TheoEndre said:Do I need to study
No.TheoEndre said:The Philosophy of Mathematics
Yes, if "all the proofs" means all the proofs as presented in a specific course on a specific subject, such as analysis or algebra. However, even in a specific context not all proofs need to be studied on the first reading. Also, re-reading a proof (or trying to re-create it yourself) helps progressive understanding of that proof and its context.TheoEndre said:all the proofs
Yes, in my view, mathematics (pure, applied, it does not matter) is ultimately about proof. However, the motivation behind formulating and proving certain (sequences of) statements is often different for pure and applied mathematicians.TheoEndre said:in order to be good at maths
No, not in general, certainly not when starting. For physics, calculation and physical interpretation are probably more important. With that being said, there is of course a lot of cross fertilization between physics and mathematics.TheoEndre said:as well as physics?
Philosophy, no, but what do you mean by "all the proofs"? You won't have to study especially proof techniques, they come automatically as mathematics is based on proofs. The interest in historical and philosophical aspects should also come with time, as if you're really curious about your field of study, these aspects are also a matter of curiosity, normally. I doubt it will be tested, so it's a matter of the books you read in your spare time. Finally these topics make the difference between knowledge and education.TheoEndre said:Hello Everyone,
Do I need to study The Philosophy of Mathematics and all the proofs in order to be good at maths as well as physics?
Krylov said:My personal opinion follows.No.
Yes, if "all the proofs" means all the proofs as presented in a specific course on a specific subject, such as analysis or algebra. However, even in a specific context not all proofs need to be studied on the first reading. Also, re-reading a proof (or trying to re-create it yourself) helps progressive understanding of that proof and its context.
Yes, in my view, mathematics (pure, applied, it does not matter) is ultimately about proof. However, the motivation behind formulating and proving certain (sequences of) statements is often different for pure and applied mathematicians.
No, not in general, certainly not when starting. For physics, calculation and physical interpretation are probably more important. With that being said, there is of course a lot of cross fertilization between physics and mathematics.
fresh_42 said:Philosophy, no, but what do you mean by "all the proofs"? You won't have to study especially proof techniques, they come automatically as mathematics is based on proofs. The interest in historical and philosophical aspects should also come with time, as if you're really curious about your field of study, these aspects are also a matter of curiosity, normally. I doubt it will be tested, so it's a matter of the books you read in your spare time. Finally these topics make the difference between knowledge and education.
Some of the best study methods for learning maths include practicing regularly, breaking down complex problems into smaller parts, using real-life examples to understand concepts, and seeking help from peers or teachers if needed.
To stay motivated while studying maths, it can be helpful to set achievable goals, reward yourself for completing tasks, take breaks when needed, and remind yourself of the importance of mastering mathematical skills for future academic and career success.
Some common mistakes to avoid while studying maths include not practicing regularly, relying too heavily on memorization instead of understanding concepts, not checking your work for errors, and not seeking help when struggling with a particular topic.
To improve problem-solving skills in maths, it is important to understand the underlying concepts and formulas, practice frequently, and approach problems systematically by breaking them down into smaller steps and checking your work for errors.
There are various resources available for studying maths, including textbooks, online tutorials and videos, math software and apps, study groups or tutoring services, and practice problems and tests provided by teachers or textbooks. It is important to find the resources that work best for you and your learning style.