Learn Math Proofs with this FREE Book

In this video I go over a book that you can use to teach yourself how to write mathematical proofs. Several people have left very positive comments about this book and I agree with them, it's a great book! This book is available for FREE in pdf version. You can also purchase softcover and even hardcover versions of this book. The book is called "Book of Proof" and it was written by Richard Hammack.
Here is the book on amazon: amzn.to/3Np7Orc
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Here is the free pdf version: www.people.vcu.edu/~rhammack/...
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Thank you:)

[@donaldmickunas8552]

I haven't even finished your video. I downloaded the pdf, saved it, then opened it to chapter one, sets. The first paragraph caught my attention immediately: "All of mathematics can be described with sets." Here is the core of all mathematics, the very foundation if you will. That caused me to read and consider what followed. Each part is an essential term and definition. I started playing with it. This is the first math book that I am going to study. I can relate to it and it will help form the foundation of my study of mathematics. I am stoked!! This is the same sense of discovery I've gotten in my study of computer software and scripting. This is going to be FUN!! Yes, yes, it is going to be hard BUT fun anyway. It will exercise my brain and make me think deeply.

[@tmann986]

I really wanted to support this author and i bought a hard copy. I hope i can teach myself this side of mathematics. I’m an engineering major but its always the math that gets me going. My friends think im weird haha

[@tmann986]

I thought i was good at math by passing calc 2 and when i first encountered proofs, i realized how little i know about math. Thank you for this opportunity to develop this skill of proof writing!

[@numericalcode]

This book is very readable for beginners. You don’t get lost because his examples are extremely detailed.

[@gamershideout89-ke2vn]

Thanks. Will check it out.

[@gamershideout89-ke2vn]

@numericalcode at the second thought, it seems to me that we need to have a basic understanding of maths first. This book is actually for intermediate level.

[@Carlos-qz7ul]

I cannot thank you enough for having shared your accessible view of the mathematics world, and for having shown how mathematicians are very often the 😎 coolest of guys, and also what mathematics has to offer to human thinking, in a plain, non pretentious way ! 🙏

[@phillair3813]

I also looked before you finished your video. I'm so impressed that I feel I'll be devoting my time to read and finish this book (PDF). Quick story: many many years ago I tried and failed integral calculus in college but actually ended up with an A when I took it one more time with a teacher who could teach- a school marm type who insisted that we students draw, derive, and practice. She was clear and precise in lecture with never a gap in logic, and gave us a full spectrum of difficult problems to practice on. This book looks to be of the same philosophy. I'm 80 y/o now and this is exciting to see. Thank you. If you know of a mathematical ecology book with this level of teaching, I would very much appreciate knowing about it

[@raghurajaram8817]

I fucking love this channel coming from a family of computer science students my pops and uncles always told me graduate mathematics was the only coursework more difficult...and that cs was noyhing compared to their math classes...im glad we got a guy like u leading the way man lol keep it up

[@TheMathSorcerer]

thanks man!

[@solarwinds5114]

My intro to proof class used this exact book, definitely was well written and laid out. Helps make the learning curve less steep

[@Anamaria-ts6bf]

Man I just saw the pdf version and I am in love. I can't explain how grateful I am. I am in the last grade of school and I love math, I am sure this will be so helpful in my university exams.

[@islomkayumov4552]

This book helped me fill some gaps in my knowledge. It is great that it has proofs in calculus section. I am a first-year math student and i had difficulty grasping delta- epsilone proofs. This book has been a great help to learn math.

