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Archon

In your experience, which of these courses is more interesting and worthwhile?

- Thread starter Archon
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- #1

Archon

In your experience, which of these courses is more interesting and worthwhile?

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marlon

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MalleusScientiarum

My vote is for Analysis.

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you will eventually need both, so just flip a coin.

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are these "advanced calc" courses really analysis courses in disguise?

MAA 4211 Advanced Calculus 1

Credits: 3; Prereq: grade of C or better in MAS 4105.

An advanced treatment of limits, differentiation, integration, series; calculus of functions of several variables. (Note: credit will be given for at most one of MAA 4211, MAA 4102 and MAA 5104.)

MAA 4212 Advanced Calculus 2

Credits: 3; Prereq: grade of C or better in MAA 4211, taken the previous semester.

A continuation of MAA 4211. (Note: credit will be given for at most for one of MAA 4212, MAA 4103 and MAA 5105.)

because this is the analysis sequence:

MAA 4226 Introduction to Modern Analysis 1

Credits: 3; Prereq: grade of C or better in MAS 4105.

Topology of metric spaces, numerical sequences and series, continuity, differentiation, the Riemann-Stieltjes integral, sequences and series of functions, the Stone-Weierstrass, theorem, functions of several variable, Stokes' theorem, the Lebesgue theory. (Note: credit will be given for at most one of MAA 4226 and MAA 5228.)

MAA 4227 Introduction to Modern Analysis 2

Credits: 3; Prereq: grade of C of better in MAA 4226, taken the previous semester.

A continuation of MAA 4226. (Note: credit will be given for at most for one of MAA 4227 and MAA 5229.)

the advanced calc sequence is required for the major while the analysis courses are not.

- #8

Archon

Course Descriptions:

Analysis: The real number system. Sequences, limits, and continuous functions in R and 'Rn'. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Mean value theorem and applications. The Riemann integral.

Algebra: Sets and relations. The integers, congruences and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions.

Thanks for the input, everyone.

- #9

quasar987

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This is an excellent argument, and I would advice analysis for that same reason.MalleusScientiarum said:

My vote is for Analysis.

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- #11

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Uhm.....

If those are the programs, take analysis.

If those are the programs, take analysis.

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yeah, that algebra class looked like it is partially an intro to number theory class. :grumpy:Maxos said:Uhm.....

If those are the programs, take analysis.

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ah, at UF, there are two advanced calc options, which fall into your classifications, i bet.gravenewworld said:

the ones that i posted are probably more like an "intro to analysis" course sequence.

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MalleusScientiarum

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My advisor said that Algebra I doesn't really cover too much more than the undergrad courses, whereas Analysis does. That makes me want to take Analysis more, but I'm more interested in algebra.

Oh well. Hopefully I'll be a grad student in math next year anyway (hope-hopefully at Berkeley).

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I've studied alot of the topics that the algebra course covers in my free time and I think they are interesting. Alot of that material is in a number theory book I am reading actually. If the analysis class opens more options for next semester, then I'd consider taking that, and maybe taking the algebra course later, if it's required for your degree. You'll probably be doing lots of proofs regardless of which you take, so if you like writing proofs you should enjoy yourself. Goodluck!Archon said:In your experience, which of these courses is more interesting and worthwhile?

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