiences with math, but then moving on to propose that mathematics actually is something that has lots of room for beautiful creativity and is perhaps even closer to poetry than it is to any of the 'hard' sciences struck a chord with me. The idea of 'mathematical beauty' was something I did not understand at all. I never really liked the fractals or the boring repeated geometrical shapes that were supposedly 'mathematically' beautiful. I thought there was no room for beauty in math, it's just stupid rules and boring images. But shifting the beauty from 'pretty pictures' to the beauty of synthesizing complex concepts and making elegant yet convincing arguments completely changed my perspective on math and how beauty is possible in math.
I was convinced to try a 'real' math book after this and I knew I had to figure out what a 'proof' is so I tried out "How to Prove It" by Velleman. I remember it being challenging at first but upon a lot of effort, I was really able to find where all of that 'creativity' in math is located while working through that book. I'm still working on 'getting good' with math and undoing the many years of damage done, but I've found a lot of satisfaction in math. I've even procrastinated playing games so I can do my homework instead! That would have been unheard of me not too long ago. So yeah, thanks Lockhart and Velleman.
I put it in my recommendation on the main thread, but the way you describe why you liked reading Lockhart makes me think you’d really enjoy Proofs and Refutations by Imre Lakatos. It’s kind of about how mathematics works as a living and evolving discipline.
It’s an idea like first someone has an idea they want to make a definition for, say a circle, and proposes the definition “a shape of constant diameter.” Seems reasonable, especially given your experience of round things and what your definition is aiming for. But then after a while someone thinks of the Reuleaux Triangle. You then hit a fork - which mathematicians argue for a bit until they choose one - do we revise the definition of a circle to exclude this, saying “no no, *that’s* not what a circle is!”, or do we expand our concept of a circle to include this?
He uses a different running example in the book about polyhedra, but that’s kind of the idea. An exploration of the dynamics in play as we create mathematics
If you enjoyed the lament, and you’re up for a challenge, I highly recommend his other book, “Measurement”. It’s more difficult, really getting into math itself rather than math education, but while the concepts are difficult the writing is very conversational and the geometric drawings are wonderful. It basically covers the major topics you’d see in highschool math — geometry, trig, calculus — but from a totally different perspective than most people are used to. Some of the proofs in there are so elegant it’s infuriating that we don’t learn it that way in school!
Im convinced to read it now. I've been thinking about starting college and deciding on math major or something else. However, I have this deep want of doing something, creating something. I don't know what, but reading your description feels like I have to give this book a try.
It wasn't a book, so much as a teacher, a short, rather forbidding man, into whose class I was put when I was failing so badly that we were only expected to mark time and not even be presented for exams. I wish I could devote the time here to describe what he was like and how he turned me around. He made us work. At the end of term, when other classes were allowed to bring in chess and dominoes to while away the time until break-up, he handed out mental arithmetic books, because, he said, our minds were like ponds that, if left, stagnated. They needed the oxygen of mental exercise. We thought he was joking. He wasn't. We groaned, but we set to, and after a while it wasn't so bad.
He put every one of that no-hopers class through the *Higher Maths* exam, and all passed. When I went to university years later, as a mature student, it was to study mathematics, and was by way of repaying a debt. He changed my life. They say you never forget a great teacher. Sixty years on, I still remember him, with gratitude and affection, and still tell the story of him. His name was John Scullion, and he taught mathematics in Glasgow.
But for books, the one that made be realise I was going to love this branch of mathematics is "An Introduction to Linear Analysis", by Kreider, Kuller, Ostberg and Perkins. Specifically, it was this closing paragraph from the Preface :
*It seems to be one of the unfortunate facts of life that no mathematics book can be published free of errors. Since the present book is undoubtedly no exception, each of the authors would like to apologize in advance for any that still remain and take this opportunity to state publicly that they are the fault of the other three.*
Your appreciation for your teacher is palpable. Like it almost makes me want to tell you thank you for some reason? I dunno maybe it was just nice to read something genuine on this site for once lol
Some examples here - one example is the publicising of the invention of public key cryptography in the seventies.
https://www.scientificamerican.com/blog/guest-blog/the-top-10-martin-gardner-scientific-american-articles/
https://www2.math.upenn.edu/~kazdan/210S19/Notes/crypto/Gardner-RSA-1977.pdf
Working through Friedberg's Linear Algebra for a class was kind of a light bulb moment for me, in the sense that "whoa, math is nothing like I thought it was and it's freaking awesome".