[@rezamostafid8810]

Math Sorcerer: Many years ago I decided that I needed to understand/learn writing and reading proofs ( ...to advance my mathematical ability ). I came across Velleman, Chartrand et al. as well as Ethan Bloch's book. Then, a few years ago I stumbled on this book on the internet. I must say that in my >very< humble opinion I felt that this book was about the same level as Chartrand's BUT the `flow` was a LOT smoother....it was like the reader was being spoon-fed ( ...at times ). One thing I noticed back then was (...as far as I can recollect ) that there was no section on Calculus proofs back then. In your video you go through the section on Calculus proofs from `The Book of Proof`....Wow!! beautifully done with a lot of detail...Richard Hammack style! Thank You Math Sorcerer!.....for this review and for the many other good videos and advice I have received from you ( ...sure everyone else is on agreement with this as well )

[@whitneyeaton5585]

thank you, this is cool. I appreciate your videos and the way you present ideas and deliver things like this. i really like you math book reviews.

[@jurrytaalib-deen7146]

I just finished this book for my Foundations of Math course. I used this alongside A Transition of Mathematics. I think he does a really good job of explaining the problems. It truly is beginner friendly.

[@daniellejdevlin8882]

Thank you so much for this video!

[@ohjoshrules]

Thank you for this review! Something I will read.

[@alexbedoian]

Started my first proofs class last week, so glad I stumbled upon this because I was having a pretty tough time grasping what was going on. Read the first chapter via PDF and had to buy it because this book shouldn't be free. Good book!

[@RunstarHomer]

This book is phenomenal. Very clear, and an excellent introduction to a formal style of mathematical writing. There are actually exercises for each individual section most of the time, not just the chapter as a whole. Chapter 4 just happens to be very short and so just has one group of exercises at the end. Worth noting that some (only a few) of the solutions in the back are not actually full solutions, but hints.

[@andrewsmith5074]

Definitely one of the most complete, well written books on introducing higher mathematics!

[@Taylor-rx4yb]

That's a great book! It's the one that I started learning about proofs from

[@TheMathSorcerer]

awesome!

[@MrCliverlong]

Agree. This is a clear, thorough book. Amazing it is available to download for free.

[@RandomNPC-sy6gj]

Thanks. I printed of the pdf in booklet format, cut and bound with fasteners so now I can read Hammack while in my hammock.

[@WaelAjam]

I am really grateful to Mr. Hammack, his book helped me so much. Thanks to you for highlighting this book.

[@sahaskarunarathne1333]

Wow! Thank you very much, the Maths Sorcerer. This will be very useful in my studies :)

[@tmendoza6]

hey that is an excellent idea! selecting an advanced math book and reading it as you see it in a live stream or recorded. The first impressions you have of the proofs would be priceless!

[@TheMathSorcerer]

That's a great idea! Yes!!!!

[@TheMathSorcerer]

thank you:)

[@martinhawrylkiewicz2025]

Thanks so much for this great info! I downloaded the free pdf version and printed out the first two chapters (set theory and logic) and bounded together into a little book for self study.

[@karlaquino7441]

Wow, just in time for my discrete math class. Thanks!

[@WitchidWitchid]

I saw a bound copy of this for sale and was thinking of buying it. But as I was scouring round online II came across the free pdf version so I downloaded it today. Although I am quite familiar with reading and understanding many proofs, as well as writing many proofs, I still want to give this book a full read. In fact I'm going to get busy on reading it right away. As far as free math books go there are so many great free math books out there.

[@lorensims4846]

Thanks! I really enjoyed geometric proofs in high school. I hoping these can help me understand some of that math I never bothered to learn since then.

[@JohnRaschedian]

This seems to be a great book! Thank you!

[@davidwoznerable6750]

I have always recommended this book! It's awesome.

[@NNKNTA]

Thank you for your videos!

[@TALKmd]

This is absolutely great book!

[@angel8fingers]

Super excited!!!

[@TheMathSorcerer]

:)

[@tGoldenPhoenix]

Thank you.

[@robertvarner9519]

Thanks for the link.

[@TheLokomente]

Thank you, sir.

[@HomeBologn]

This is very well written, unpretentious, and downright exciting. Thank you for this video, Sorcerer.

[@HomeBologn]

Btw, I finished ODE and my AAS in Math. I made an A in ODE. It’s not easy, but it’s possible. Hard to learn, and, I imagine, extremely difficult to teach.

