Principles and strategies for mathematics study

• Make mathematics study a habit with dogged perseverance

  • Don't build mansion on top of loose sand. Concrete a solid foundation by allocating at least one hour for math study every day to make it a habit like reciting English words. Morning time after you getting up is recommended, during which you are facing least interruptions, your mind has its prime status and your mood is most optimistic.

  • Study math in focused mode by adopting the conception of deep work.

  • Interweave studying new knowledge and reviewing old knowledge (from which new understandings can be obtained). Interweave multiple topics from different sources to prevent Einstellung.

• When facing difficulties

  • Don't stuck in one book or paper. Compare materials on the topic from different sources to find clues and hints.

  • Don't stuck at the topic or problem for too long time. Circumvent it and progress forward. This is similar to practicing flute: playing a segment or a piece all the time is not recommended, during which the initial mindful action will gradually degrade to mechanical repetitions.

  • Overconfidence about your wisdom and creativity to grapple with the problem without asking anyone or referring to any materials is a bad habit. It wastes too much time with little harvest. Just be humble to learn from others. Ask questions on a forum and don't be shy or afraid of trouble and inconvenience.

• Use the problem solving approach

  • Doing exercises is an indispensable measure to achieve a real understanding and final mastering of the knowledge.

  • A certain amount of exercises are mandatory for both deepening your understanding and making you proficient in applying mathematical concepts and techniques. However, there is no need to complete all the exercises if you are not going to publish a book on the whole exercise collection.

  • Be brave, open and confident to apply the learned mathematical concepts and techniques to problems in real world. Any success or even financial income derived from such competent or irreplaceable work will produce positive feedback on your diligent and perennial study. Furthermore, you may discover new meanings from it besides the pure and sublime beauty of the mathematical edifice with its rigorousness and delicacies.