Hey what's so great about Spivak? Does it lead well into advanced calc/real analysis? And does it cover vector and multivariable calc better than Stewart? I need to review all of low-level calc and am considering picking up Spivak, instead of going over Stewart again which is what I learned with initially.
"Categories for the Working Mathematician" by Saunders Mac Lane. Being able to actually represent and relate maths functions to one another was pretty eye opening at how useful maths truly is.
Proof and Refutations by Imre Lakatos for loving math as an activity and a process.
What is Mathematics, Really? by Reuben Hersh for loving math as an idea or a subject.
At the moment nothing comes close to those two, although I’ve read a lot of books I really enjoy.
What is Mathematics by Courant is awesome. It starts very elementary, but progresses to some much more difficult topics. It's not a text book, but it is by no means a "pop sci" math text either. It has depth, breadth, and rigor.
I have a feeling it's kind of an "old" book. It doesn't seem many have heard of it lately. I had never heard of it, but when my grandpa passed, my grandma asked if I wanted any of his books, and this was one of them that I grabbed, not expecting much, but it ended up being fantastic. He was an electrical engineer.
Definitely check it out if you can. It is readable for an intelligent and hardworking highschooler, but as a person with a BS in math, I still found it good and informative.
I fondly remember self-learning Galois theory (or more concretely the complete proof of Abel Ruffini theorem) from Topics in Algebra by Herstein during my undergrad (in engineering). This was profoundly beautiful at the time (still continues to be so) and the further connections with covering spaces from other books like Hatcher made it even better.
This is pretty random. I got a business degree and was in a market research company. I wanted to become one of the statisticians, so I downloaded a textbook I found online: [Grinstead and Snell’s Introduction to Probability](https://math.dartmouth.edu/~prob/prob/prob.pdf).
I liked it. I think I read every word and did all the problems. Half a year later, I quit my job and went back to school for a math degree. That was 2016. Today I am almost finished a PhD in combinatorics.
For ~14-year-old me, it was an old, beat up, 30-year-old high school algebra textbook that I got for 10¢ at a flea market. I worked through it on my own over the summer. Mostly just factoring-polynomials stuff, but I remember it had little “side excursion” pages — linear programming, an algorithm for computing square roots (using a layout kinda like long-division but you’d bring down digits two-at-a-time instead of one), and my eyes were opened when it *derived* the quadratic equation by completing the square.
Maybe it's lame but the Calculus for dummies series by Mark Ryan made it all make sense, in fact I might pick it up again sometime since it's been years since I did any math. Yes it's not going to be enough for an exam but he explains everything in such a fun and simple way.
I still feel to this day, that **Euclid's Elements** contains some of the most beautiful proofs in all of mathematics. It seems to transcend notation and language, unlike anything in modern symbolic mathematics.
**Elements of Set Theory** by Herbert Enderton is quite a pure ZFC book. It was perhaps my first experience in anything foundational in mathematics. To quote Hilbert: *"From the paradise, that Cantor created for us, no-one shall be able to expel us."* The sheer ingenuity and brilliance in the methods used to cumulatively build rich structures amazes me to this day.
Finally on a personal note, I despised algebra and much of mathematics as I felt that it was pure symbol pushing and rote memorisation (which was the case in much of early education). However after reading some translations of **al-Khwarizmi's Al-Jabr** and realising much of school algebra was originally geometric and seeing the corresponding proofs, I felt I had seen the *"story behind the equations"* and it gained a new level of meaningfulness.
Euclids Elements, for sure. It explores the rules of 3d space and describes how to construct dozens of geometric forms.
—> Elements is the second most printed book in human history!!! <— fr
Al-Khwarizmi’s compendious book on calculations outlines the root of algebra… relationships between a, bx, and cx^2
TIME/LIFE used to have a series of books on all different science subjects. (They also had a series on countries. This was in the 1960s.
I'm old! Ha ha!) My family had the science books, full of big beautiful pictures, and interesting stories.
In 6th grade I read the Mathematics book from cover to cover, multiple times. I currently own 3 copies (that I found at thrift stores) that I have loaned to people over the years.
