Excellent Proof Writing Book For Beginners

[@jojo031]

I took Dr. Cummings for my "Intro to Formal Mathematics" class during the Fall, 2020 semester. My class was actually the first class that was taught using this book, as it was being written! It was a very interesting class, given the circumstances of the pandemic. Each week, Dr. Cummings would release the next section of this book and our class would read over it, have discussions, and also point out any errors if we ever found any 😂. I really appreciated Dr. Cummings's presentation of the material; everything felt like it was being presented in layman's terms, and it made it much easier to ask questions and discuss the material. I also really liked how at the end of each section Dr. Cummings would provide an "intro to ____", where he provides a small section dedicated to discussing a different field of math (number theory, analysis, algebra, etc.). It really helped give some insight to what we could expect in upper-division coursework, and which emphasis we might want to follow in our math degrees.

[@awvz_1194]

I was in that class with you 😂

[@soheilbeygi240]

According to Math Sorcerer he commented on this video, I can't find it. :( kzbin.info/www/bejne/eKW7fWaFadOeaZo

[@AutomationDnD]

cool story

[@tribebuddha]

I am 35, suffered a lot of trauma, couldn't study STEM and focused more on philosophy because of all the hurt. I want to begin with my mathematics education. Edit: Thank you. I will be using your channel as my teacher and guide. I want to be really good at math.

[@cryptopatrick]

I'm rooting for you. Just keep learning and enjoy the process.

[@suic86]

IMO it's worth it. As a philosophy major, I have to say that learning math is way more rewarding than reading and learning philosophy (can it be even learned?), but YMMV.

[@marbles7649]

Check out his other videos, specifically his video titled _Learn Mathematics from START to FINISH (2nd Edition)_ . If you keep up on the studying, you _can_ be really good at math and learn math at a high level (even a graduate level). Maybe consider going back to college too, that way you could make a career out of it. Keep up the good work and know that you can do this. I am rooting for you

[@abhishekmazumdar2072]

Sure man. All the best.

[@Living_for_Him_Alone]

All the best. Almighty is with you. It's never too late to start something. You are never too old to dream another dream. All the very best again. ❤

[@andrewesquibel9614]

You should TOTALLY write an abstract algebra book (in this style). There are NO good, comprehensive abstract algebra books for self study. I flipped through every abstract algebra book at my university library. None of them were this good. There is absolutely a need for an abstract algebra book of this kind -- conversational style, generous explanations, slightly illustrated, solutions in the back, pro tips, an organized list of theorems, etc. It would be a CLASSIC!

[@takforalt]

I ordered the book. Thanks for sharing. I, however, never bought the excuse for not providing the answers worked out in detail in math books in general. Even if all the questions were answered, there would be no shortage of problems, only a shortage of imagination and interest and effort to formulate them. Everyone says doing problems is of utmost importance, and therefore I am aghast at how so little effort is spent providing the student with the opportunity to see if their answers are correct. We needn't be considered children, and we will sneak a peek before trying to solve the problems. If a student does that, it is on him anyway. So many texts are written not to convey a concept elucidating it carefully. Rather, the authors often write tersely and "rigorously," so students won't understand it until they find another resource for clarification. Where is their concern for us children, then?

[@zgennaro]

I agree, it’s ridiculous. Often times you can find solutions or great hints online if not actual manuals.

[@takforalt]

@@zgennaro yes

[@branpod]

If it's true that all the solutions are on his website, I'm sure it's merely a matter of marketability (at least in regard to this book)

[@takforalt]

@@branpod That is fine. I was speaking in general as to what is common. Jay's book looks fantastic. And I purchased it.

[@lgbtthefeministgamer4039]

christ, bro, put away the thesaurus

[@ShaolinMonkster]

Jay Cummings is a young person. And is writing better books than old teachers. Plus his prices are very good. I believe we should buy his books

[@devon9374]

Yea I bought both to support him

[@unthawedwater747]

Hmm... I'm getting into computer science and I get the feeling this book would be VEEEEERY useful 🤔🤔🤔

[@crnojaje9288]

Look into How to prove it in and Chartrand Intro to advanced math or something like that. Both books are great for proofs. Im going to buy all three of them

[@Nessy211]

Yes in cs too and I am getting this book.

