In which order should I study the following?

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Discussion Overview

The discussion revolves around the optimal order for studying a variety of mathematics and physics topics, as listed by a participant. The scope includes theoretical and applied subjects, with an emphasis on how to approach learning these topics effectively.

Discussion Character

  • Debate/contested
  • Exploratory
  • Conceptual clarification

Main Points Raised

  • One participant lists a series of books they wish to study and seeks advice on the order of study.
  • Another participant expresses skepticism about relying solely on Schaum's outline series for education, suggesting that while some books may be useful, they may not provide a comprehensive education.
  • A participant agrees with the skepticism and mentions using the books primarily for review and introductory purposes, as they plan to take these topics in college later.
  • A different participant attempts to categorize the books into tiers based on perceived prerequisites and suggests that the order within tiers matters, particularly emphasizing that real analysis should precede complex analysis.
  • This participant expresses uncertainty about the meanings of some course titles and their prerequisites, indicating a need for clarification on what each subject entails.
  • There is a suggestion that rigorous engagement with the material is necessary for effective learning, rather than passive study methods.

Areas of Agreement / Disagreement

Participants generally do not reach a consensus on the best order to study the topics, and multiple competing views regarding the effectiveness of the Schaum's series and the categorization of subjects remain present.

Contextual Notes

Some participants express uncertainty about the definitions and prerequisites of the listed topics, indicating that the discussion may be limited by varying interpretations of course titles and content.

cesaruelas
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Ok so I got hold of a good amount of schaum series books that I would like to study.
The most advanced topic in math I know so far is basic differential and integral calculus and I can deal rather good with calculus-based introductory courses in physics (Newtonian mechanics).

The books are:
advanced algebra
abstract algebra
modern algebra
fourier analysis
vector analysis
astronomy (algebra-based intro)
advanced calculus
differential equations
electromagnetism
statistics
applied physics (algebra-based intro)
analytic geometry
geometry
college mathematics
theoretical mechanics
probability and statistics
General topology
complex variable
real variable

In which order would you suggest that I study them? Also, if anyone would like one of this books I could send them to you or upload them here (I don't know if that's possible). Some of them are in spanish, though so, yeah...
 
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I don't want to be a downer but I don't think its a good idea to get your whole education from the Schuams outline series. Though some of them are good.
 
deluks917 said:
I don't want to be a downer but I don't think its a good idea to get your whole education from the Schuams outline series. Though some of them are good.

I agree with you, I will be using those on topics I already know as review material and the ones I don't know as an introduction, for I am going to take most of these topics later on in college anyway. Thanks for your reply!
 
Not exactly sure what many of these course titles even mean, or what their pre-reqs are.. But I tried splitting it up as best as I could off their vague titles. I split it into 3 tiers where you could (probably) learn anything within the same tier at the same time. But the order in my listing still does matter a bit. Namely, taking real analysis should be before complex analysis, etc.

I did it out of boredom (took like 5 minutes) and my general inclination to classify things. Also, I strongly agree. You probably won't get much (even an intro) out of learning these online unless you are extremely rigorous and dedicated; this means doing actual problems rather than some passive learning experience.

Tier 1:
modern algebra [is this middle school algebra, or another name for abstract algebra?]
advanced algebra [is this just more middle school algebra?]
geometry [high school geometry? not sure on this one either]

Tier 2:
astronomy (algebra-based intro)
electromagnetism
statistics
applied physics (algebra-based intro)
probability and statistics

college mathematics [what is this..?]
advanced calculus
differential equations

Tier 3:
theoretical mechanics

vector analysis [I assume this is (mainly) linear algebra?]
real variable [I assume this is real analysis?]
abstract algebra
complex variable [I assume this is complex analysis?]
fourier analysis
General topology
analytic geometry [uh.. I would have some relation to arithmetic/algebraic geometry]
 

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