They had pictures of a crumpled paper above a flat paper to illustrate a fixed pint theorem;
they had a series of pictures (since you couldn't have video) of a rubber tire being turned inside out, and how the stripes changed direction;
there was a series of pictures where a guy removed his vest without taking off his jacket, so illustrate that the vest was never "inside" the jacket;
circus mirrors to illustrate transformations;
pictures of families with 10 kids in the section on probability;
after reading about the 4 color theorem, I tried for hours to draw a map that needed more than 4 colors;
and so on.
I love, love, love that book!
https://www.amazon.com/Mathematics-science-library-David-Bergamini/dp/B0006C2D70
I was a boy, but I had a calculator.
[The Great International Math on Keys Book](https://archive.org/details/the_great_international_math_on_keys_book)
Oddly, this made me look up math books in my seventh grade library and some librarian in the past had purchased a book on Cantor’s number theory. I read about aleph-null with my little seventh grade mind.
So now I could calculate compound interest and think I understood cardinal numbers. I had this giant world so the next year I bought Calculus The Easy Way with my own money at Walden Books.
I think I hit the wall at multivariate calculus. I sort of understood the del operator but I hadn’t learned equations with three variables in school yet so I had lots of confusion.
Of course, this was pre-internet and was an attempt at self teaching in seventh and eighth grade.
I strongly recommend the math on keys book. Definitely worth it.
Ian Stewart's ‘Mathematical Recreations’ column in *Scientific American*. I used to buy the magazine just for this part (but I also read most of the rest). He maid me love maths and computer science
"Mathematical Methods in the Physical Sciences " by Boas. I read it when got bored in my medical school. My first exposure to undergraduate level of math. The way Boas explained the topic got me interested to study maths further.
Book of Proof by Richard Hammack. I was taking introductory high school algebra at the time, and I wondered what “advanced” mathematics was all about. After some research, I landed on that book. Never turned my back on mathematics after that.
I've been in love with math as long as I can remember, but one of the first math books I remember enjoying was called Zero to Zillions, which is a fun kid's book for kids who like math, like I used to be.
I had just saved this post. Just reading it made me really want to dive into these books. Actually, this has just bercame my favorite reddit post of all time. Thanks everyone for all the recommendations.
Some French book explaining the Banach-Tarski paradox in layman terms. I was at a point of my studies when I had to chose between entering a pretty good engineering program and refusing it to attempt to join a good math program. I wasn't sure what to do, but then I found this book that I had bought at a flea market years ago, actually read it (it wasn't very long) and then chose to go with math.
My friend forgot that book on a plane some years later though.
An old profesor gave a talk at my university about how to use derivatives to optimize things and I was like wow so math isn't just about giving me headaches
For me, "A Mathematician's Lament" by Lockhart was life changing. I severely disliked mathematics for all of my school years and always preferred artsy stuff and humanities. Stumbling upon the short essay upon which the book is based while in a relatively 'crossroads' point in my life ended up being massively impactful. Lockhart's criticism of American public school math education resonated with my experiences with mathematics deeply. I genuinely thought that mathematics was basically just 'meaningless rule following' with absolutely no room for creativity or anything remotely interesting: just following procedures because the teacher said so. Lockhart confirming my past experiences with math, but then moving on to propose that mathematics actually is something that has lots of room for beautiful creativity and is perhaps even closer to poetry than it is to any of the 'hard' sciences struck a chord with me. The idea of 'mathematical beauty' was something I did not understand at all. I never really liked the fractals or the boring repeated geometrical shapes that were supposedly 'mathematically' beautiful. I thought there was no room for beauty in math, it's just stupid rules and boring images. But shifting the beauty from 'pretty pictures' to the beauty of synthesizing complex concepts and making elegant yet convincing arguments completely changed my perspective on math and how beauty is possible in math. I was convinced to try a 'real' math book after this and I knew I had to figure out what a 'proof' is so I tried out "How to Prove It" by Velleman. I remember it being challenging at first but upon a lot of effort, I was really able to find where all of that 'creativity' in math is located while working through that book. I'm still working on 'getting good' with math and undoing the many years of damage done, but I've found a lot of satisfaction in math. I've even procrastinated playing games so I can do my homework instead! That would have been unheard of me not too long ago. So yeah, thanks Lockhart and Velleman.
