Abstract Algebra self study question -- Are Calc I, II, III prerequisites?

[heff001]

Hi,

Are Calculus I, II, III courses a prerequisite requirement for studying Abstract Algebra? I have read that Proofs and a willingness to work hard is. I am studying Logic and Set Theory and want to study Abstract Algebra in the distant future. I am focused on Foundational and Pure Mathematics.

Thanks

 

[micromass]

No, calculus is not at all a requirement. At most, you'll see some examples from calculus which are not really essential and safe to skip. That said, you must have a certain level of mathematical maturity. As you mentioned, proofs and willingness to work hard is most important.

 

[heff001]

No, calculus is not at all a requirement. At most, you'll see some examples from calculus which are not really essential and safe to skip. That said, you must have a certain level of mathematical maturity. As you mentioned, proofs and willingness to work hard is most important.

Thanks!

 

[mathwonk]

abstract algebra has very few prerequisites. e.g. ask yourself how many rotational symmetries a cube has. this is a problem in abstract algebra. more precisely theanswer is that the total number of symmetries equals the product of the number of vertices, times the numer of rotations leaving one vertex fixed. Thus the prerequisites for abstract algebra are mostly arithmetic.

The prerequisites of calculus are arithmetic, geometry, polynomial algebra, trigonometry,...

of course it depends how abstract your book makes it. the only reason for all the prerequisites is that some people feel you should have a lot of experience with many mathematical courses before essaying any "abstract" course.

so logically the answer is no. maybe in practice the answer can be yes for some people. but only someone with a really numerical approach could go through calc 3 before being prepared for abstract algebra. actually number theory is in a sense the first abstract algebra course, and it is a favorite topic chosen to teach young children.

 

[Luis Gomez]

Hi,

Are Calculus I, II, III courses a prerequisite requirement for studying Abstract Algebra? I have read that Proofs and a willingness to work hard is. I am studying Logic and Set Theory and want to study Abstract Algebra in the distant future. I am focused on Foundational and Pure Mathematics.

Thanks

Sorry for a late reply but I'm new in this "forum". From experienced, calculus is not a prerequisite for abstract algebra. Many books on abstract algebra presuppose that its readers are familiar with arithmetic among the number systems. They also presuppose that its readers are familiar with deductive logic and hence be able to derive/proof an argument from a given set of assumptions. The best book I can recommend on deductive logic is, "The Logic Book" by Bergmann. Two good books that I recommend for elementary abstract algebra are, " Number Systems...ect" by Elliot Mendelson and "Number Systems...ect" by Soloman Feferman. These two books do not presuppose familiarity with arithmetic since they both construct the number systems from Zermelo's axioms of set theory and prove every claimed property among them. Properties such as (Z,+,*,<) is an ordered integral domain, (Q,+*,<) is an ordered field, any two peano systems are isomorphic, among many others are proved. So to sum it up, first learn deductive reasoning. Then learn elementary abstract algebra from Mendelson and Feferman.

 

[mathwonk]

the only exception to this I can think of is the notes I am writing on linear algebra. In this subject the various normal forms like especially Jordan form, are especially useful for studying solutions of ordinary differential equations with constant coefficients, so withiout calculus you miss appreciating one of the main examples. (Nilpotent operators are key to Jordan form, and the derivative operator acting on the space of polynomials of degree ≤ n is a basic example. Eigenvalues are also fundamental, and derivatives of exponential functions provide a nice example.) Linear algebra is not usually taught this way though, i.e. the link with differntial equations is often omitted in a first course.

 

[QuantumCurt]

As already mentioned, it's not really a conceptual prerequisite, but it typically is a formal prerequisite. This means essentially that although the material may not depend on knowledge of calculus, it does assume that one has developed some mathematical maturity while completing the calculus sequence and that one is at least somewhat familiar with writing formal proofs.