[@thenbaplayer9485]

@@crnojaje9288 could you name the books

[@chickenstrangler3826]

@@thenbaplayer9485 he did? Proofs, How to prove it and Chartand Intro to advanced math.

[@chickenstrangler3826]

@@crnojaje9288 There is also "Proofs from THE Book"

[@cw2448]

I purchased this book because of your review. I was hesitant to purchase this book because I have other books on proof writing. However, I am so glad that I found this video review and this book. The writing, humor, and exposition make this an incredibly easy-to-digest book. This book is a great tool that you can use to build your knowledge of proof writing and mathematics from beginner to intermediate and beyond. Thank you, Math Sorcerer, for such a great review!

[@mincedmeatchops3208]

Wow, I’m really impressed by the structure and breadth of this book! Probably the most unique and comprehensive proof-writing book I’ve seen. I think it will make a fine addition to my bookshelf. Thank you for sharing :)

[@TheMathSorcerer]

☺️😊

[@Swordfish393]

Not including answers in math books but providing them in teacher’s editions, with the justification that teachers don’t want the students to have the answers, smacks of academic gatekeeping, and the claim itself is preposterous in a world with stack overflow, wolfram alpha, and matlab. It’s one thing to have questions that aren’t answered as curiosities, but when the answers exist, the only point in concealing them is to force people to spend hundreds or thousands to take a class, just for the privilege of accessing the field. Thanks for coming to my Ted Talk. BTW I bought this book on this recommendation, thanks!

[@samueldeandrade8535]

Not including answers in Math books always was a dumb decision.

[@valeriereid2337]

I have to admit hearing you say it once took you a long time to write a proof makes me feel better. I think you are an excellent proof writer so I feel encouraged.

[@MCJSA]

"Indeed, the fact that it is an arbitrary prime is important". Knowing when to state the obvious is the hallmark of a good teacher. Doing maths is a lot about having confidence, and the less confident student will constantly question themself, wondering whether something is missing, misunderstood, invisible, non-existant.... I need to get this book!

[@oblivion591]

Hi Math Sorcerer, it caught my attention that you mentioned many people ask you to write a math book. I believe it could not only be helpful for us (students, math-lovers, ...), but also for you. I think it can make you better at Mathematics, because you'd push yourself out of your current 'comfort zone' (which is pretty advanced already lol). When writing a book, some continuity is required. I've personally always had at least 1 topic in a chapter that I did not understand well enough to be able to explain it someone else - I just let it slip away. When writing a book, this escape is not an option. I love your content, your explanation and your use of English, but I gotta admit I prefer studying from textbooks rather than on KZbin as I want to be fully immersed in what I do without any distraction. It'd be super cool if we could purchase a Maths book written by you some years from now. :)

[@ntvonline9480]

I ordered it an hour ago from Amazon. Hopefully it went through your channel. It was only $17. Now I have both of his books. Wish me luck!!

[@breadboard4538]

Our professor is using this book for our Discrete Math class, and I love it! It's honestly so fun to read. I never thought of math as enjoyable, more like a means to an end, but this book really made me passionate and curious about it. I'm so glad you're talking about this book, it has really changed the way I see math!

[@wilhufftarkin8543]

I envy you. My professors either use the most dullest books imaginable or they upload their own messy scripts three weeks too late.

[@Daniel-Pap]

Since you mentioned, that you really like the book, I would like to ask you, if you think it would be useful for an engineering student? or is it mostly for math majors? (I recently started studying for building engineer, and the math is giving me some serious challenge)

[@434mp]

@@Daniel-Pap learning proof writing never hurts

[@honkhonk8009]

Ima pray it does the same to me. Feynman changed my perspective on physics and made it alot easier to approach it. I wish math had a similar Feynman. Someone who explained away the beauty behind all these proofs and why its actually fun. Physics is fun cus you use math as a tool to solve problems. Math by itself is wierd because your taught how to make those tools.

