# How can I develop “mathematical thinking” as a student? [closed]

In my humble opinion as a math student and considering that my main area of interest is computer science, I see that one of the most important skills required to solve problems is the mathematic thinking - a skill that involves the ability to look into a problem and extract informations.

With my background from high school, I developed a "mechanical way" to look into solutions for a problem, searching for formulas, techniques and theories that can be applied towards the solution. This can be problematic for many reasons: this "mechanical way" can lead to wrong formulas, bad abstraction of the problem, etc.

As I see, many people share this way of thinking. I'd like to receive a constructive feedback to start building confidence and think as a mathematician.

## closed as primarily opinion-based by Delta-u, Strants, José Carlos Santos, Aloizio Macedo♦Sep 26 '18 at 21:25

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

• Kind of trivial answer, but imo the only way to develop mathematical thinking is to do mathematics. Start with any book written as a first course for mathematics students. For example, you might be interested in the following book: link.springer.com/book/10.1007/978-1-4419-9479-0 It should be easy to follow to anyone who did mathematics in high school. – Václav Mordvinov Sep 26 '18 at 15:00
• To be honest, I don't think there is a special method that can give you that skill. It's all about practice. The more problems you will solve and understand, the better your mathematical thinking will become. Sometimes I see problems that I can't solve, then look at a solution and I don't understand how one can even think about such tricks. But I learn from these problems and next time I think in more creative ways. – Mark Sep 26 '18 at 15:02
• I can perfectly agree that the best way to learn is practicing. But how come abilities such as abstraction and induction are improved when training? – joann2555 Sep 26 '18 at 16:28
• I don't know if any such general advice is helpful here, except the usual "take courses, ask questions, do problems". Although to be successful as a mathematician, you eventually need to also learn to think independently. – Jair Taylor Sep 26 '18 at 16:54