I came to mathematics from a background in philosophy and math never really “clicked” for me until I hit proof writing. It felt very similar, proving tight logical arguments in the apriori world of abstraction. Proof writing really should be taught more in K12. Once you fall in love with the logical flow, it’s a game changer.
That's awesome. I had a calculus professor who told us, while working through the few proofs we covered, that if we could follow them, we should consider becoming either a math major or a lawyer. That comment always stuck with me and fascinated me. I've always loved logic the most as a field of study because it truly reveals the interconnectedness of all the disciplines of human understanding.
I’m not originally a math person, but have gotten heavily into it recently mostly due to watching things like this channel. I’m getting deeper into proof writing and I truly feel my understanding of math has advanced significantly in a relatively short time. It really might be the key to understanding what mathematics really is, what makes it so unique as a discipline. Thanks for all the work you put into these videos, they’re invaluable.
The rigor, attention to detail, patience and humility that is required to handle theorems and proofs can, potentially, make one better at "everything" difficult 'forever'. I tell myself this, as I recall struggling through Linear Algebra proofs decades ago in college.
My favorite math class was titled Foundations of Higher Mathematics and the professor used "The Book of Proof" as the course textbook. It's a great book that I will always remember because it helped me get through all of the proofs I had to do as an undergrad in Computer Science. Thank you for sharing these books and the rest of your videos!
This is great because i started a couple of years a pure maths course where every homework question and exam question is rigorous proofs, but we never got any explanation of anything to do with logic or quantifiers or proofs, and so it came as such a shock. I'm sure if we had a dedicated module covering all of this, the rest of our course would have been so much easier.
I never learned how to write proofs in high school and I've been struggling in university math classes because of it (many kids at my college went to private schools where they took math past calculus, but I went to public school). Thank you for these suggestions! I knew that I needed to get a better mathematical foundation if I am to do well in these hard classes, but I had no idea where to start
I purchased Velleman’s “How To Prove It” after you recommended it in a previous video. I expect it to be delivered later today. I look forward to learning from it! ❤
I'm an octogenarian who has kept one book from my university days: Principles of Mathematical Analysis (2nd. Ed.) by Walter Rudin, which among mathematicians is referred to as "Rudin". I understand that is still being used (3rd. Ed., around 1976) in some undergraduate analysis courses. It made me think more deeply than I thought possible, instilling the elegance and beauty of mathematical proofs.
The great thing about it is that everyone can learn this stuff. Picking up some quantifiers and proof strategies is arguable 10 times easier than a lot of the mathematics covered in school, and yet, with this understanding, you realize you have never truly studied mathematics until now.
I bought some time ago the third edition of How to Prove it and I was amazed at how helpful it would have been if I had a book like that when I was first learning proof writing. In my EE&CS degree we didn't even have a class to learn proof writing, it was just glossed over in a discrete math course (which was optional!). If there wasn't the common course for grads/undergrads that I took back in the day, I wouldn't even have the chance to follow my dream. Thank you math sorcerer for covering such interesting books, some of us would not be able to navigate in the convoluted mess of academia without you 😂.
That's by design. The majority of academic administrators and coursewriters either don't want you to succeed at whatever your motivation to take the course is or at the course itself or truly don't care whether you succeed. That's also true of a minority of educators at all levels. The reasons and intents behind that malice and apathy are greatly varied, including but not limited to avarice and true malice and benevolent malice all in the general sense, but it is overwhelmingly the state of the field.
Beautiful book review! Last year I studied Book of Proof which I found to be pretty good actually based on your recommendation. This year I am devoting my time and energy to studying How to Prove it by Velleman (3rd edition). I really like how Velleman shows you his motivation and thought process in the scratch work before every proof. Really like his in-depth discussions and challenging problems.
THIS IS ALL TRUE. I took Discrete math 12 years ago and it was so much fun. It was all that math that was easy, but I had always wondered about. It should of been my introduction to proofs but I did this Geometry w/ proofs book first and I did it line by line. I read 100% of it. I don't know the name of the book and I don't have it anymore. Cliffs notes word problems was super helpful and I recommend before pre-calc and trig.
I very recently did my first proof, or at least I think I did. during the process of learning how to do it I ran across the Book of Proofs along with a few other documents for download. Book of Proofs is a little daunting but I'm going to try to wade through it over time in my old age
I've only started "Book of Proof" online so I can't say much about it. Honestly, I don't get the adoration for Velleman. There's a lot of math I've studied that I can't even see how you could apply anything from the book to help you do the proofs. It's been a while since I went through it so maybe another look will change my thinking. Solow, for me, is THE proof book. I like how it explains all the basic types of proof techniques and does it in plain English without lots of symbols. And the techniques could be used all the way down to high school geometry. Also, every book in this video has updated editions.
