{"product":{"product_id":"0521675995","title":"How to Prove It: A Structured Approach, 2nd Edition","price":"26.01","image_url":"https://m.media-amazon.com/images/I/417vp8AYizL._SL500_.jpg","url":"https://www.amazon.com/dp/0521675995"},"comments":[{"body":"I'm 33 and I did not learn coding in school either. \r\n\r\n[*How to Prove It: A Structured Approach, 2nd Edition*](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995) by Daniel Velleman, is *very* good. He does reference computer coding, but no background in coding or proofing is required. Literally anyone can pick it up and get started.","subreddit_name":"learnmath","author":"ListenHereDumbass"},{"body":"I would recommend the book \"How To Prove It\". \r\n\r\nhttps://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995\r\n\r\nIt helped me in my transition into proof based mathematics. It will teach common techniques used in proofs and provides a bunch of practice problems as well.","subreddit_name":"learnmath","author":"spihms46"},{"body":"220 - do all your projects early and don't cheat. this class will teach you how to really \"program\". start the programs early and you will be fine.\r\n\r\n250 - i recommend this book: http://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995\r\n\r\nthis book is pretty good when combined with barrington's \"teaching\" style. this book doesn't have all the topics covered, but if you find yourself struggling to understand concepts i recommend ordering this book (or find a PDF online of it) and just work through every practice problem you can. answers for a bunch are in the back. i think this book does a better job explaining conceptually what everything means in the class.\r\n\r\ngood luck!","subreddit_name":"umass","author":"itsgreater9000"},{"body":"The common metaphor is like a sequence of dominoes.\r\n\r\nIf \r\n\r\n(1) You line up all the dominoes so that each one would knock over the next one\r\n\r\nand\r\n\r\n(2) You knock over the first one\r\n\r\nThen they will all fall.\r\n\r\nThe first one will fall because you knocked it over (2). \r\n\r\nThe second one will fall because you knocked the first one over (2), and because the first one will knock over the second one (1). \r\n\r\nThe third one will fall because you knocked over the first one (2), and because the first one will knock over the second one (1), and because the second one will knock over the third one (1).\r\n\r\nMathematically, if you want to prove some statement about every number, say greater than or equal to 0, then you have to prove it about 0 and about 1 and about 2, and so on.\r\n\r\nSo what you do is you prove that if a statement about each number is true then the statement about the next number is true (1)\r\n\r\nAnd that the statement about zero is true (2).\r\n\r\nThen you've proved the statement about all numbers.\r\n\r\nYou've proved it about 0 from (2)\r\n\r\nAnd you've proved it about 1 because you've proved it about 0 from (2) and because you've proved that if you've proved it about 0 then you've proved it about 1 from (1).\r\n\r\nAnd you've proved it about 2 because you've proved it about 0 from (2) and because you've proved that if you proved it about 0 then you've proved it about 1 from (1), and you've proved that if you proved it about 1 then you've proved it about 2 from (1), \r\n\r\nand so on.\r\n\r\nFor a text, I recommend [Velleman](http://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995)","subreddit_name":"math","author":"skaldskaparmal"},{"body":"I was literally in the same boat as you. Started at a community college, with the intent on going into engineering, and went into engineering having picked up math along the way. Ended up liking math a lot more than engineering, yet finished undergrad with both. Now, currently doing a PhD in pure math. \r\n\r\nOne book I’d recommend is [How to Prove It](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/ref=nodl_). Accessible, yet definitely not easy. It really shows you what mathematics truly is. Definitely is a stepping stone into the world of mathematics, yet doesn’t require much background math.","subreddit_name":"math","author":"AccomplishedTour9370"},{"body":"Of course, no worries! \r\n\r\nIf you don’t mind suggestions, I highly recommend [How to Prove It](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/ref=nodl_) as a book to use when you want to learn proofs. I, along with many others, find this book to be very accessible (compared to other intro to proof writing books) and it also doesn’t rely on too much foundational math (e.g. you can probably read most of this without having taken calculus at all…from what I recall). \r\n\r\nAnd yes, I agree that you shouldn’t rush things. Although don’t be too worried if you don’t understand 100% of the things you learn, especially the first time around. I think if you feel like you understand most things, you can move on to the next subject/topic and if you need, you can always come back to it later. Good luck and don’t forget to enjoy!","subreddit_name":"math","author":"AccomplishedTour9370"},{"body":"Get used to proof based mathematics. [How to Prove It: A Structured Approach](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995), by Daniel J. Velleman, would be a great start.\r\n\r\nEDIT: Ok math that's useful for a STEM major, maybe forget about the proof based math unless you're considering mathematical physics. It's still a good book though.","subreddit_name":"math","author":"the_shape89"},{"body":"You don't need linear algebra for a first class in calculus, but you will need it eventually if you want to move on to multivariable or differential equations.\r\n\r\nSome ideas from linear algebra/calculus can be helpful in the other, but it's not necessary. You'll eventually see that a derivative (a key idea from calculus) is an example of a linear function (the center piece of linear algebra). \r\n\r\nProof based vs applicable comes down to your own goals. If you want to get deeper into math, you'll need to learn it with proofs. If all you want to do is something like physics, you might never need to see the proofs. A course with proofs would definitely be harder (especially since it's your first time), but you'd learn more.