Analysis or Abstract Algebra?

In summary, there is a choice between taking Analysis and Abstract Algebra in the upcoming fall semester. Both courses seem interesting, with Algebra being more so. However, Analysis would open more options for the spring semester as it is a prerequisite for other courses. In the conversation, there is a debate on which course is more interesting and worthwhile, with some recommending taking both courses and others suggesting one over the other. Ultimately, it is important to eventually take both courses. There is also a discussion on the difference between "advanced calculus" and "analysis" and the course descriptions for both courses are provided. Some students have different experiences with the workload for these courses.
  • #1

Archon

This coming fall semester, I have a choice between taking Analysis and Abstract Algebra. Unfortunatly, I'm having a great deal of trouble deciding which to take. Both seem interesting (though Algebra more so). On the other hand, Analysis would open more options for spring semester (in particular, it's a prerequisite for Differential Geometry, Differential Topology, and Complex Analysis).

In your experience, which of these courses is more interesting and worthwhile?
 
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  • #2
Both courses are extremely important. I am a bit surprised you are not required to take them both. What is the algebra course about, exactly ?

marlon
 
  • #3
i will echo what marlon said and go a bit further; take both. very very very very important classes. if you have to, i would take Analysis first, since it's the foundation of calculus. but take both classes
 
  • #4
if you can only take one I will hands down vote for algebra. it is much more interesting. advanced calc makes you go :zzz:
 
  • #5
I would advise the opposite. If you're a physics major, there are about a dozen good books out there with abstract algebra tailered to physicists. I would advise the Analysis course, even though I have to agree that it is really boring, it is full of useful information that you might not get from a book. The course will push you through the boring stuff, while if you were to pick up a book you might just put it back down after the second chapter.

My vote is for Analysis.
 
  • #6
you will eventually need both, so just flip a coin.
 
  • #7
piggyback question:

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
I know that I'll eventually need both, but I can't take both now because I'm still in High School, and one of these classes in addition to my other work is going to be hard enough.

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
MalleusScientiarum said:
I would advise the opposite. If you're a physics major, there are about a dozen good books out there with abstract algebra tailered to physicists. I would advise the Analysis course, even though I have to agree that it is really boring, it is full of useful information that you might not get from a book. The course will push you through the boring stuff, while if you were to pick up a book you might just put it back down after the second chapter.

My vote is for Analysis.

This is an excellent argument, and I would advice analysis for that same reason.
 
  • #10
different school have different meanings for advanced calculus. at some schools advanced calculus means "analysis" and at others it just means a harder calculus class. if you learn epsilon-delta proofs and only have 2 or 3 homework problems per week to do, you are definitely doing analysis.
 
  • #11
Uhm...

If those are the programs, take analysis.
 
  • #12
Maxos said:
Uhm...

If those are the programs, take analysis.

yeah, that algebra class looked like it is partially an intro to number theory class. :grumpy:
 
  • #13
gravenewworld said:
different school have different meanings for advanced calculus. at some schools advanced calculus means "analysis" and at others it just means a harder calculus class. if you learn epsilon-delta proofs and only have 2 or 3 homework problems per week to do, you are definitely doing analysis.

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

the ones that i posted are probably more like an "intro to analysis" course sequence.
 
  • #14
2 or 3 analysis homework problems per week? I think I did half the problems in the Bartle during my first semester.
 
  • #15
Yeah I only had 2 or 3 homework problems per week. They were all proofs of statements that my professor gave us, they didn't come out of the book.
 
  • #16
I find myself in a pretty similar situation. I'm a fifth-year senior, finishing up my chemical engineering degree, but I've already got all the requirements for my math degree, so I'm taking grad courses. I'm signed up for 13 hours of Chem E. and both the Real Analysis I and Algebra I grad courses. My advisor just told me it's complete suicide, so I'm torn between following his advice and not wussing out on my second-to-last semester. But if I do wuss out, I'm still torn between Algebra and Analysis.

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. :frown:

Oh well. Hopefully I'll be a grad student in math next year anyway (hope-hopefully at Berkeley).
 
  • #17
Archon said:
In your experience, which of these courses is more interesting and worthwhile?
I've studied a lot 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!
 

1. What is the difference between Analysis and Abstract Algebra?

Analysis and Abstract Algebra are both branches of mathematics, but they have different focuses. Analysis is concerned with the study of continuous functions and their properties, while Abstract Algebra is concerned with the study of algebraic structures such as groups, rings, and fields.

2. What are some common applications of Analysis and Abstract Algebra?

Analysis has many practical applications, such as in physics, engineering, and economics. It is used to model and solve problems involving continuous processes. Abstract Algebra, on the other hand, has applications in computer science, cryptography, and coding theory, among others.

3. What are some key concepts in Analysis and Abstract Algebra?

In Analysis, key concepts include limits, continuity, derivatives, and integrals. In Abstract Algebra, key concepts include groups, rings, fields, and vector spaces. Both fields also involve the study of functions and their properties.

4. How does one approach problem-solving in Analysis and Abstract Algebra?

In Analysis, problem-solving often involves using the properties of continuous functions to find solutions to equations or optimize functions. In Abstract Algebra, problem-solving often involves applying algebraic operations and properties to manipulate equations and solve for variables.

5. What are some resources for learning Analysis and Abstract Algebra?

There are many textbooks, online courses, and video lectures available for learning Analysis and Abstract Algebra. Some popular resources include "Analysis I" by Terence Tao and "Abstract Algebra" by David S. Dummit and Richard M. Foote. Additionally, many universities offer courses and resources for self-study in these subjects.

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