I have the two books on either end, but I'm missing the middle book. Math is a language, and Proof Writing is English for Math Students. I'm tutoring a few students in Geometry, who thought that it would only be about shapes, and finding area and volume. The difficult part is teaching them proofs. They're first learning how to think logically, and also learning about the basics of rigor. It's extremely challenging, because they're still learning how to write well in English and support their topics in essays. It's worth it.
Hi, The Math Sorcerer! I have this textbook called " Alan Agresti, Statistical Methods for the Social Sciences (5th edition). New Jersey, Prentice-Hall. " and it is for my Sociology Statistics Course. I was wondering if you by any chance have the book and would be willing to talk about it in a video, as I am kind of understanding the material and I am passing my class. However, I will be using the book again for more advanced statistics in the next semesters, so it has been a struggle to get all the necessary info for exams. Thank you!
I read solow a lot of times and even though I got some good ideas from it, it was until I read velleman that I truly undersstood logic and proof structure.
While doing integration, we use LIATE or ILATE. But i dont understand why it makes sense, like what is the logic behind this rule? Hope u make a video on this.
Hi math sorcerer I love watching your videos Keep on reviewing books Do you have any idea about a book on solving PDEs with numerical methods especially in fluid dynamics?
Proof methods are structured in a way that if the conclusion is true than the propositions must be true. Sometimes this is called a vacuous truth. Sometimes though, the antecedent can be false, but the consequent must always be true for it to be a true statement. That is part of forming arguments in Real Analysis. Jk.
This video us so good, these books look awesome and I cant wait to buy how to prove it soon and learn propfs in highschool Btw I would really love to purchase your signed copy of stewarts calculus if you ever wish to sell it😊
I've been constructing a family Library for the last 8 years its full of subjects from Music, to Law, religion, and Maths and Physics; I'm currently enjoying Music, have a rough idea for my library and am content with its overall shape, I have 6 months learning guitar and I already know that it's not going to last forever eventually I will be content with my overall skills at that moment I know I will want to try my hand at Maths; I'm 28 years old if I play guitar for 10 years I know I will be 38, I'll travel for 2 years, at 40 I'm going to sit down and revisit Euclid and probably start with Set theory and discrete mathematics before I start algebra 1 and 2. My question is am I stupid to consider a math journey at 40? Is 40 too old to be a beginner?
Hello Math Sorcerer! I just finished calc 3 and am hungry for more math! I really want to start self-studying differential equations. Do you have any recommendations for a diff eq's book? This is what I want for Christmas!
There is a Calculus book available for free on MIT open courseware called Calculus by Gilbert Strang which I have been following for a long time. It begins with basic ideas and ends with vector calculus. How does it compare to other calculus text books ?
I hear a lot of people saying Micheal Spivak was a very good writer, mentioning his Calculus book. I wanted to know if Calculus on Manifolds is also good.
In order to fully understand a topic in mathematics. Is it enough to make our own examples and problems on that topic and then work on it. Instead of doing the exercises in the book.?
I want to know when to start learning proof writing, i am in grade 10 Egyptian system and i am relatively good at maths, i am starting my journey in self studying math and i got a discreet maths book, so now i wanna know should i start with proofs before i even start my journey or when exactly?
there have been a couple other videos on this channel titled "how to learn mathematics from start to finish" and in fact these books are recommended in those videos to read very early with the caveat that you don't need to 100% understand them by the time you are done. They are a foundational subject that you will revisit again and again and will help you read and understand other more intimidating texts earlier. but It's like learning music theory before picking up an instrument. some of the advanced stuff will not come easy until you have more practical experience in other areas.
I remember years ago I took an abstract algebra course in university. The majority of the class struggled big time because nobody knew how to write proofs. We never had a proof writing course at our university. Is this a common thing?
Can proof-based math be taught to high school students or even younger students? It seems like at least some level of it should be taught to kids as early as possible.
Yes!! Most colleges will put in like a pre-req of calc 2 or something similar. But honestly, it's just words. If you can read carefully you can get through it and learn!!
@@TheMathSorcerer Wow, thank you for taking the time to reply! And thank you for clarifying that. For a math John Doe like me, your recommendations are pure gold.