\r\n\r\nThat would count as algebra. Spivak essentially builds calculus from scratch, and you need significant amounts of regular high school algebra to do calculus. The first few chapters essentially go through proving all the algebra you'll need for the actual calculus. If you have a hard time with this, consider a book like [this](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995).\r\n\r\nMost people do differential and integral calculus at the same time. I don't know much about any books besides Spivak and Apostol, the standard proof-based introductions.\r\n","subreddit_name":"math","author":"namesarenotimportant"},{"body":"I also tried to learn calculus through spivak and found it very difficult; I stopped at then 4th chapter and switched to an easier textbook. If it's your first time learning calculus choosing an easier and verbose text like Stewart may suite you better. It's important to remember Spivak's Calculus is more like a textbook on Analysis (the theory of calculus), which is what often comes junior or senior year for math majors/minors.\r\n\r\nIf you have already learned calculus I'd suggest the book[How to Prove It](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995) which helps think of math in a more concrete way that can help with proofs, even though no calculus is presented. Also, remember that Spivak likely didn't intend for people to find his questions easy, so don't feel like you are unprepared if it takes a while to do a single question.\r\n\r\n","subreddit_name":"learnmath","author":"Zusunic"},{"body":"If you happen to have the UCLA edition of Friedberg's Linear Algebra (the one you'll likely use for 115A) already, there's a section at the end with an intro to proofs. [This book](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995) is pretty popular at universities with a dedicated intro to proofs class, so it might be worth checking out; I read a bit of it before taking the upper divs. Hope that helps!","subreddit_name":"ucla","author":"Zaculus"},{"body":"Advanced math is subjective. Discrete math is a lot of topics mixed together into one class. A little bit of logic, graph theory, set theory, number theory, modular arithmetic, combinatorics, introduction to proofs, algorithm analysis and some other stuff I might be missing. The only prerequisite for it is pre-calculus. The difficulty of the class is subjective some people find it hard and some people find it easy. If you can remember definitions and theorems and string them together to construct a proof you should be fine. [How to prove it](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995) is recommended a lot as an intro to writing proofs.","subreddit_name":"learnprogramming","author":"ordnance1987"},{"body":"Don't worry, a lot of people are struggling as noted above. The class average was 70% so it's very likely that half the class did worse than that. Also, don't forget 20% of the grade is from the online quizzes.\r\n\r\nI was in a similar position when I took Math 347. Between Math 347 and CS 173 I found this book [*How to Prove It: A Structured Approach*](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/ref=sr_1_1?ie=UTF8\u0026amp;qid=1476336548\u0026amp;sr=8-1\u0026amp;keywords=how+to+prove+it) by Daniel J. Velleman.  I'm not one to use hyperbole but the book is nothing short of phenomenal. The book might not cover specific topics but it does cover all of the basics of proof writing in detail and in way designed for novices. From basic logic to induction the book covers just about every technique required for an intro proof class. It also happens to be relatively inexpensive. You can check the reviews online if you don't believe me (or even ask your math major friends).","subreddit_name":"UIUC","author":"topretype"},{"body":"Oh man 2011 was probably the hardest MATA31 revision. Don't worry, about that midterm though, the course content is really different now, that was when CSC/MATA67 used to be merged with MATA31, so they did a lot more set theory/number theory in MATA31 than they do now. I doubt most people who took MATA31 (and did well) could even pass that midterm just because we don't learn that stuff in MATA31 anymore. If you're trying to get started on studying for MATA31 now, I actually recommend you don't learn MATA31 material. Instead, improve on your critical thinking skills which your high school has definitely not given you. \"Find\" a book called [how to prove it](https://www.amazon.ca/How-Prove-Structured-Daniel-Velleman/dp/0521675995) and go through maybe the first two or so chapters which just introduce proofs, and start to build up your proof skills. Becoming comfortable with proofs will come in handy immensely for CSCA67, MATA37, and in a big chunk of MATA31.","subreddit_name":"UofT","author":"Fakesantaclaus"},{"body":"I'm self-studying BR right now (working the exercises for Ch 6) with great success. As others have said, definitely make sure you are comfortable understanding and writing proofs because you will be doing a lot of that. If you're not there yet I recommend working through [How to Prove It](http://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/ref=sr_1_1?ie=UTF8\u0026amp;qid=1463508384\u0026amp;sr=8-1\u0026amp;keywords=how+to+prove), which you are most definitely prepared for based on what you have already studied. If and when you do end up trying to tackle BR stop by /r/babyrudin or feel free to PM me if you have any questions, I'd be happy to help. I'm also happy to help with HTPI if you decide to go that route instead.","subreddit_name":"math","author":"kyp44"},{"body":"Yes, I would make sure you are really comfortable with proofs before tackling Rudin. If you're not that comfortable you might check out [How to Prove It](http://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/ref=sr_1_1?ie=UTF8\u0026amp;qid=1458574380\u0026amp;sr=8-1\u0026amp;keywords=how+to+prove+it). If you think you are comfortable enough and want to try Rudin stop by /r/babyrudin. It's a group of us who are self-studying it. We're generally all at different points in the book but feel free to post any questions you might have once you get started.","subreddit_name":"math","author":"kyp44"}]}