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mathboy
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I love doing proofs, but hate doing computational questions. If I become very good with proofs but remain just so-so with calculational problems, can I still become a good mathematician? My favourite subject is topology.
mathboy said:I love doing proofs, but hate doing computational questions. If I become very good with proofs but remain just so-so with calculational problems, can I still become a good mathematician? My favourite subject is topology.
mathman said:Yes you can. In my case, I am lousy in arithmetic, but I still managed to get a math Ph.D.
mathboy said:can I still become a good mathematician?
I think 80% of all gifted mathematicians has trouble with numbers, but they're good at variables, equations and geometric shapes. I don't know how this works, but for me, I love arithmetic.mathboy said:I love doing proofs, but hate doing computational questions. If I become very good with proofs but remain just so-so with calculational problems, can I still become a good mathematician? My favourite subject is topology.
mgb_phys said:Isn't there a quote that junior school kids need to count upto 1000, high school needs to count to 100, a maths undergrad needs 1-10,e,pi, and a maths PhD needs to count to 0.
So, you're saying that for example, simplifying 3x - 2x + (2 + 2x + 3x^6)^2 kind of stuff is calculation stuff, right?mathboy said:By computation, I did not mean just arithmetic. For example, being able to manipulate a complicated algebraic expression to get it in a desired form; computing that all overlaps in an atlas on a manifold are smooth; searching for a regular topological space that is not completely regular, and then computing (with the bizarre topology you've congured up) that it is indeed regular but not completely regular, etc...
JWHooper said:So, you're saying that for example, simplifying 3x - 2x + (2 + 2x + 3x^6)^2 kind of stuff is calculation stuff, right?
mathboy said:By computation, I did not mean just arithmetic. For example, being able to manipulate a complicated algebraic expression to get it in a desired form; computing that all overlaps in an atlas on a manifold are smooth; searching for a regular topological space that is not completely regular, and then computing (with the bizarre topology you've congured up) that it is indeed regular but not completely regular, etc...
Hmm? I always thought arithmetic was considered the basic operations of addition, inverse addition, multiplication, and inverse multiplication for numbers only, not variables. Where does the arithmetic line stop and the more advanced stuff begin?mathboy said:That's still arithmetic.
mathboy said:That's still arithmetic.
Daniel Y. said:Hmm? I always thought arithmetic was considered the basic operations of addition, inverse addition, multiplication, and inverse multiplication for numbers only, not variables. Where does the arithmetic line stop and the more advanced stuff begin?
Computational skill refers to the ability to use computers and software to perform mathematical calculations, simulations, and analyses. It is important for mathematicians because it allows them to handle complex and large-scale mathematical problems efficiently and accurately.
While computational skills are an essential tool for mathematicians, they are not the only requirement for becoming a mathematician. Strong analytical thinking, problem-solving abilities, and a deep understanding of mathematical concepts are also necessary.
Computational skills can enhance one's mathematical abilities by allowing them to explore and solve complex problems that would be difficult or impossible to solve by hand. It also allows for faster and more accurate calculations, freeing up time for deeper understanding and analysis of mathematical concepts.
Computational skills can be learned through practice and training, just like any other skill. While some individuals may have a natural aptitude for computational thinking, anyone can improve their skills with dedication and effort.
While computational skills are an important tool for mathematicians, relying too heavily on them can lead to a lack of understanding of the underlying mathematical concepts. It is important for mathematicians to strike a balance between using computational tools and developing a deep understanding of the mathematics behind them.