[@marbles7649]

I've discovered so many books from you. I didn't really step out of what was taught at my specific college for learning materials, but after discovery your content I've learned so much. Such an excellent book, as was the case for every other book I purchased that you recommended. I'm eager to study math at a graduate level; I wish I could attend graduate school sooner lol. Thanks a ton, Mr. Math Sorcerer

[@WitchidWitchid]

I just got this book delivered today. I was looking out my front door and noticed a large brown envelope on the front step almost completely hidden under a heavy layer of damp autumn leaves. Fortunately the book within didn't get soggy or damaged. Its a large book and filled with lots of great stuff from cover to cover.

[@TheMathSorcerer]

awesome!!

[@mrericdodson]

Going to buy this book right now! I’ll study it this summer as prep for grad school in the fall

[@gmcenroe]

Sometimes it seems that math books are written to impress other mathematicians, other book are written for those who wish to learn mathematics. This book does both. Picked it up almost immediately. Thanks for sharing and your thoughts on this book.

[@NachoSchips]

I just bought it after failing to get further on my first Real Analysis book I bought. It's really helpful to gain intuition and it's like the hidden link between high school math and undergraduate math

[@karolissad.4270]

Did u mean the cummings real analysis book or just some other book?

[@rich_in_paradise]

I studied computer science and we had to read and write proofs on our discrete math course. I didn't really get it at the time - it was by far my worst grade - and I still mostly skip the proofs when I'm reading math and computer science books like Knuth. But I think I'll get this book and set aside some time to study it now given your glowing recommendation.

[@StaticBlaster]

I purchased this book about 6 months ago. It's a really great and clear book on proof writing.

[@jonahvasquez6210]

My favorite channel. It's cathartic and meditative 🧘‍♂️

[@Maths_Shorts_]

You are an angel not a sorcerer! I needed that book, just in time Thank you so much 🥰

[@TheMathSorcerer]

You’re welcome 😊

[@granteckhardt4878]

There's something about that book that entices me to want to dive in and learn. I love that simple minimalist cover design As well the real analysis book.

[@TheMathSorcerer]

Yeah it's a fantastic book:)

[@FelipeMendez]

I bought both jays book based on you previous review and what a nice surprice finding this review to reinstate what I suspected that his other book was good too

[@ke30_]

I'm not even into maths but I want this book now. Writing proofs for "obvious" things is interesting!

[@pauldavies7746]

I've just picked up a book called, 'How to think like a mathematician - A companion to undergraduate mathematics' by Kevin Houston. It covers writing statements, logic as well as reading and writing proofs. It's early days but it looks a very useful book.

[@orang1921]

Just got this book delivered yesterday. Was not expecting it to be so large! Very excited, though.

[@lachenmann]

I wish you could interview Jay for your channel. He's such a great guy.

[@crnojaje9288]

I knew you would do this one after the analysis one. Proof is in the pudding 😄

[@amorfati4559]

I still think you should write a math book. You have spent so much time teaching us how to learn and working with people who have doubts or struggles with math that I think your writing or pedagogical style would be far and away better than other books I have read.

[@gloriosatierra]

Jay Cummings loves to use as many trees as possible 😊

[@alexanderbaumgarten]

Recently bought both of these books by Cummings. The only one I like more is Weissman's Illustrated Number Theory.

[@robertfajt2102]

I bought and read this book a few months ago. It's not for everyone. His style is informal, and the descriptions he provides can be pretty tedious if you're even slightly familiar with the content. But it is a fantastic beginner book.

[@Crimson_Thief007]

Wow this book is exactly what I’ve been looking for to prep for linear algebra! I can’t wait to buy it! Update: book came in, going to start learning proof writing!

[@nollix]

This book looks like exactly what I need. It seems like a dream book for me. I have gladly purchased it using your affiliate link :D

[@TheMathSorcerer]

Awesome, thank you!!

[@eleazaralmazan4089]

This book looks amazing! I'm excited to purchase it!

[@samueldeandrade8535]

It looks like a great book. The cover image is brilliant.

[@JB-sp6sn]

Instapurchased this! I have a cs degree and just bought how to prove it because i eventually wanted to learn topology. So now I have two great books to get started

[@TheMathSorcerer]

Wonderful!