Math Soscer, every time you review that book by professor Dan Velleman it gives me goosebumps because he was my professor in math at university. But I never encountered that book. Hopefully, I will get my hands on it in due course.
STOP recommending either _How to Prove It_ by Vellman and _How to Read and Do Proofs_ by Solow. Both are bad books and there exist far better books, including one you reviewed. Including that book, another I suggest you recommend instead is my favourite of the bunch, _Bridge to Abstract Mathematics_ by Ronald Morash
I came to mathematics from a background in philosophy and math never really “clicked” for me until I hit proof writing. It felt very similar, proving tight logical arguments in the apriori world of abstraction. Proof writing really should be taught more in K12. Once you fall in love with the logical flow, it’s a game changer.
Totally agree, proof writing is super cool.
Man, i'm a former lawyer and i love doing self study math and financie, it help me a Lot as a profesional!!!
That's awesome. I had a calculus professor who told us, while working through the few proofs we covered, that if we could follow them, we should consider becoming either a math major or a lawyer. That comment always stuck with me and fascinated me. I've always loved logic the most as a field of study because it truly reveals the interconnectedness of all the disciplines of human understanding.
How to Prove It was the textbook for my first year undergrad course. Love this book. The chapter on infinite sets had me captivated.
That's so cool that you used it for an actual course in college.
I’m not originally a math person, but have gotten heavily into it recently mostly due to watching things like this channel. I’m getting deeper into proof writing and I truly feel my understanding of math has advanced significantly in a relatively short time. It really might be the key to understanding what mathematics really is, what makes it so unique as a discipline. Thanks for all the work you put into these videos, they’re invaluable.
The rigor, attention to detail, patience and humility that is required to handle theorems and proofs can, potentially, make one better at "everything" difficult 'forever'.
I tell myself this, as I recall struggling through Linear Algebra proofs decades ago in college.
They don't even talk about these books where I study higher mathematics 😅 Thank You for reviewing these books.
My favorite math class was titled Foundations of Higher Mathematics and the professor used "The Book of Proof" as the course textbook. It's a great book that I will always remember because it helped me get through all of the proofs I had to do as an undergrad in Computer Science. Thank you for sharing these books and the rest of your videos!
Oh wow that's awesome that they used that book!
3:00 that is so me, I always smell nostalgic books, takes me back in time.
me too!
Velleman's book is a gem; the book is straight forward and has a lot of great examples
This is great because i started a couple of years a pure maths course where every homework question and exam question is rigorous proofs, but we never got any explanation of anything to do with logic or quantifiers or proofs, and so it came as such a shock. I'm sure if we had a dedicated module covering all of this, the rest of our course would have been so much easier.
i always do the little whiff before reading a book and it's awesome that you do it as well!
I never learned how to write proofs in high school and I've been struggling in university math classes because of it (many kids at my college went to private schools where they took math past calculus, but I went to public school). Thank you for these suggestions! I knew that I needed to get a better mathematical foundation if I am to do well in these hard classes, but I had no idea where to start
I purchased Velleman’s “How To Prove It” after you recommended it in a previous video. I expect it to be delivered later today. I look forward to learning from it! ❤
Book of Proof is excellent!!! And has usually detailed answers for ALL odd numbered problems!!! I'm self-studying.
I'm an octogenarian who has kept one book from my university days: Principles of Mathematical Analysis (2nd. Ed.) by Walter Rudin, which among mathematicians is referred to as "Rudin". I understand that is still being used (3rd. Ed., around 1976) in some undergraduate analysis courses. It made me think more deeply than I thought possible, instilling the elegance and beauty of mathematical proofs.
Been a while since I’ve heard “publish or perish” good stuff.
The great thing about it is that everyone can learn this stuff. Picking up some quantifiers and proof strategies is arguable 10 times easier than a lot of the mathematics covered in school, and yet, with this understanding, you realize you have never truly studied mathematics until now.
I bought some time ago the third edition of How to Prove it and I was amazed at how helpful it would have been if I had a book like that when I was first learning proof writing. In my EE&CS degree we didn't even have a class to learn proof writing, it was just glossed over in a discrete math course (which was optional!). If there wasn't the common course for grads/undergrads that I took back in the day, I wouldn't even have the chance to follow my dream.
Thank you math sorcerer for covering such interesting books, some of us would not be able to navigate in the convoluted mess of academia without you 😂.
