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Dragonfall
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Is it worth it that I take it as a class? I'm a last year undergraduate.
Did manifolds become boring once we learned they can all be embedded in R^n? No! In fact the exact opposite is true -- manifolds were originally interesting precisely because they allowed you to get rid of the ambient space!mathwonk said:notice that freyd himself says the main result in the subject at the time was the theorem that all abelian categories can be viewed as subcategories of the category of abelian groups. which pretty much took the fun out of them. i.e. how do you persuade people of the generality and power of axiomatic euclidean geometry when the only euclidean geometry is R^2?
(we'll see if we can wake hurkyl up again.)
In Cat, yes: adjunctions are pairs of adjoint functors (together with their units).mathwonk said:what is an adjunction? adjoint functors?
That is one aspect of it, and the one most people seem to focus on. But there is another side to category theory, in that you can define richer structures than you can with set theory.to me the main point of category theory is that one should always think not merely in terms of spaces but in terms of maps between spaces.
Interesting way to put it!mathwonk said:category theory is worth knowing if only to realize it is mostly horse ***. i.e.you cannot laugh at it unless you know something about it.
Taking an additional class as an undergrad can have numerous benefits, such as expanding your knowledge and skills in a particular subject area, improving your GPA, and increasing your chances of being accepted into graduate school or landing a job. It can also provide the opportunity to explore new interests and potentially discover a new career path.
The worth of a class can depend on various factors, including your academic and career goals, the relevance of the subject to your major, and the difficulty of the class. It is important to research the course syllabus, talk to professors or advisors, and consider the workload and time commitment before deciding if a class is worth taking.
It is possible that taking an additional class can have a negative impact on your GPA, especially if the class is challenging or if you are already struggling to maintain a strong GPA. However, if you are able to successfully manage your workload and perform well in the class, it can also have a positive impact on your GPA.
Taking a class outside of your major can be beneficial in many ways. It can help you develop a well-rounded education, expose you to new perspectives and ways of thinking, and potentially open up new opportunities for internships or jobs. However, it is important to consider if the class aligns with your academic and career goals before enrolling.
Some potential drawbacks of taking an additional class as an undergrad include increased workload and time commitment, potential impact on your GPA, and potential conflicts with other classes or extracurricular activities. It is important to carefully consider these factors and weigh them against the potential benefits before making a decision.