[@ipodtouch470]

@@HomeBologn Ordinary Differential equations is very hard to teach I assume. I’m very glad my class was engineering oriented, we were giving real life word problems and then had to model the problem using differential equations. Then we could use any tools to solve the differential equations or if that wasn’t possible use approximations/visual techniques. Of course though we had to write a report to go along with the solution 😂

[@cosmicgaussian1881]

This is awesome, thanks

[@TheMathSorcerer]

:)

[@greatloverofmusic1]

There are a lot of good options to choose from, such as: Mathematical Proofs...Chartrand, How to Solve It... Polya (though it's not for me a lot of older math students swear buy it), Calculus...Spivak (motivates proof through a topic every math geek can appreciate though the homework problems can be brutal), the same could be said, more or less, about Calculus...Apostol and my favorite Discrete math book, Discrete Math...Epps. My two cents. What do you folks think? Cheers.

[@mouhammadshahrezaie6174]

thnk you my teacher

[@cubic-h6041]

Love this book.

[@aperson9375]

Wow ordered on Amazon...❤️

[@martinhawrylkiewicz2025]

Love this book after watching your vid reccomendation. After finishing it, I started a new book How to Prove It by Daniel Velleman. Its really wonderful. Studying it every day.

[@noahpinel]

My proof writing course at school uses this book!

[@Shashank_Shahi1989]

Thank you for your videos. I just wanted to know "How to read & understand the depth of mathematics formula" so that we can understand any mathematics formula & equation and solve it without any hesitation. Thank you 👍

[@renemendy8912]

Thank you

[@StrikerLeKing]

Can you do videos about tensors ?

[@Rumeel12708]

Just got mine!!!!

[@harkonen1000000]

Your PDF reader should let you navigate through the whole book by sections, if you haven't noticed that function yet, you should find it. Also, I sometimes find inverting the colors to be easier on the eyes, but not every PDF reader may have that, or have that feature as very convenient.

[@howmathematicianscreatemat9226]

Problem 7 can even be done WITHOUT the square function: Let ka= b (k € IN) b^2 = kaka=k^2a^2 = la^2 (l€ IN). q.e.d. But I agree, we are essentially still the same proof. Different way would be via prime factorization

[@tedjerin2966]

U should livestream this content!!

[@franciscogerardohernandezr4788]

What do you think of using proofs and Montecarlo simulations together to show your system equations hold?

[@navierstokes2356]

What do you think about Judson's book on abstract algebra? Also is free

[@Jonathan-wo6kf]

How would you compare this book to the two intro to proof books shown in your Learn Math From Start to Finish video?

[@davebordenkircher8131]

Heyyy, the author is a professor at my school, Virginia Commonwealth University. Very cool to see.

[@jayantachoudhury4397]

Is it ok to go through abstract algebra before linear algebra?

[@armandolara8210]

How does this book compare to Cummings’ proof book?

[@renatohugoviloriagonzalez4881]

Muy valiosa información para facilitar el Aprendizaje bajo el gran Enfoque of The Math Sorcerer, Gracias por ayudar. El Secreto de Facilitar el Aprendizaje-

[@satyamparija7614]

Wow,, i love books which is free. Anyhow , i i have the calc. Book written by serge lang, will read it together. Thankyou the maths sorcerer,♾️♾️♾️♾️

[@paperstars9078]

which of the math sorcerer courses deals with measure theory and proofs about the lebesgue integral using measure theory? My prof decided he wants to use the lesbegue integral over the rieman integral, and I am kind of lost at the moment.

[@shimadabr]

Do you have an opinion on Solow's "How to Read and Do Proofs" and Velleman's "How to Prove It"? I wonder how they compare with this one and against each other.

