Is Calculus a Prerequisite for Abstract Algebra?

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Discussion Overview

The discussion centers on whether calculus is a necessary prerequisite for a course in abstract algebra, particularly in the context of a student's concurrent enrollment in calculus II. Participants explore the relationship between calculus and abstract algebra, considering the implications for mathematical maturity and course content.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses concern about taking abstract algebra while concurrently enrolled in calculus II, questioning the necessity of calculus for understanding abstract algebra.
  • Another participant suggests that the prerequisite of calculus is likely to ensure mathematical maturity rather than direct application of calculus concepts in abstract algebra.
  • A later reply emphasizes the importance of verifying course requirements with school officials, noting that the syllabus for the abstract algebra course does not specify calculus as essential.
  • One participant mentions that while calculus may not be directly used in abstract algebra, it could be relevant in related courses, such as those involving groups and symmetries, which may require knowledge of differential equations.
  • Another participant asserts that they have never encountered calculus in a first course in abstract algebra, reinforcing the idea that the calculus prerequisite is primarily about maturity.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of calculus for abstract algebra. While some believe it is not essential, others suggest it may be relevant for broader mathematical understanding. The discussion remains unresolved regarding the specific role of calculus in the course.

Contextual Notes

There is uncertainty regarding the exact content of the abstract algebra course and its relationship to calculus, as well as the potential need for knowledge of differential equations in related courses.

Howers
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Hi, I want to take this course next term. One reason is because I think it will help me with mechanics, classical and quantum, which are taken next year at advanced level.

The problem is I'm taking calc2 atm, and its a listed prereq for this group course. I got all the other prereq's, including linear alg 2 and abstract math intro(number fields and congruences). I don't know if asbtract algebra really requires calc, and my assumption is they want you to have calc 2 in order the have the proper mathematical maturity. Maybe I'm wrong, because I don't know a thing about abstract algebra aside from the bits from linear algebra. I always thought it logical to do algebra before the required calc, as its more fundamental. So can I take this course while concurrently taking calc 2?

Course text: CONTEMPORARY ABSTRACT ALGEBRA by GALLIAN

Course Desrp:
Congruences and fields. Permutations and permutation groups. Linear groups. Abstract groups, homomorphisms, subgroups. Symmetry groups of regular polygons and Platonic solids, wallpaper groups. Group actions, class formula. Cosets, Lagrange’s theorem. Normal subgroups, quotient groups. Classification of finitely generated abelian groups. Emphasis on examples and calculations.
 
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Hang on if you are taking calc 2 currently, then how would you be taking this class conceuurently with calc 2? I don't really think there would be a problem with taking the two classes at the same time, however, because they are rather different in nature, and you will probably use almost nothing directly from calculus, so the only reason it is a prerequisite is probably to assure that you have the mathematical maturity.
 
co-currently? lol

next term id do algebra, calc2 is a year course which I am doing now. and you sort of rephrased my question into an answer =P
 
Howers, to state the obvious: you should verify your tentative conclusions with officials at your school. It seems that you gave an outline syllabus for the abstract algebra course but not for the groups and symmetries course. At a guess, the latter might require knowledge of differential equations, for example in order to treat a "flow" (the one parameter group of transformations generated by a vector field). For example, this is how Killing vector fields on some Riemannian manifold are related to the isometry group of the manifold. This is also how one defines the "symmetries" of a differential equation, or system of differential equations, e.g. Maxwell's equations (which gives an interesting group including the Lorentz group, which was more or less the genesis of relativistic physics).
 
Last edited:
Chris Hillman said:
Howers, to state the obvious: you should verify your tentative conclusions with officials at your school. It seems that you gave an outline syllabus for the abstract algebra course but not for the groups and symmetries course. At a guess, the latter might require knowledge of differential equations, for example in order to treat a "flow" (the one parameter group of transformations generated by a vector field). For example, this is how Killing vector fields on some Riemannian manifold are related to the isometry group of the manifold. This is also how one defines the "symmetries" of a differential equation, or system of differential equations, e.g. Maxwell's equations (which gives an interesting group including the Lorentz group, which was more or less the genesis of relativistic physics).

Groups and Symmetries is the course title, but I'm pretty sure its a course on abstract algebra judging by the book we're using. In Canada, we don't use the term system (ie calc I, calc II, calc III), we do it by year, ie. calc 1 = calcI+calcII and calc2 = calcIII+vectorcalc.

I asked the prof he said the course changes every year and he said some calc may be used...
 
Howers said:
I asked the prof he said the course changes every year and he said some calc may be used...

Yeah right. I've never seen Calculus in a first course in Abstract Algebra.

It's probably only for mathematical maturity.
 

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