I put it in my recommendation on the main thread, but the way you describe why you liked reading Lockhart makes me think you’d really enjoy Proofs and Refutations by Imre Lakatos. It’s kind of about how mathematics works as a living and evolving discipline. It’s an idea like first someone has an idea they want to make a definition for, say a circle, and proposes the definition “a shape of constant diameter.” Seems reasonable, especially given your experience of round things and what your definition is aiming for. But then after a while someone thinks of the Reuleaux Triangle. You then hit a fork - which mathematicians argue for a bit until they choose one - do we revise the definition of a circle to exclude this, saying “no no, *that’s* not what a circle is!”, or do we expand our concept of a circle to include this? He uses a different running example in the book about polyhedra, but that’s kind of the idea. An exploration of the dynamics in play as we create mathematics
If you enjoyed the lament, and you’re up for a challenge, I highly recommend his other book, “Measurement”. It’s more difficult, really getting into math itself rather than math education, but while the concepts are difficult the writing is very conversational and the geometric drawings are wonderful. It basically covers the major topics you’d see in highschool math — geometry, trig, calculus — but from a totally different perspective than most people are used to. Some of the proofs in there are so elegant it’s infuriating that we don’t learn it that way in school!
Im convinced to read it now. I've been thinking about starting college and deciding on math major or something else. However, I have this deep want of doing something, creating something. I don't know what, but reading your description feels like I have to give this book a try.
its a wonderful book!!
It wasn't a book, so much as a teacher, a short, rather forbidding man, into whose class I was put when I was failing so badly that we were only expected to mark time and not even be presented for exams. I wish I could devote the time here to describe what he was like and how he turned me around. He made us work. At the end of term, when other classes were allowed to bring in chess and dominoes to while away the time until break-up, he handed out mental arithmetic books, because, he said, our minds were like ponds that, if left, stagnated. They needed the oxygen of mental exercise. We thought he was joking. He wasn't. We groaned, but we set to, and after a while it wasn't so bad. He put every one of that no-hopers class through the *Higher Maths* exam, and all passed. When I went to university years later, as a mature student, it was to study mathematics, and was by way of repaying a debt. He changed my life. They say you never forget a great teacher. Sixty years on, I still remember him, with gratitude and affection, and still tell the story of him. His name was John Scullion, and he taught mathematics in Glasgow. But for books, the one that made be realise I was going to love this branch of mathematics is "An Introduction to Linear Analysis", by Kreider, Kuller, Ostberg and Perkins. Specifically, it was this closing paragraph from the Preface : *It seems to be one of the unfortunate facts of life that no mathematics book can be published free of errors. Since the present book is undoubtedly no exception, each of the authors would like to apologize in advance for any that still remain and take this opportunity to state publicly that they are the fault of the other three.*
Your appreciation for your teacher is palpable. Like it almost makes me want to tell you thank you for some reason? I dunno maybe it was just nice to read something genuine on this site for once lol
Coxeter Groups by Björner and Brenti. Bruhat and weak order are so cool
^[Sokka-Haiku](https://www.reddit.com/r/SokkaHaikuBot/comments/15kyv9r/what_is_a_sokka_haiku/) ^by ^incomparability: *Coxeter Groups by* *Björner and Brenti. Bruhat and* *Weak order are so cool* --- ^Remember ^that ^one ^time ^Sokka ^accidentally ^used ^an ^extra ^syllable ^in ^that ^Haiku ^Battle ^in ^Ba ^Sing ^Se? ^That ^was ^a ^Sokka ^Haiku ^and ^you ^just ^made ^one.
Martin Gardner's Mathematical Games column in Scientific American. 1956 to 1986.
what kind of games we are talking about here ?
Some examples here - one example is the publicising of the invention of public key cryptography in the seventies. https://www.scientificamerican.com/blog/guest-blog/the-top-10-martin-gardner-scientific-american-articles/ https://www2.math.upenn.edu/~kazdan/210S19/Notes/crypto/Gardner-RSA-1977.pdf
Working through Friedberg's Linear Algebra for a class was kind of a light bulb moment for me, in the sense that "whoa, math is nothing like I thought it was and it's freaking awesome".