That's by design. The majority of academic administrators and coursewriters either don't want you to succeed at whatever your motivation to take the course is or at the course itself or truly don't care whether you succeed. That's also true of a minority of educators at all levels. The reasons and intents behind that malice and apathy are greatly varied, including but not limited to avarice and true malice and benevolent malice all in the general sense, but it is overwhelmingly the state of the field.
I'm going to read the book of proof for my first proofs based class starting in January! I am planning on reading part 1 over the break
Beautiful book review! Last year I studied Book of Proof which I found to be pretty good actually based on your recommendation. This year I am devoting my time and energy to studying How to Prove it by Velleman (3rd edition). I really like how Velleman shows you his motivation and thought process in the scratch work before every proof. Really like his in-depth discussions and challenging problems.
Yes exactly! That is what I love about Velleman too!
I like the book " Proof Patterns " which is an actual toolkit to do proofs.
I like Daniel Velleman's book. I have seen several other proof books reviewed here but I find Velleman's book to be very readable and easy to follow.
THIS IS ALL TRUE. I took Discrete math 12 years ago and it was so much fun. It was all that math that was easy, but I had always wondered about. It should of been my introduction to proofs but I did this Geometry w/ proofs book first and I did it line by line. I read 100% of it. I don't know the name of the book and I don't have it anymore. Cliffs notes word problems was super helpful and I recommend before pre-calc and trig.
every mathematician being great at a computer theorem prover will be a good thing.
I very recently did my first proof, or at least I think I did. during the process of learning how to do it I ran across the Book of Proofs along with a few other documents for download. Book of Proofs is a little daunting but I'm going to try to wade through it over time in my old age
The mats sorcerer sounds like Jason from maths an science....
you always delivered with books recommendations
How to Prove It is my favorite proof book
Yeah it's really good. I even love the physical size of the book!
Thank you, Sir
I've only started "Book of Proof" online so I can't say much about it. Honestly, I don't get the adoration for Velleman. There's a lot of math I've studied that I can't even see how you could apply anything from the book to help you do the proofs. It's been a while since I went through it so maybe another look will change my thinking. Solow, for me, is THE proof book. I like how it explains all the basic types of proof techniques and does it in plain English without lots of symbols. And the techniques could be used all the way down to high school geometry.
Also, every book in this video has updated editions.
I have the two books on either end, but I'm missing the middle book. Math is a language, and Proof Writing is English for Math Students. I'm tutoring a few students in Geometry, who thought that it would only be about shapes, and finding area and volume. The difficult part is teaching them proofs. They're first learning how to think logically, and also learning about the basics of rigor. It's extremely challenging, because they're still learning how to write well in English and support their topics in essays.
It's worth it.
I wished I had known about these books back in my 1st year undergrad.
I just found third edition Book of Proof from Richard Hammack online for free.Thank you for informations.
What about Proofs by Jay Cummings? Is it good?
Yes I have that book, it's awesome!
Hi, The Math Sorcerer!
I have this textbook called "
Alan Agresti, Statistical Methods for the Social Sciences (5th edition). New Jersey, Prentice-Hall. " and it is for my Sociology Statistics Course.
I was wondering if you by any chance have the book and would be willing to talk about it in a video, as I am kind of understanding the material and I am passing my class. However, I will be using the book again for more advanced statistics in the next semesters, so it has been a struggle to get all the necessary info for exams.
Thank you!
I was watching your reviews of How to Prove It last night wondering if you still cared about this book. Thank you! I'm finally at the end of it.
It’s a great book!
Have you had a look through the Beast Academy books or the follow-up series Art of Problem Solving? If so, what are your thoughts?
I read solow a lot of times and even though I got some good ideas from it, it was until I read velleman that I truly undersstood logic and proof structure.
While doing integration, we use LIATE or ILATE. But i dont understand why it makes sense, like what is the logic behind this rule? Hope u make a video on this.
I love books and i hate the lack of time to speedrun books within 24 hours.
I love you sir❤❤❤❤❤❤❤❤❤❤
Hi math sorcerer
I love watching your videos
Keep on reviewing books
Do you have any idea about a book on solving PDEs with numerical methods especially in fluid dynamics?
Proof methods are structured in a way that if the conclusion is true than the propositions must be true. Sometimes this is called a vacuous truth. Sometimes though, the antecedent can be false, but the consequent must always be true for it to be a true statement. That is part of forming arguments in Real Analysis. Jk.