[@kenmeyer100]

I love this book. Worked through the first edition, right when it was published. Even though it had been offered as a free pdf, I bought the paperback as well

[@cobe-2012]

I have a question do you know any books that gives a proof of logic

[@Poopmeiser]

Vcu most slept on math department

[@Yensu.Gaming]

@The Math Sorcerer - I am a very logical an analytical person and once upon a time I considered myself good at math. By that I mean in high school as compared to other students, because I never studied but passed all my math classes easily. However. I have learned bad habits and things in my passiveness. I am interested in re-learning math from the ground up. Where would you recommend I start? What resources are available? For those that recommend Khan Academy - let me just say right now I don't like that site. So, please provide alternatives.

[@acdude5266]

We used Fletcher and Patty, "Introduction to Higher Mathematics" for Math 300. But, I will download this book.

[@TheMathSorcerer]

I will check it out, thank you!

[@anilsowri4466]

Where can i get solutions of this book?

[@gamershideout89-ke2vn]

Non-math student here. Can I apply this maths into trading? Forex, gold, etc.

[@VinodKumar-wt3nt]

Brother make some review of physics book also 👍👍 Love from India❤️❤️❤️❤️❤️

[@romansynovle990]

What do you do if you have no way to prove what question youre not sure of…like, i can see the answers, but i dont know which questions they are linked to?

[@dhickey5919]

I was wondering why you haven't written your own math book. It will be awesome and everyone will buy it.

[@TheMathSorcerer]

I know, I should do it:)

[@Aba-ic9ge]

Free books are great specially if you are in a place where finding used books is not easy. I usaually use the open textbook library to find free books. They have very good reviews. Also the American institute of mathematics has a page of free approved maths textbooks but I tend to prefer the open textbook library. They have more books. Links are in first comment if anybody wants.

[@ClearOutSamskaras]

When you know how to write proofs, you have a type of skill. In the world of working in industry (not in academia) where in industry would proof writing be a skill that one would need and an employer would want from employees? I've heard that computer programmers sometimes want to do something but that something needs to be checked by a mathematician to see if the something as a desired idea is practically/mathematically possible, is this true? This has never seemed a believable claim to me, since I imagine computer programmers learn enough math to do their own checks on the mathematical plausibility of a desired something.

[@mastershooter64]

I'm a self-learner and I try to do lots of exercises in the book I'm using, but since I'm not university student yet i dont have someone to correct my mistakes and see if my solutions the exercises are correct. So what do I do in order to check my solutions to the exercises when i dont have access to a professor or a solutions manual?

[@mastershooter64]

@jhulian they're not computation problems, they're all undergrad math proofs lol pure math is all about proofs

[@pinedelgado4743]

Hey! I've already got a copy of that book. LOL!! I bought it online. ;) ;)

[@TheMathSorcerer]

So cool!

[@Lucretia9000]

Why do they always provide solutions to odd numbers only?

[@filthyrevenant619]

I have that textbook as the introduction to proofs. Unfortunately, the professor who uses said textbook makes the problems become curveballs in his quizzes, and I loathe that kind of learning. Doesn't help I am forced to solve them in under 12 minutes.

[@aikidograndmaster1781]

This is a good book , I have a physical copy .A big problem with this book is that the chapter on the Cardinality of sets does not develop enough math , so that the average student can actually do the exercises. It is the only part of the book that does develop some heavy machinery, but does not do a good job . He should have given more worked out examples in that Chapter..

[@RunstarHomer]

I don't know if I agree. It's been a few years since I read this book, but I was basically an absolute beginner, only having taken math classes in high school up through AP Calculus. The concepts of an injection, surjection, and bijection are explained prior to the chapter on cardinality, and the bulk of the cardinality chapter is dedicated to how to find a bijection, or prove that one doesn't exist. I don't think I felt like anything was missing when I did the exercises. I remember having a lot more trouble with the limit proofs and induction.

[@ivolva]

The PDF of this book is apparently a very good quality. You can navigate from table of contents to any page even on iPad.

[@chickenstrangler3826]

Have you seen books by Hung-Hsi Wu? -Understanding numbers in elementary school mathematics -pre-algebra -algebra

[@TheMathSorcerer]

I have not, I should check them out!