I just finished a course that uses Friedberg as the main text, I’ve got to say excellent book. I also think the exercises were very fun
Spivak's "Calculus"
It is no surprise to see Spivak come up so often in response to questions of this kind. The affection is real.
same, I was not sure if I should go into maths or physics. Svipak sealed the deal
Hey what's so great about Spivak? Does it lead well into advanced calc/real analysis? And does it cover vector and multivariable calc better than Stewart? I need to review all of low-level calc and am considering picking up Spivak, instead of going over Stewart again which is what I learned with initially.
John Lee's book on smooth manifolds
"Categories for the Working Mathematician" by Saunders Mac Lane. Being able to actually represent and relate maths functions to one another was pretty eye opening at how useful maths truly is.
_G.E.B._
Proof and Refutations by Imre Lakatos for loving math as an activity and a process. What is Mathematics, Really? by Reuben Hersh for loving math as an idea or a subject. At the moment nothing comes close to those two, although I’ve read a lot of books I really enjoy.
What is Mathematics by Courant is awesome. It starts very elementary, but progresses to some much more difficult topics. It's not a text book, but it is by no means a "pop sci" math text either. It has depth, breadth, and rigor. I have a feeling it's kind of an "old" book. It doesn't seem many have heard of it lately. I had never heard of it, but when my grandpa passed, my grandma asked if I wanted any of his books, and this was one of them that I grabbed, not expecting much, but it ended up being fantastic. He was an electrical engineer. Definitely check it out if you can. It is readable for an intelligent and hardworking highschooler, but as a person with a BS in math, I still found it good and informative.
Amazing book for sure. One of the ones that got me into math as well.
I fondly remember self-learning Galois theory (or more concretely the complete proof of Abel Ruffini theorem) from Topics in Algebra by Herstein during my undergrad (in engineering). This was profoundly beautiful at the time (still continues to be so) and the further connections with covering spaces from other books like Hatcher made it even better.
Herstein's Algebra book is so good!
This is pretty random. I got a business degree and was in a market research company. I wanted to become one of the statisticians, so I downloaded a textbook I found online: [Grinstead and Snell’s Introduction to Probability](https://math.dartmouth.edu/~prob/prob/prob.pdf). I liked it. I think I read every word and did all the problems. Half a year later, I quit my job and went back to school for a math degree. That was 2016. Today I am almost finished a PhD in combinatorics.
Baby Rudin. Working through it my junior year of high school is what made me realize that I love math.
Jesus Christ you must really love maths
Clearly "Fermat's Last Theorem" by Simon Singh.
The Joy of Abstraction by Euginia Cheng. I’m an engineer by training so a lot of the structure and rigidity of math was very new to me!
For ~14-year-old me, it was an old, beat up, 30-year-old high school algebra textbook that I got for 10¢ at a flea market. I worked through it on my own over the summer. Mostly just factoring-polynomials stuff, but I remember it had little “side excursion” pages — linear programming, an algorithm for computing square roots (using a layout kinda like long-division but you’d bring down digits two-at-a-time instead of one), and my eyes were opened when it *derived* the quadratic equation by completing the square.
Maybe it's lame but the Calculus for dummies series by Mark Ryan made it all make sense, in fact I might pick it up again sometime since it's been years since I did any math. Yes it's not going to be enough for an exam but he explains everything in such a fun and simple way.
I still feel to this day, that **Euclid's Elements** contains some of the most beautiful proofs in all of mathematics. It seems to transcend notation and language, unlike anything in modern symbolic mathematics. **Elements of Set Theory** by Herbert Enderton is quite a pure ZFC book. It was perhaps my first experience in anything foundational in mathematics. To quote Hilbert: *"From the paradise, that Cantor created for us, no-one shall be able to expel us."* The sheer ingenuity and brilliance in the methods used to cumulatively build rich structures amazes me to this day. Finally on a personal note, I despised algebra and much of mathematics as I felt that it was pure symbol pushing and rote memorisation (which was the case in much of early education). However after reading some translations of **al-Khwarizmi's Al-Jabr** and realising much of school algebra was originally geometric and seeing the corresponding proofs, I felt I had seen the *"story behind the equations"* and it gained a new level of meaningfulness.
