|
@@ -0,0 +1,108 @@
|
|
|
|
|
+# Reading Maths Books
|
|
|
|
|
+
|
|
|
|
|
+## Finding Texts for Study
|
|
|
|
|
+
|
|
|
|
|
+You start first with a topic you want to learn about. Then you
|
|
|
|
|
+research texts to study from. Broadly speaking, they are:
|
|
|
|
|
+
|
|
|
|
|
+* Easy-reading high school books. Good if you are very short on
|
|
|
|
|
+ time.
|
|
|
|
|
+* Undergrad textbooks, such as Springer undergraduate books. They
|
|
|
|
|
+ are a good intro to a subject, or if studying an advanced book
|
|
|
|
|
+ then you will want one or two of these as supplementary material
|
|
|
|
|
+ for understanding difficult concepts.
|
|
|
|
|
+* Graduate level books usually are the best but require a lot of
|
|
|
|
|
+ effort put in. Concepts and questions will need to be looked up
|
|
|
|
|
+ and cross referenced with other materials.
|
|
|
|
|
+ Examples include the yellow Springer books.
|
|
|
|
|
+
|
|
|
|
|
+
|
|
|
|
|
+
|
|
|
|
|
+Usually you will follow one main text on a topic, but with a few other
|
|
|
|
|
+supplementary books as backup. Often you get stuck on a concept in the
|
|
|
|
|
+main text, and the supplement books will assist you to make sense by
|
|
|
|
|
+looking at things from a different explanation. Re-phrasing the same idea
|
|
|
|
|
+using different words can make a big difference in dicephering some
|
|
|
|
|
+theorem or object.
|
|
|
|
|
+
|
|
|
|
|
+## Video Courses
|
|
|
|
|
+
|
|
|
|
|
+There are many high quality online courses following important texts.
|
|
|
|
|
+They explain the main core forums, focusing your attention on the key ideas
|
|
|
|
|
+and explaining things in an intuitive non-formal manner.
|
|
|
|
|
+
|
|
|
|
|
+Favourites:
|
|
|
|
|
+
|
|
|
|
|
+* [Elliptic Curves by Alvaro Lorenzo](https://alozano.clas.uconn.edu/math5020-elliptic-curves/#).
|
|
|
|
|
+ This course uses the Springer book on Elliptic Curves by Silverman.
|
|
|
|
|
+* Harpreet Bedi
|
|
|
|
|
+* Zvi Rosen
|
|
|
|
|
+* Boucherds
|
|
|
|
|
+
|
|
|
|
|
+## Getting Excited, Taking a High Level View
|
|
|
|
|
+
|
|
|
|
|
+Take a look at the contents. Familiarize yourself with the structure of the book.
|
|
|
|
|
+Make note of topics that you will learn and master. Get excited about the truths
|
|
|
|
|
+that you will unlock. You will come back here every periodically to remember why
|
|
|
|
|
+you are studying and where you are going.
|
|
|
|
|
+
|
|
|
|
|
+Make a lesson plan. Often the first chapter of a new topic is important, but if
|
|
|
|
|
+you're already familiar then maybe you can jump to advanced material.
|
|
|
|
|
+
|
|
|
|
|
+Be aware if you struggle too much at the advanced level, and make no progress at
|
|
|
|
|
+all then it's a signal to swallow your pride, be humble and go down to a lower level
|
|
|
|
|
+before moving up again. We take shots, but sometimes we have to take a few steps
|
|
|
|
|
+back. The tortoise beats the hare.
|
|
|
|
|
+
|
|
|
|
|
+However you must struggle. Don't be a weakling. Fight to rise up. Give it your
|
|
|
|
|
+focus, dedication and attention. Get into the zone, or [rausch](https://youtu.be/BTXj6ZEANFg?t=443).
|
|
|
|
|
+You evolve because it is hard.
|
|
|
|
|
+
|
|
|
|
|
+## Reading the Chapter
|
|
|
|
|
+
|
|
|
|
|
+Now you've chosen your chapter. Do a light first-pass read through it. Focus not
|
|
|
|
|
+on the details but the main theorems and structure of what you're learning.
|
|
|
|
|
+Try to understand from a conceptual level the main ideas and how they will fit
|
|
|
|
|
+together.
|
|
|
|
|
+
|
|
|
|
|
+It's normal for the end of the chapter to feel increasingly cryptic and unintelligible.
|
|
|
|
|
+
|
|
|
|
|
+Now return to the beginning of the chapter and begin seriously reading it.
|
|
|
|
|
+Make sure to follow the logic of ideas and understand what new objects are.
|
|
|
|
|
+You might get stuck on a difficult idea or long proof. Feel free to skip over
|
|
|
|
|
+these and return back to them after. Many of the concepts will be new, and
|
|
|
|
|
+you will be awkward in your dealing with them. Do not worry as the more familiar
|
|
|
|
|
+you become with this subject, your understanding will become solid.
|
|
|
|
|
+
|
|
|
|
|
+As you work through the chapter towards the end, you are learning where all the theorems,
|
|
|
|
|
+definitions and proofs are. You will likely return back to these as you try to
|
|
|
|
|
+solve questions.
|
|
|
|
|
+
|
|
|
|
|
+While you're reading through, you will likely pass back over theorems you tried
|
|
|
|
|
+to understand earlier but skipped over. If they still don't make sense, then it's
|
|
|
|
|
+fine to again put them to the side and return back to them again after.
|
|
|
|
|
+
|
|
|
|
|
+In this way we are reading a chapter in several passes, going back through past
|
|
|
|
|
+material as we go forwards or try to solve questions. We also might sideline material
|
|
|
|
|
+in the beginning and decide to look more into them later.
|
|
|
|
|
+
|
|
|
|
|
+Eventually our familiarity with the chapter is strong, and everything (more or less)
|
|
|
|
|
+makes sense.
|
|
|
|
|
+
|
|
|
|
|
+## Solving Questions
|
|
|
|
|
+
|
|
|
|
|
+When you are stuck, feel free to ask others in the team, or post questions on math
|
|
|
|
|
+stackexchange if nobody knows.
|
|
|
|
|
+
|
|
|
|
|
+You will need to research things, searching the web and studying the supplement books.
|
|
|
|
|
+
|
|
|
|
|
+I tend to slightly prefer books with solutions to questions for self study.
|
|
|
|
|
+
|
|
|
|
|
+You should always do questions. As many as possible. For core subjects, always attempt
|
|
|
|
|
+to do all or most of the questions, unless there are far too many.
|
|
|
|
|
+
|
|
|
|
|
+When you are shorter on time or studying a subject on the side, you may choose to pick
|
|
|
|
|
+out a sample of questions with a mix of important looking topics and others which grab
|
|
|
|
|
+your attention or pique your curiosity.
|
|
|
|
|
+
|
|
|
|
|
+
|
