Reddit reviews How to Prove It: A Structured Approach
We found 9 Reddit comments about How to Prove It: A Structured Approach. Here are the top ones, ranked by their Reddit score.
Reddit reviews How to Prove It: A Structured ApproachWe found 9 Reddit comments about How to Prove It: A Structured Approach. Here are the top ones, ranked by their Reddit score.
I think because manipulating mathematical symbols algebraically would be a lot more cumbersome if they are too long. I think you'd benefit a lot from reading this book. It might open up a world obscured by mathematical notation.
You mentioned some issues that sound like code cleanliness and structural issues. Getting better at algorithms really comes down to practice and exposure, there's no shortcut to this. But there's no reason to suffer from bad coding practices if there's room to improve.
A few books come to mind, which may seem like they're coming from left field, and may not seem immediately useful to the task of solving algorithm puzzles, but might be useful in the long term for you to learn how to write correct, clean code and reduce uncertainty:
EDIT: One other thing is to make sure you understand the limitations of how computers represent numbers. The need for this understanding will become clear very quickly on, say, Project Euler problems. Look into bits, values, integers, signed vs unsigned, IEEE754 floating point.
And one other thing is that it's easy to compare your solutions against some of the best solutions that exist for those problems and think you're doing a bad job when in fact you're doing an alright job if you manage to solve the problems with decent runtimes. Mind your 80/20 rule here. The extra time it probably took those people to craft those solutions is not 0, which includes whatever time they spent over the years becoming an expert at that language, etc.
I would highly suggest How to Prove it. It's a book that teaches you to think logically about problems and (inevitably) also teaches you a lot about logic. I read it as a freshman coming into an undergrad as a math major and it was super helpful.
Have seen a lot of peoplr praise this book. Bought it myself but didn’t have the time yet to to sit down and actually solve the problems. Link: https://www.amazon.com/How-Prove-Structured-Daniel-Velleman-ebook/dp/B009XBOBL6
I would say that it's difficult for most students. Getting an A is certainly not impossible, but it is going to take a lot of work. I took it with Truman and I sat in on some of Manning's office hours so I can only really speak to those two professors.
If you've never seen proofs before, then I would suggest getting an introductory textbook and working out of it over the summer. A really good one that I recommend is How to Prove It by Daniel Velleman. Since 310 is an introductory course, you don't necessarily need to be familiar with proofs beforehand. But it will definitely make the transition much easier. Even a basic understanding of elementary logic and basic proof strategies will be helpful. The book I recommended goes at a much slower pace than I think is warranted, but it can be very helpful nonetheless.
If you have experience writing proofs, then the transition into the class shouldn't be too bad. But be warned that the class may be more rigorous than you're used to. If you've taken a class like CMSC250, you should keep in mind that my opinion, as well as that of everyone I know who's taken both classes, is that MATH310 requires much more time and patience.
Kate is an awesome professor. She does a good job of conveying the material and she makes expectations very clear. The homeworks are definitely on the long side and I often found myself using other resources, both online and from textbooks, to get an intuition for how to solve problems. With that said, the exams were easier than the homework assignments. That's not to say that the exams were easy, just easier than other assignments.
While I can't speak to how good Dr. Manning is as an educator, I can say that, without a doubt, his exams were much more difficult. I got a glimpse of one of his midterms and I tried to use his finals from the testbank to practice for our own final. It always seemed that his problems were a step up in difficulty from Kate's.
All I know about Dr. Williams and Dr. Halperin is what is readily accessible from the usual sources.
That is what I thought you'd say.
...teach a bitizen to fish and you feed him for life.
Hey mate, if you're still looking for introductory logic books, I just came across a book which looks great for that. It looks like an introduction to thinking about mathematical proofs, and introduces basic logic and set theory to do so. I'm sure I've covered all the material in the book in courses I've taken and other books I've read already, but I'm tempted to get it anyway because it looks great!
+1.
OP: You might also want to brush up on your proof skills, in case they're rusty. How to Prove It: A Structured Approach by Velleman is a good place to start.
Oh, I'm terrible at calculus, haha. I teach discrete maths and logic, and never have to touch calculus at all, thank goodness :)
But a younger friend of mine is doing calculus just now, so I'll find out what he found useful and PM you. He did say that some of the books I'd recommended him were immensely useful for maths generally (not necessarily calculus in particular). In roughly ascending order of difficulty:
So you could pick one of those, and see if it meets the level you're after. There are also some standard books on "how to write proofs" which often get recommended: Velleman, How to Prove It: A Structured Approach <https://www.amazon.com/How-Prove-Structured-Daniel-Velleman-ebook/dp/B009XBOBL6&gt;, and
Solow, How to Read and Do Proofs: An Introduction to Mathematical Thought Processes <https://www.amazon.com/How-Read-Proofs-Introduction-Mathematical/dp/1118164024&gt;, and they might be useful. I've never read either, shamefully, tho I probably should.
Also: something that can be handy once you're past the basics is the amazing (but large and expensive) Princeton Companion to Mathematics. Which has something useful and interesting to say about pretty much every major area of modern mathematics.
I hope that helps!