This video us so good, these books look awesome and I cant wait to buy how to prove it soon and learn propfs in highschool
Btw I would really love to purchase your signed copy of stewarts calculus if you ever wish to sell it😊
I've been constructing a family Library for the last 8 years its full of subjects from Music, to Law, religion, and Maths and Physics; I'm currently enjoying Music, have a rough idea for my library and am content with its overall shape, I have 6 months learning guitar and I already know that it's not going to last forever eventually I will be content with my overall skills at that moment I know I will want to try my hand at Maths; I'm 28 years old if I play guitar for 10 years I know I will be 38, I'll travel for 2 years, at 40 I'm going to sit down and revisit Euclid and probably start with Set theory and discrete mathematics before I start algebra 1 and 2. My question is am I stupid to consider a math journey at 40? Is 40 too old to be a beginner?
Hello Math Sorcerer! I just finished calc 3 and am hungry for more math! I really want to start self-studying differential equations. Do you have any recommendations for a diff eq's book? This is what I want for Christmas!
There is a Calculus book available for free on MIT open courseware called Calculus by Gilbert Strang which I have been following for a long time. It begins with basic ideas and ends with vector calculus. How does it compare to other calculus text books ?
Hey math sorcerer. Can you please review Calculus on Manifolds by Spivak?
I hear a lot of people saying Micheal Spivak was a very good writer, mentioning his Calculus book. I wanted to know if Calculus on Manifolds is also good.
It's excellent!
In order to fully understand a topic in mathematics. Is it enough to make our own examples and problems on that topic and then work on it. Instead of doing the exercises in the book.?
what do you think about The Story of Proof: Logic and the History of Mathematics by John Stillwell
I want to know when to start learning proof writing, i am in grade 10 Egyptian system and i am relatively good at maths, i am starting my journey in self studying math and i got a discreet maths book, so now i wanna know should i start with proofs before i even start my journey or when exactly?
Start now:)
I want to get started with maths. Where do I start, any books or recommendation will be great thanks.
Start here, with one of these. Try book of proof, it's free:)
there have been a couple other videos on this channel titled "how to learn mathematics from start to finish" and in fact these books are recommended in those videos to read very early with the caveat that you don't need to 100% understand them by the time you are done.
They are a foundational subject that you will revisit again and again and will help you read and understand other more intimidating texts earlier.
but It's like learning music theory before picking up an instrument. some of the advanced stuff will not come easy until you have more practical experience in other areas.
Can I read these books while in my second year of college?
Yup
I am taking real analysis in my first semester as an undergraduate, without a background in calculus and proofs, so its killing me🙃
How to get these books for personal use.
I remember years ago I took an abstract algebra course in university. The majority of the class struggled big time because nobody knew how to write proofs. We never had a proof writing course at our university. Is this a common thing?
I apparently already know how to make basic proofs 💀
I study computer science, and I have had to make logical proofs in a couple subjects.
Had to watch this🙌
Thank you!!
any book you can suggest on computer science compiler construction task-based theorem and can it be used to create proofs?
Can proof-based math be taught to high school students or even younger students? It seems like at least some level of it should be taught to kids as early as possible.
Geometry -- It's not only English for math students, but when taught properly, it introduces them to basic proofs.
@ I was thinking about that, too.
Hey, would you mind if I use this footage in my cinema?
Wow
:)
The fact that there are books and courses on proof writing shows how dumb the world has become, or at least, how low education has sunk.
Are those books aimed at laymen?
Yes!! Most colleges will put in like a pre-req of calc 2 or something similar. But honestly, it's just words. If you can read carefully you can get through it and learn!!
@@TheMathSorcerer Wow, thank you for taking the time to reply! And thank you for clarifying that. For a math John Doe like me, your recommendations are pure gold.
Math cannot be without it's foundations of axioms and the various algebraic structures that form from them. Jk.
❤❤❤
Math Soscer, every time you review that book by professor Dan Velleman it gives me goosebumps because he was my professor in math at university. But I never encountered that book. Hopefully, I will get my hands on it in due course.
Math Socerer, professor Velleman, as a teacher in the classroom he was awesome. We, students were in awe of him and we considered him a god.
It is not free
0123
The fact that you recorded this video is enough math proof for me, as is the fact that you are even existing and talking about a whole lot of nothing.
STOP recommending either _How to Prove It_ by Vellman and _How to Read and Do Proofs_ by Solow. Both are bad books and there exist far better books, including one you reviewed.
Including that book, another I suggest you recommend instead is my favourite of the bunch, _Bridge to Abstract Mathematics_ by Ronald Morash
❤❤❤❤❤