Is there a key to thinking more mathematically?

• Anti Hydrogen
In summary: Fundamental theories are important, but they are not the only thing that makes someone good at maths. Practice, practice, and more practice is what makes someone good at maths.
Anti Hydrogen
Are there some fundamentals or elements for thinking mathematically?

Thanks

Lots and lots of practice and hanging around other people who think mathematically is how I got to be good at it.

I don't think there are any short cuts. But there can be some organizing principles for approaching different classes of textbook type problems.

A solid foundation for solving lots of textbook type problems in physics, chemistry, and math eventually provides a big toolbox for other kinds of problems that occur in other contexts. But building up the toolbox takes years of practice and homework in courses with lots of textbook type problems.

berkeman, StoneTemplePython and Anti Hydrogen
Dr. Courtney said:
Lots and lots of practice and hanging around other people who think mathematically is how I got to be good at it.

I don't think there are any short cuts. But there can be some organizing principles for approaching different classes of textbook type problems.

A solid foundation for solving lots of textbook type problems in physics, chemistry, and math eventually provides a big toolbox for other kinds of problems that occur in other contexts. But building up the toolbox takes years of practice and homework in courses with lots of textbook type problems.
Thanks for replying. Once I read in Quora that some of most important theories in maths are: Set theory, number theory and functions

Klystron
Anti Hydrogen said:
Are there some fundamentals or elements for thinking mathematically?

Thanks
Always ask "why" and don't be satisfied by an answer which didn't convince you. Because the professor said or because it is written in the book are no valid answers.

Anti Hydrogen
Anti Hydrogen said:
Are there some fundamentals or elements for thinking mathematically?
One fundamental from information theory that helps me think mathematically and solve difficult problems can be called step-wise refinement in the context of the modular hypothesis, now theory. Given a large intractable problem, breakdown or refine the problem into simple steps that you can solve. Faced with a difficult landscape, consider simple shapes that combine to define or map the actual terrain.

Examples abound such as how NASA solved the unique problem of putting people on the moon. The early manned rockets launched astronauts into space with recovery, then into orbit around the earth. Later refinements had spacecraft dock in space and then orbit the moon and return. Finally, these various steps combined into a successful lunar landing, docking in orbit and a safe return to earth.

The Apollo spacecraft consisted of many modules performing diverse functions such as the large boosters to lift from earth, smaller modules for life support and flight control, and the lunar excursion module (LEM) that conveyed astronauts to the lunar surface, provided habitat then launched the explorers into orbit to dock with the service module for return to earth.

Even pure mathematical problems may be refined into sets and functions as you describe to either solve the problem or demonstrate lack of a viable solution.

Anti Hydrogen
Anti Hydrogen said:
Thanks for replying. Once I read in Quora that some of most important theories in maths are: Set theory, number theory and functions

You are mistaking tools for skill.

Anti Hydrogen and fresh_42

What does it mean to think mathematically?

Thinking mathematically involves using logical and analytical reasoning to solve problems and make sense of numerical and quantitative information. It also involves understanding and applying mathematical concepts and principles.

Can anyone learn to think mathematically?

Yes, anyone can learn to think mathematically with practice and effort. While some people may have a natural inclination towards mathematical thinking, it is a skill that can be developed and improved upon over time.

Is there a specific key or method for thinking more mathematically?

There is no one specific key or method for thinking more mathematically, as different strategies and approaches may work for different individuals. However, some common strategies for developing mathematical thinking include breaking down problems into smaller steps, using visual aids or diagrams, and practicing regularly.

Is mathematical thinking only useful for solving math problems?

No, mathematical thinking can be applied to many areas of life, including problem-solving in various fields such as science, engineering, economics, and technology. It also helps develop critical thinking skills and logical reasoning, which are valuable in decision-making and understanding the world around us.

How can I improve my mathematical thinking skills?

To improve your mathematical thinking skills, you can engage in activities such as solving math problems, practicing mental math, learning new mathematical concepts, and applying math in real-life situations. Additionally, seeking feedback and guidance from teachers or peers can also help you improve your skills.

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