[@aryansaxena4978]

Please write a book dude.! Don't worry about producing the same standards as other authors

[@alexh.4514]

You're saying your graduate professor was Harold with the Purple Crayon? I'm so glad that there are folks out there generous enough to offer quality education at a reasonable price. The lowest new price for my next semester proof text was around $160!!

[@elisabethdabrowski1098]

thankyou for revisiting this topic, not super easy doing unsupervised for the first time since highschool

[@JayJay-ku8gp]

I didnt get this book til after my degree in computer science ended but man it is a great book

[@TheMathSorcerer]

Yeah I know what you mean. I wish I had this book when I was learning!

[@newmanhiding2314]

“I don’t see how I could do any better than this.” So what? If every book had to be better than last that was written, there wouldn’t be very many books. That would be a tragedy. We’d love to see you write a math book.

[@TheMathSorcerer]

:)

[@SequinBrain]

He seems to write TO the audience, which most textbooks have a problem doing. AND, the intended audience ISN'T people who already have 500 PhDs, like most textbook authors seem to think is a fantastic idea. 4:00 From my very short experience with EoC (end of chapter) problems, if we can look back in the text and see the PROCESS for solving the question, then a solution is almost redundant. Also, there's Chegg, but Chegg has wrong answers sometimes and their handwriting is impossible to read in too many cases.

[@cabritoguitarrista]

jay cummings seems the kinda guy you'd laugh while reading his books, even though they are about a tough subject

[@wilhufftarkin8543]

If Jay Cummings wrote a book about Linear Algebra, we would have the holy trinity for Math beginners.

[@pig8817]

i picked this book up before i took calc 4 and it helped me so much!

[@claudiorebelo]

Ordered :) thanks for sharing!

[@JD-nh7vb]

Jay’s books are excellent! I wish he would come out with a Kindle version.

[@littlefighter8785]

Thanks. I mean its redicioulsley amazing that you are so much hard working on math eventhough I know you love it. And about writing a math book : you yourself in one of the videos told us that different people have different views about math and its amazing to have every kind of math books on one subject. I know you are very able to write a book so please dont let yourself down, think postive and do things so. May the lord bless you. Best wishes from Iran.

[@carpballet]

I love this book. Like you, I really like this book’s size. Very important for a Proof book. I bet his wife convinced him that size really does matter. I just hope he’s not “compensating”

[@AnthonyLauder]

I have this book, and I also recommend it for folks new to proofs.

[@guitaristxcore]

I have this and Jay Cummings other book on Real Analysis in my amazon shopping cart. Looking forward to digging into them soonish.

[@davidguerrero2782]

Thanks! Great recommendation, I've just ordered my copy.

[@gregglind]

Re: Purple Crayon / "Clear". I would have found that comment crushing and defeating. As an often idiosyncratic or autodidactic learning, I struggle with modeling what 'others find obvious'. I have gotten feedback for both "skips steps", and "too much detail". What feedback did you want instead? What were they trying to communicate, and how could it have been communicated instead?

[@rook839]

Hi. I had a question for you guys. But first let me tell a bit about my background. I have never been a math guy. And struggled with math probably mostly not because I was a slow learner but because I have never met a teacher that would make sense out of all the 'you need learn this by heart' and explain how and why it works and from where they are coming from. Then I started learning math by myself during 10th grade by watching videos of topics of 6th graders in khan academy. I really love khan academy as it provides easy to digest lessons and all the color coding and visualization make it easy to understand and some relatively real life word problems make you feel that you are not learning just some random topic that is useless in every sense possible. I reached with all the videos of khan academy and some other great you tube channels from grade 6 all the way up to calculus. But when i started calculus with all the proof reading that was required and the language started to get formal i.e. real algebraic definitions, proofs, and the like, i started struggling again. I always feel there are some gaps in my math though don't know where. even the easiest proofs don't make sense to me. i am also majoring in economics, so i don't need real analysis and topology and stuff. but really want to at least to be able to read math proofs and definitions at least of the subjects that are related to my field i.e. statistics, calculus, linear algebra. I feel like the book in the video is too much for me in terms of mathematical knowledge and background that it requires. could you please recommend me what can i do at least to minimize the feeling of having gaps in my math and maximize the understanding of math textbooks? from where should i start? thank you a lot in advance.