[@tastytesty]

Hello Mr. Sorcerer, I am currently taking Calculus courses, and planning to take Linear Algebra after Calc, should I learn proofs as a pre-req for Linear Algebra? And is it possible to take Linear Algebra after Calc1?

[@TheMathSorcerer]

It’s up to you if you should learn proofs before linear algebra, you could do a lot without proofs. I think it is always good to work on proofs. They can be very fun once you learn how to prove things. There is a certain elegance to it IMO❤️

[@TheMathSorcerer]

Sure you can take it after calc 1👍

[@tastytesty]

@@TheMathSorcerer thank you for your reply, really like your Calc courses on Udemy by the way.

[@user-be6xq6jy1c]

Is this book all about the mathematical logic? This is what I’ve been interested in, but if so, I would skip this because I learned a bit about the logic

[@albale94]

Really interesting! What do you think about the book "How to prove It: a structured approach" by Daniel J Velleman?

[@TheMathSorcerer]

I will check it out!

[@darkokrljar8101]

The best book for learning proofs! I've done 5 chapters so far, and I've done all the exercises! Proper amount of rigor and conversational style.

[@ass09tube]

Daniel J Velleman was editor to American Mathematical Monthly in the previous decade. He didn't publish much during then. He surely knows how to construct proof and interesting way of expressing them. Very different from intimidating style of Hungarian math style of Rudin n others.

[@michaelovadiyah659]

I’ve taken discrete math twice, I didn’t fail but my school requires a C or better. I still can’t fully understand what proofs are supposed to be.

[@gmmr9847]

Hello, I have a question for you based on an exam I recently took. Let's say we have a function like x+ln(x^2-15) and the derivative is 1+2x/(x^2-15). Can the domain of the derivative include parts that are not included in the original function? Because the original function has domain x>sqrt15 and x

[@HomeBologn]

The Cee Lo theorems are Crazy. ;)

[@timothycontreras3799]

When you write your own proof and compare it to the proof in the key. How do you know the process of your proof is correct?

[@christophermball]

For self-study cases, posting to math forums for occasional confirmation is probably ideal if you aren't convinced by your own proof. That's what I plan to do anyhow :).

[@xriz1211]

A while ago I found this book at the airport while waiting to board . The math gods were trying to tell me something.

[@charlessmyth]

With my eyesight, pdf works a lot better for me :-)

[@renatohugoviloriagonzalez4881]

What counts the Motivational Approach, que el Matemático Hechicero knows.

[@darkokrljar8101]

You should do a review on: How to prove it A Structured Approach, by D. Velleman. One of the best books for learning how to do proofs! Much better then this one IMO...

[@TheMathSorcerer]

will do, thank you!!

[@anubhabbhattacharjee476]

I really like to read from books, it is hard to read from pdf everytime I got distracted. But the price of these books are so high so now I print these books it is less cheaper now! 😂

[@romansynovle990]

🌀

[@Simon-xi8tb]

I'm confused, why wasn't i subscribed to your channel already??

[@Nathan00at78Uuiu]

Give it a whiff. Ahhh that digital scent.

[@Goldtiger927]

''American Institute of Mathematics' Open Textbook Initiative'' Nice.

[@lisareed5669]

Gonna need a bigger box of pencils.

[@AndersBjornTH]

The author certainly has a love affair with LaTeX. :-)

[@jennifertate4397]

Hi Math Sorcerer. Roughly what percentage of proofs out there, have more than one way to be proven?➕➖➗

[@howmathematicianscreatemat9226]

That’s incredibly hard to answer. We need to make case distinctions to answer this: in beginner proofs like in the book, every second task will have at least two ways to do it. More advanced tasks in multidimensional calculus will sometimes have even more than 10 proofs. That’s one of the true beauty facts of maths. 😊

[@user-di6bm3pw8v]

Thank you.

[@user-di6bm3pw8v]

Math is the Universe language.