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robertjford80
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How difficult is abstract algebra or group theory, plus complex analysis in relation to calculus?
robertjford80 said:but proofs are just too hard for me, they're written in a highly opaque language so now I mostly skip over them but a few proofs I understand.
robertjford80 said:could you go into a bit more detail. why are understanding proofs essential to abstract algebra. can't you just learn the algorithms and do the problems?
robertjford80 said:what about complex analysis? Also I thought group theory was used for Quantum Field Theory. Certainly they use number in QFT
robertjford80 said:How difficult is abstract algebra or group theory, plus complex analysis in relation to calculus?
Undecided Guy said:I found it easier. Calculus professors have a tendency to wave their hands at justifications that are at the heart of most conceptual misunderstandings. If you do not understand a single line in a proof, you should not move on until you understand it completely. To do otherwise is cheating.
This is so trueNumber Nine said:I found it far easier as well, but for a different reason -- calculus (particularly integral calculus) requires long and involved computations that offer many opportunities for errors to slip in unnoticed, even if you've mastered a technique.
WannabeNewton said:I think you are underestimating the level of mathematical rigor in QFT textbooks. Sure they aren't the typical proofs found in mathematics textbooks but, for example, some of the very first problems in Srednicki's QFT text are proof type problems. The whole plugging something in and getting a number answer isn't frequent at all.
robertjford80 said:So you mean QFT is more about how the objects relate to each other rather than what the quantity of the objects are? Feel free to go into more details.
robertjford80 said:How difficult is abstract algebra or group theory, plus complex analysis in relation to calculus?
Sankaku said:More than tuesdays but less than a rabbit.
algebrat said:That was awesome, did you make that up?
Robertjford80, many students who try out college math get to the level where proofs begin to creep slowly in, and greatly resent this uncomfortable step in their education. But look at it this way, the alternative is writing 20 page papers for a humanities class, or long technical reports for other science classes. Not that there is anything unusual in this discomfort, but in any of the disciplines, including math, it is of benefit to you to learn how to perform and communicate your ideas at a professional level.
algebrat said:That was awesome, did you make that up?
robertjford80 said:logic proofs are rather simple, there are only 18 operations acting on essentially two numbers, True and false, math employs I don't know how many operations acting on an infinite set of numbers. But don't get me wrong, logic proofs can be quite difficult, but they deal with situations that would never arise in an actual argument.
Undecided Guy said:If you do not understand a single line in a proof, you should not move on until you understand it completely. To do otherwise is cheating.
Abstract algebra is a branch of mathematics that studies structures such as groups, rings, and fields, and their properties. It is closely related to calculus as many of the concepts in calculus, such as functions and transformations, can be represented using abstract algebraic structures.
Abstract algebra can be considered difficult because it requires a strong foundation in mathematical concepts, including algebra, geometry, and number theory. It also involves abstract thinking and proof-based reasoning, which can be challenging for some students.
Abstract algebra differs from calculus in that it focuses on the study of abstract structures and their properties, while calculus deals with the study of change and rates of change in continuous quantities.
No, it is not necessary to know calculus to understand abstract algebra. However, having a strong understanding of algebra and other foundational mathematical concepts can make it easier to grasp abstract algebraic concepts.
To prepare for learning abstract algebra in relation to calculus, it is important to have a strong foundation in algebra, geometry, and other basic mathematical concepts. It may also be helpful to review topics in calculus, such as functions and transformations, that are closely related to abstract algebra before starting your studies.