[@devon9374]

This proofs book’s only prerequisite is a basic understanding of arithmetic, algebra and properties of numbers. I mean super basic, like the PEMDAS from elementary school. Just touch up on these basics from a book or ChatGPT and you can do this book!!

[@jamesedward9306]

Great book, it definitely covers the topics I'd like to learn. But I have to say, not providing solutions to the exercises/problems is a big turn off for me. How is somebody trying to self-learn this material supposed know if they're on the right track and understanding the material and get practice in? If you are enrolled in a course, you could ask the professor during their office hours after attempting the problems I suppose, but what about those of us trying to learn on their own? The excuses just don't cut it for me. It's too difficult? Ok, so the writer wanted to half ass his book? They want their students to not look at the answers? Huh? We're not trusted that much? Great review Sorcerer, saved me from purchasing it.

[@iQmliAwyrMRyPWfV]

Is this more or less better for beginners? What about your udemy courses? Which ones are best for going in order easiest --> hardest please? Also when your's would come into play at any time (in the following or prior order to this)

[@dialgos7574]

This is the first time that a book that you present is actually in my repertoire! I really liked this book although i never got to finish it :/

[@Handlebrake2]

How come?

[@WitchidWitchid]

I just ordered a copy of this book. Although I am familiar with many of the topics covered this book looks too good to pass up.

[@dylangonzalez2457]

the book that ramanujian needed

[@asimian8500]

Math Sorcerer: that story about the purple crayon is hilarious (and cruel). Was your Professor named Harold of Harold and the Purple Crayon fame? If he were, you were lucky he didn't draw monsters on your homework.

[@xaviergonzalez5828]

Nice book. I'm gonna get one copy! Thank you Sir!

[@digitaldaemon74]

You should write a math book about mathbooks and mathematical reasoning and learning in general.

[@schrodingcheshirecat]

One thing that had me messed up for so long...my ex was such a horrendous liar. If and when she was ever to say 'this statement is false.', you'd know she'd have been lying and it'd have still somehow worked out mathematically

[@ottoomen5076]

It appears to be a great self-study book. Not to equation dense. As I get to higher level math and engineering I really prefer a more modern book. Unfortunatly, they are quite expensive.

[@Tabu11211]

Just got my copy!!

[@patrosky13]

i just bought it!

[@abstractnonsense3253]

I wish I had enough time and patience to write something that is sorely missing in mathematics: an introductory survey of logic, model theory, set theory, computability, and proof theory. If you want to learn logic and its main fields you have to combine different books with different notations and conventions, with a lot of overlapping material. It's maddening.

[@NoobleeGt]

Then maybe you should help Jay by writing a book on another math topic, with the same spirit used in those 2 books 🤔 maybe complex analysis, or linear algebra (but strang already has a very nice and easy to understand book)

[@johnnichols6073]

How would you compare this to How To Prove It?

[@scottmandel6536]

I had a similar "purple crayon" experience in my first assembly language course. The professor insisted that we include lots of comments in our programs. For a bit shift command my comment was "multiply by 2." When I received the graded listing back this comment was circled in red ink with the phrase, "I can read!"

[@GrahamCrannell]

1:22 - fun fact, the dedication is a haiku, but only if you pronounce "entire" with three syllables as "en - tie - er"

[@sujayd1767]

well said sir why to write a book when we have one already. sir how about giving a thought on writing research papers instead of a book? just suggestion. on a side note: today i started proofs from discrete maths book and ytube recommended this, what a coincidence.

[@Furkan-yv5ew]

Even though i know how to prove things i still feel like a beginner. Because there are obviously some parts I don't know in that book. İ am not a beginner. I proved a lot of things in math by myself. I even tried to discover things by myself on the paper. There is a question that i thought about for like 5 years and still couldn't find an answer. And I am sure about all of them.

[@omarwest2430]

Great video as always. I was wondering, which book would you recommend for a complete beginner, this or Velleman's?

[@mr0market]

Only book I have seen on Amazon with 4.8 rating out of 711 reviews.

[@byronwilliams7977]

Just bought the book using your affiliate link. I may have missed it, but I don't see an affiliate link for the REAL ANALYSIS textbook ?

