In which order should I study the following?

[cesaruelas]

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...

 

[deluks917]

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.

 

[cesaruelas]

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!

 

[Anonymous217]

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]

 

[Matrix0]

I would suggest studying the books in the following order:

1. College mathematics - This will provide a solid foundation for the other topics and help refresh your knowledge of basic math concepts.
2. Analytic geometry - This will build upon your knowledge of basic geometry and prepare you for more advanced topics.
3. Real variable - This will introduce you to the concepts of limits, continuity, and convergence, which are important for understanding advanced calculus.
4. Differential equations - This is a fundamental topic in math and physics, and it will help you understand more complex concepts in electromagnetism and mechanics.
5. Advanced calculus - This will expand upon your knowledge of basic calculus and prepare you for more advanced topics like Fourier analysis and vector analysis.
6. Vector analysis - This is an important topic in physics and will help you understand concepts in electromagnetism and theoretical mechanics.
7. Fourier analysis - This is a valuable tool for understanding signals and systems, and it will also prepare you for advanced topics like complex variable and general topology.
8. General topology - This is a foundational topic for advanced mathematics and will help you understand abstract algebra and complex variable.
9. Abstract algebra - This is a broad and important topic in mathematics, and it will help you understand concepts in modern algebra and algebra-based introductory astronomy.
10. Modern algebra - This is a more advanced topic in algebra and will build upon your knowledge of abstract algebra.
11. Complex variable - This is an essential topic for understanding advanced mathematics and physics, and it will also prepare you for topics like Fourier analysis and general topology.
12. Probability and statistics - This is a crucial topic in both math and science, and it will help you understand and analyze data in your studies.
13. Theoretical mechanics - This will build upon your knowledge of Newtonian mechanics and prepare you for more advanced topics like electromagnetism.
14. Electromagnetism - This is a fundamental topic in physics and will build upon your knowledge of theoretical mechanics.
15. Applied physics (algebra-based intro) - This will provide practical applications for the concepts you have learned in electromagnetism.
16. Astronomy (algebra-based intro) - This will introduce you to the basics of astronomy and provide a practical application for your knowledge of algebra.
17. Geometry - This will build upon your knowledge of analytic geometry and provide a foundation for more advanced topics.
18. Advanced