Where can I find mathematical book titles like this one?
82 karma · joined December 11, 2019
I would say this if this step was taking early while Kotlin is still a new language in the market, but I think their late decision to develop an official LSP for Kotlin is because of reasons you just mentioned, but maybe they changed their minds because they saw other benifits including a wide adoption of Kotlin.
So, knowing exactly the words being said is of utter importance.
In my case, I am currently learning Go at the moment. So, a learning session will contain at least one browser tab for the website I'm using, a window for VS Code, and a third browser tab in case I need to look something up.
What if it turned out to totally wrong? standing by it would just make thing even worse.
- Be an active reader. Open to the page you need to read, get out some paper and a pencil.
- If notation is defined, make sure you know what it means. Your pencil and paper should come in handy here.
- Look up the definitions of all words that you do not understand.
- Read the statement of the theorem, corollary, lemma, or example. Can you work through the details of the proof by yourself? Try. Even if it feels like you are making no progress, you are gaining a better understanding of what you need to do.
- Once you truly understand the statement of what is to be proven, you may still have trouble reading the proof—even someone’s well-written, clear, concise proof. Try to get the overall idea of what the author is doing, and then try (again) to prove it yourself.
- If a theorem is quoted in a proof and you don’t know what it is, look it up. Check that the hypotheses apply, and that the conclusion is what the author claims it is.
- Don’t expect to go quickly. You need to get the overall idea as well as the details. This takes time.
- If you are reading a fairly long proof, try doing it in bits.
- If you can’t figure out what the author is doing, try to (if appropriate) choose a more specific case and work through the argument for that specific case.
- Draw a picture, if appropriate.
- If you really can’t get it, do what comes naturally—put the book down and come back to it later.
- You might want to take this time to read similar proofs or some examples.
- After reading a theorem, see if you can restate it. Make sure you know what the theorem says, what it applies to, and what it does not apply to.
- After you read the proof, try to outline the technique and main idea the author used. Try to explain it to a willing listener. If you can’t do this without looking back at the proof, you probably didn’t fully understand the proof. Read it again.
- Can you prove anything else using a similar proof? Does the proof remind you of something else? -
- What are the limits of this proof? This theorem?
- If your teacher is following a book, read over the proofs before you go to class. You’ll be glad you did.
[1] Reading, Writing, and Proving: A Closer Look at Mathematics By Ulrich Daepp and Pamela Gorkin.
Here [1] you can find Sheldon Axler himself explaining the topics of the book in his YouTube channel! How wonderful is that!
Here [2] you can find the solutions to the exercises in the book.
[1] https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmS...
Linear Algebra Done Right is a text for beginners who want to study linear algebra in a proof based, mathematically rigorous way.
So, if you want that I think it's a good fit as a first linear algebra book.
This is an introduction written by the original author of the list:
"Somehow I became the canonical undergraduate source for bibliographical references, so I thought I would leave a list behind before I graduated. I list the books I have found useful in my wanderings through mathematics (in a few cases, those I found especially unuseful), and give short descriptions and comparisons within each category. I hope that this list may serve as a useful “road map” to other undergraduates picking their way through Eckhart Library. In the end, of course, you must explore on your own; but the list may save you a few days wasted reading books at the wrong level or with the wrong emphasis.
The list is biased in two senses. One, it is light on foundations and applied areas, and heavy (especially in the advanced section) on geometry and topology; this is a consequence of my interests. I welcome additions from people interested in other fields. Two, and more seriously, I am an honors-track student and the list reflects that. I don't list any “regular” analysis or algebra texts, for instance, because I really dislike the ones I've seen. If you are a 203 student looking for an alternative to the awful pink book (Marsden/Hoffman), you will find a few here; they are all much clearer, better books, but none are nearly as gentle. I know that banging one's head against a more difficult text is not a realistic option for most students in this position. On the other hand, reading mathematics can't be taught, and it has to be learned sometime. Maybe it's better to get used to frustration as a way of life sooner, rather than later. I don't know." - by original author.
Here [1] you can find Sheldon Axler himself explaining the topics of the book in his YouTube channel! How wonderful is that!
Here [2] you can find the solutions to the exercises in the book.
This [3] Lectures might help as well, among the books this course follow is Algebra Done Right.
Good luck learning the subject of Linear Algebra you'll have fun doing so.
[1] https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmS...
This will surely make you more appreciative of subjects and concepts you are learning.
History of mathematics will give you a very subtle entry into the minds of mathematicians and the motivation behind their theorems.
This will surely make you more appreciative of subjects and concepts you are learning.
This! learning materials who master this way of information giving based on their importance is key to effective learning, and I think a lot of them don't give importance to it.
So it's all about remembering, but what differs is how someone approaches it depending on their level and understanding of the topic they are trying to learn.