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I am beginning my mathematics major and I am experiencing many problems with reading math textbooks.

I find that there are many theorems and definitions on the texts. On the other hand most of the texts are in English which is not my native language.

My problem is the speed. I read very slow because I feel I need to do many things on the way: Read the text, understand the text, remember all definitions which are involved, to verify the theorem using an example in order to understand completely, etc...

Is there any method to increase my speed?

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MathHack
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    Maybe How to read a book in mathematics? could be helpful – Sil Oct 14 '20 at 20:16
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    Faster is not necessarily better. I suggest building your stock of examples as you read. Check each theorem to see what it tells you about the examples you know. See what happens when one of the hypotheses fails. – Ethan Bolker Oct 14 '20 at 20:17
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    "Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?" Halmos. – Shaun Oct 14 '20 at 20:17
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    The slower you go now, the faster you can go later. Most of mathematics builds upon itself, so having a strong understanding of the basics will go a long way. For example: I spent 6-8 months reading one paper proving something in $\mathbb{R}^3$. Now I'm reading a paper that proves something similar, but in $\mathbb{R}^n$. The $\mathbb{R}^n$ paper is going much faster, since a lot of the proofs are variations of the proofs in the first paper. – Ryan Oct 14 '20 at 20:25
  • Do the exercises, you don't learn maths by reading – Mummy the turkey Oct 14 '20 at 21:40
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    It's completely normal to take a long time when learning a new subject, because you need to get used to a new "way of thinking". It is pretty normal to take, say, a week on just five pages of a book, if those pages are particularly conceptually challenging. – YiFan Tey Oct 14 '20 at 23:56

1 Answers1

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Here is the complete answer provided by the textbook Algebra and Trigonometry Structure and Method Book 2 by Mary P. Dolciani et al

Reading Your Algebra Book

An algebra book requires a different type of reading than a novel or a short story. Every sentence in a math book is full of information and logically linked to the surrounding sentences. You should read the sentences carefully and think about their meaning. As you read, remember that algebra builds upon itself; for example, the method of factoring that you'll study on page 188 will be useful to you on page 697. Be sure to read with a pencil in your hand: Do calculations, draw sketches, and take notes. To take full advantage of your book, begin your study of each lesson by getting an idea of the goal of the lesson. Read the lesson title and the stated objective. You may find it useful to skim the lesson first. Vocabulary: Important words whose meanings you'll learn first are printed in heavy type. Symbols: You must be able to read these symbols in order to understand algebra. Diagrams: They contain information that will help you understand the concepts under discussion. Study the diagrams carefully as you read the text that accompanies them. Displayed Material: Be sure to read and understand the material in these boxes. Reading Aids: They will help you become a more effective reader and problem solver. Try doing the examples on your own, before reading the solutions that are given following the examples. Accurate reading is a vital part of problem solving. When you read a problem, do so slowly and carefully to be sure you fully understand every word, fact, and idea. Attempt to break the problem down. You may be able to use the parts that you understand to make sense of the parts that you do not. Sometimes, substituting simpler data and solving a simpler, related problem may help you see how to solve the given problem. Make connections between what you know and what is new. Good problem solvers learn from their mistakes as well as their successes. Exercises. Tests. and Reviews. A Chapter Summary: that lists important ideas from the chapter. Although it is important to work quickly. You must be sure not to work so quickly that you lose accuracy.

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