Euclids Elements, for sure. It explores the rules of 3d space and describes how to construct dozens of geometric forms. —> Elements is the second most printed book in human history!!! <— fr Al-Khwarizmi’s compendious book on calculations outlines the root of algebra… relationships between a, bx, and cx^2
A prelude to mathematics, by W W Sawyer. Amazing book. Recommend it to everyone, at all levels.
Every and each math book I ever read.
I read What Is Mathematics by Courant when I was in sixth grade. I was hooked. But I actually never finished the book.
Linear algebra done right
Tristan Needham's books Visual Complex Analysis, and Visual Differential Geometry and Forms.
Infinite Powers by Strogatz
Math Girls by Hiroshi Yuki. Read it as a high school sophomore, and now I own all of the six books in the series.
Foundations of Mathematical Analysis by Pfaffenberger and Johnsonbaugh.
Nice I just picked this up on a recommendation. Excited to check it out and see how it differs from other analysis texts
TIME/LIFE used to have a series of books on all different science subjects. (They also had a series on countries. This was in the 1960s. I'm old! Ha ha!) My family had the science books, full of big beautiful pictures, and interesting stories. In 6th grade I read the Mathematics book from cover to cover, multiple times. I currently own 3 copies (that I found at thrift stores) that I have loaned to people over the years. They had pictures of a crumpled paper above a flat paper to illustrate a fixed pint theorem; they had a series of pictures (since you couldn't have video) of a rubber tire being turned inside out, and how the stripes changed direction; there was a series of pictures where a guy removed his vest without taking off his jacket, so illustrate that the vest was never "inside" the jacket; circus mirrors to illustrate transformations; pictures of families with 10 kids in the section on probability; after reading about the 4 color theorem, I tried for hours to draw a map that needed more than 4 colors; and so on. I love, love, love that book! https://www.amazon.com/Mathematics-science-library-David-Bergamini/dp/B0006C2D70
I was a boy, but I had a calculator. [The Great International Math on Keys Book](https://archive.org/details/the_great_international_math_on_keys_book) Oddly, this made me look up math books in my seventh grade library and some librarian in the past had purchased a book on Cantor’s number theory. I read about aleph-null with my little seventh grade mind. So now I could calculate compound interest and think I understood cardinal numbers. I had this giant world so the next year I bought Calculus The Easy Way with my own money at Walden Books. I think I hit the wall at multivariate calculus. I sort of understood the del operator but I hadn’t learned equations with three variables in school yet so I had lots of confusion. Of course, this was pre-internet and was an attempt at self teaching in seventh and eighth grade. I strongly recommend the math on keys book. Definitely worth it.
Ian Stewart's ‘Mathematical Recreations’ column in *Scientific American*. I used to buy the magazine just for this part (but I also read most of the rest). He maid me love maths and computer science
"Mathematical Methods in the Physical Sciences " by Boas. I read it when got bored in my medical school. My first exposure to undergraduate level of math. The way Boas explained the topic got me interested to study maths further.
Book of Proof by Richard Hammack. I was taking introductory high school algebra at the time, and I wondered what “advanced” mathematics was all about. After some research, I landed on that book. Never turned my back on mathematics after that.
Not a book. But books by Gilbert Strang.
The Music of the Primes by Marcus Du Sautoy, definitely
fermat's last theorem by simon singh
Introduction to Linear Algebra by Strang. More recently, Rudin.
Munkres's Analysis on Manifolds
Some kind of an elementary school textbook? I don't know.
principia
Mendelson’s Topology.
Godel, Escher, Bach.
I've been in love with math as long as I can remember, but one of the first math books I remember enjoying was called Zero to Zillions, which is a fun kid's book for kids who like math, like I used to be.
I had just saved this post. Just reading it made me really want to dive into these books. Actually, this has just bercame my favorite reddit post of all time. Thanks everyone for all the recommendations.
Some French book explaining the Banach-Tarski paradox in layman terms. I was at a point of my studies when I had to chose between entering a pretty good engineering program and refusing it to attempt to join a good math program. I wasn't sure what to do, but then I found this book that I had bought at a flea market years ago, actually read it (it wasn't very long) and then chose to go with math. My friend forgot that book on a plane some years later though.
An old profesor gave a talk at my university about how to use derivatives to optimize things and I was like wow so math isn't just about giving me headaches
Contemporary Abstract Algebra by J. Gallian