[@econhelp583]

How does this book compare to "How To Prove It" by Daniel Velleman? I am trying to figure out the optimal amount of time that should be spent studying deductive proof techniques by someone who uses math in an applied way (e.g. a scientist or an engineer). In the Velleman book, it is noted that deductive reasoning is the foundation of mathematical proofs. What I find interesting is that in my favourite math book of all time (the book was published in 1987), "Precalculus Mathematics in a Nutshell" by George F. Simmons, Prof. Simmons (Professor of Mathematics, Colorado College), downplays deductive reasoning. From pages 2-3 of Simmons, "Deductive Reasoning is an interesting idea...It was very popular among philosophers and scientists of the 17th century...Science shook off its grip 200 years ago, but geometry has continued to be strangled by this outmoded philosophical doctrine down to the present day." Prof. Simmons' book uses some very well-thought-out graphical proofs that I have found to be very very helpful. Any comments on this? Also, have you reviewed the book by Prof. Simmons? Lastly, I like your video, "All unicorns are good at math" (according to math logic), but I am unable to find this video when I search your channel. Is there an easy way to find it?

[@TheMathSorcerer]

Hmm I should check out that book by Simmons, thank you!! Here is the video you requested:) kzbin.info/www/bejne/rYK6hphooNKqe7M Both are very good books. I should make a video comparing them more carefully at some point!

[@econhelp583]

@@TheMathSorcerer Thanks for the link! Regarding the Simmons book, I am lucky to have a huge collection of math and stats books. I am more of a statistician (M.S. in Statistics) but I do like math a lot and over the years (I’m 58) I have had to look at a lot of math and stats books. I continue to marvel at the book by Simmons in particular. It is so short, and yet so clear and to the point. I would definitely appreciate a mathematician’s thoughts on this book. Thanks for your reply, and I greatly hope that you have the chance to review Prof. Simmons’ book sometime. Your KZbin content is great and very much appreciated!

[@Maths_3.1415]

Nice book sir I have just downloaded it's pdf :)

[@lamp2208]

What website did you use?

[@worldboy9684]

Awesome, getting it!

[@mellowtube]

Christmas gift to myself.

[@thomasmolina6698]

What background do you have to have to read the book first?

[@TheMathSorcerer]

In theory, no background other than some basic math. The more math you have the easier it will be to learn what is presented. There are examples from different areas of math so the more you know before hand the better, but you could in theory just jump into it and try it. It's a fun book:)

[@cokesucker9520]

I ordered this book over the weekend since I was finding proofs to be a limiting factor for my learning. It's encouraging to see so many people have good things to say about it, knowing that my money is well spent.

[@venkataaraadhya]

nice name :)

[@homamthewise6941]

A great vid as always

[@Anonymous-qw]

It is very reasonably priced for a higher mathematics book as well.

[@jimpim6454]

Strange the online copie are not as complete at the print ones. Does anyone have links to a complete online copy?

[@solides7541]

Seems amazing.

[@kanpurunplugged9970]

Mathematical Proof evidence is essential for new math learner

[@CD-dm7sf]

Excellent review

[@yehah]

After going through a few textbooks, many books state answers to a lot of exercises are omitted after the requests of instructors. Perhaps some teachers want the students to really think hard about solving a problem, even if they can't see the solutions?

[@freeman4899]

Please do review the book "The Art of Proof: Basic Training for Deeper Mathematics" by Matthias Beck, if possible .

[@CalBruin]

Looks like a good book.

[@salkinfamilychiropractic3142]

is this any better than the Vellemann book "How to Prove It: A Structured Approach, 2nd Edition"???

[@azimuth4850]

Really cool!

[@Carlos-qz7ul]

Amazing! 👌

[@AlephCasara]

Im starting a course in data science, but i have stopped studying math more than 10 years ago, but i never really dedicated myself, but know suddenly i feel desire to learn all the math i can, is this a goodbook for a complete noob? (I did calculus in college like 10 years ago)

[@declanfarber]

If you’re so inclined, this would be a good book to read if you’re transitioning from a math degree into law school. I’m absolutely not kidding.

[@ronaldjorgensen6839]

i think own it i know i used it for class's before