1  # Reading Maths Books
  2  
  3  ## Finding Texts for Study
  4  
  5  You start first with a topic you want to learn about. Then you
  6  research texts to study from. Broadly speaking, they are:
  7  
  8  * Easy-reading high school books. Good if you are very short on
  9    time.
 10  * Undergrad textbooks, such as Springer undergraduate books. They
 11    are a good intro to a subject, or if studying an advanced book
 12    then you will want one or two of these as supplementary material
 13    for understanding difficult concepts.
 14  * Graduate level books usually are the best but require a lot of
 15    effort put in. Concepts and questions will need to be looked up
 16    and cross referenced with other materials.
 17    Examples include the yellow Springer books.
 18  
 19  ![](springer-intro-to-that-thing.png)
 20  
 21  Usually you will follow one main text on a topic, but with a few other
 22  supplementary books as backup. Often you get stuck on a concept in the
 23  main text, and the supplement books will assist you to make sense by
 24  looking at things from a different explanation. Re-phrasing the same
 25  idea using different words can make a big difference in dicephering
 26  some theorem or object.
 27  
 28  ## Video Courses
 29  
 30  There are many high quality online courses following important texts.
 31  They explain the main core forums, focusing your attention on the key
 32  ideas and explaining things in an intuitive non-formal manner.
 33  
 34  Favourites:
 35  
 36  * [Elliptic Curves by Alvaro Lorenzo](https://alozano.clas.uconn.edu/math5020-elliptic-curves/#).
 37    This course uses the Springer book on Elliptic Curves by Silverman.
 38  * Harpreet Bedi
 39  * Zvi Rosen
 40  * Boucherds
 41  
 42  ## Getting Excited, Taking a High Level View
 43  
 44  Take a look at the contents. Familiarize yourself with the structure of
 45  the book. Make note of topics that you will learn and master. Get
 46  excited about the truths that you will unlock. You will come back here
 47  every periodically to remember why you are studying and where you are
 48  going.
 49  
 50  Make a lesson plan. Often the first chapter of a new topic is
 51  important, but if you're already familiar then maybe you can jump to
 52  advanced material.
 53  
 54  Be aware if you struggle too much at the advanced level, and make no
 55  progress at all then it's a signal to swallow your pride, be humble and
 56  go down to a lower level before moving up again. We take shots, but
 57  sometimes we have to take a few steps back. The tortoise beats the hare.
 58  
 59  However you must struggle. Don't be a weakling. Fight to rise up. Give
 60  it your focus, dedication and attention. Get into the zone, or
 61  [rausch](https://youtu.be/BTXj6ZEANFg?t=443). You evolve because it is
 62  hard.
 63  
 64  ## Reading the Chapter
 65  
 66  Now you've chosen your chapter. Do a light first-pass read through it.
 67  Focus not on the details but the main theorems and structure of what
 68  you're learning. Try to understand from a conceptual level the main
 69  ideas and how they will fit together.
 70  
 71  It's normal for the end of the chapter to feel increasingly cryptic and
 72  unintelligible.
 73  
 74  Now return to the beginning of the chapter and begin seriously reading
 75  it. Make sure to follow the logic of ideas and understand what new
 76  objects are. You might get stuck on a difficult idea or long proof.
 77  Feel free to skip over these and return back to them after. Many of the
 78  concepts will be new, and you will be awkward in your dealing with
 79  them. Do not worry as the more familiar you become with this subject,
 80  your understanding will become solid.
 81  
 82  As you work through the chapter towards the end, you are learning where
 83  all the theorems, definitions and proofs are. You will likely return
 84  back to these as you try to solve questions.
 85  
 86  While you're reading through, you will likely pass back over theorems
 87  you tried to understand earlier but skipped over. If they still don't
 88  make sense, then it's fine to again put them to the side and return
 89  back to them again after.
 90  
 91  In this way we are reading a chapter in several passes, going back
 92  through past material as we go forwards or try to solve questions.
 93  We also might sideline material in the beginning and decide to look
 94  more into them later.
 95  
 96  Eventually our familiarity with the chapter is strong, and everything
 97  (more or less) makes sense.
 98  
 99  ## Solving Questions
100  
101  When you are stuck, feel free to ask others in the team, or post
102  questions on math stackexchange if nobody knows.
103  
104  You will need to research things, searching the web and studying the
105  supplement books.
106  
107  I tend to slightly prefer books with solutions to questions for self
108  study.
109  
110  You should always do questions. As many as possible. For core subjects,
111  always attempt to do all or most of the questions, unless there are far
112  too many.
113  
114  When you are shorter on time or studying a subject on the side, you may
115  choose to pick out a sample of questions with a mix of important
116  looking topics and others which grab your attention or pique your
117  curiosity.
118  
119  ## Post-Chapter Review
120  
121  After reading the chapter, be sure to do a quick review and write down
122  any theorems and proofs that caught your attention. You may wish to
123  write them on flash cards or on a special notebook so later you can
124  come back to them.