What Math Branches Can You Explore Without an Advanced Background?

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Various branches of mathematics can be explored without an advanced background, including graph theory, combinatorics, and linear algebra, which are noted for being self-contained. Abstract algebra is also accessible, focusing on definitions and proofs, making it suitable for those new to mathematics. Suggested resources include "A First Course in Abstract Algebra" by Fraleigh and "Contemporary Abstract Algebra" by Gallian, which are recommended for beginners. Additionally, number theory is mentioned as a field that can be approached without extensive prior knowledge. Overall, there are many resources available for self-study in mathematics, even for those starting from a basic level.
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I was wondering if there are any branches of maths that I can work through, that don't require a very deep math background. I am working through the Calculus sequence for university so I am very limited. I know graph theory is something that I can probably work through (correct?) and I BELIEVE I read somewhere that I could work through Combinatorics and/or enumeration without knowing any maths since the postulates and axioms are self-contained.

If anyone can provide to me any and all branches of maths that I could work through to broaden my knowledge, that would be chill.

Peace homies!
 
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Linear algebra is also nice, and useful.
 
arildno said:
Linear algebra is also nice, and useful.

I am very interested in linear algebra (and it's applications to quantum physics) and that is a class that I will be taking very soon after I finish Calculus II this semester. I will definitely purchase the text and start working through it early but are there any other interesting and perhaps abstract fields that I could work through? I am just curious what I have available to me.

Thank you for your reply.

Peace!
 
Algebra as such, learning about groups, fields and so on. Also very useful
 
arildno said:
Algebra as such, learning about groups, fields and so on. Also very useful

What background do I need to work through algebra (I assume you are referring to what is colloquially known as 'abstract algebra' correct?)? I am very new to mathematics, as I didn't learn basic algebraic and geometric arithmetic until a year ago which was two years after I graduated high school. I never took math higher than Algebra in high school (which I failed because I never went to class) and just finished Calculus I with an A. My passion for math and physics emerged after high school, so I am way behind. I want to do mathematical physics and I am prepared to study as much as I need to.

I feel really behind (especially with kids on here doing calculus at age 11), hence my reasons for wanting to learn as much as I can when I can.
 
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Abstract algebra is self-contained; you need to focus on definitions, axioms, and take particular care in not only understanding proofs generated by these, but also develop the skill of doing the proofs yourself (holding your hand over the book's proof should do nicely)

group theory is used in various quantum mechanics models of physics.

To hone your proving skills, Euclidean geometry contains much material for your benefit, even if perhaps the actual results gained is not particularly ground breaking, or part of the mathematical research frontier.
 
arildno said:
Abstract algebra is self-contained; you need to focus on definitions, axioms, and take particular care in not only understanding proofs generated by these, but also develop the skill of doing the proofs yourself (holding your hand over the book's proof should do nicely)

group theory is used in various quantum mechanics models of physics.

Thank you very much, this looks interesting. Are there any texts that you can suggest for me concerning any mathematics that you think I might be able to work through? I am very interested in working through the abstract algebra that you mentioned as well as group theory (if that's available to me).

Thank you again!
 
I haven't studied it in any detail myself, so there are others here at PF who could guide you to a good book.
 
complexPHILOSOPHY said:
Thank you very much, this looks interesting. Are there any texts that you can suggest for me concerning any mathematics that you think I might be able to work through? I am very interested in working through the abstract algebra that you mentioned as well as group theory (if that's available to me).

Thank you again!

A first course in Abstract Algebra by Fraleigh is pretty cute for a beginner. Some seem to like Gallian's Contemporary Abstract Algebra, but I think it lacks some material which Fraleigh includes.

May I also recommend you to look for used versions, or new low price/international editions, of the books at www.abebooks.com or similar marketplaces. Will save you a lot of money in the long run.
 
  • #10
you can learn any first-3rd yera(canadian level) mathematics on your own.
Mostly the basics of many fields
Graph Theory, Combinatorics, STatistics, Langauge THeory, Complexity & computability, Numerical Methods, real analysis,vector calc, etc
 
  • #11
I went to my library (it is a community college so it's not that tight) and picked up John Moore's Elements of Abstract Algebra Second Edition as well as Richard Andree's Selections from Modern Abstract Algebra to get started. If there are better books for me to work through, please let me know. Also, is anyone familiar with the books I listed?
 
  • #12
every math genius knew less math than you at one point. why be afraid to go deeper in math?
 
  • #13
complexPHILOSOPHY said:
I went to my library (it is a community college so it's not that tight) and picked up John Moore's Elements of Abstract Algebra Second Edition as well as Richard Andree's Selections from Modern Abstract Algebra to get started. If there are better books for me to work through, please let me know. Also, is anyone familiar with the books I listed?
Get Herstein's Topics in Algebra. I've never seen a math book flow as beautifully!
 
  • #14
I vote for Gallian's Contemporary Abstract Algebra, for an introduction to the subject it is very accurate and elegant. Also the last 10 chapters are somewhat sketchy and so it is easier to read and is presented as (I think) motivational material, which is good for self-study.

why be afraid to go deeper in math?

For fear of becoming 'professionally deformed' :biggrin:
 
  • #15
Number Theory is another subject you can work through without any previous knowledge.
 
  • #16
Depends weither you want to undersstand all the proofs or not...You may need some knowledge in other fields...Eg Elliptic Curves and Modular Forms, for FLT
 
  • #17
Gib Z said:
Depends weither you want to undersstand all the proofs or not...You may need some knowledge in other fields...Eg Elliptic Curves and Modular Forms, for FLT

What is FLT?
 
  • #18
What is FLT?

Faster-than-light travel!:-p
 
  • #19
complexPHILOSOPHY said:
What is FLT?

Fermat's last theorem.
 
  • #20
Lol Faster Than Light travel niice.

But yep, its Fermats Last theorem:
a^z + b^z can not equal c^z, where a, b and c are positive integers, and z is an integer greater than 2.
 
  • #21
Gib Z said:
Lol Faster Than Light travel niice.

But yep, its Fermats Last theorem:
a^z + b^z can not equal c^z, where a, b and c are positive integers, and z is an integer greater than 2.

OHHHHHH! Didn't make that correlation <3

I love how all of these elegant proofs seem to have gotten lost :P
 
  • #22
O yes..Id like to see Fermats Proof very much :)
 
  • #23
My school's library sucks and doesn't have any of the texts that you guys mentioned and neither does the San Diego County Library branch. It appears that I am stuck with two books that I can't even find reviews for on the internet, lol.

Do you guys have any other algebra texts that might be available to me? I am way too poor to purchase the text right now, so I guess I will ahve to wait.

Until then, I might as well work through some of the books that I have.
 
  • #24
MIT OCW: online Courseware
 
  • #25
complexPHILOSOPHY said:
My school's library sucks and doesn't have any of the texts that you guys mentioned and neither does the San Diego County Library branch. It appears that I am stuck with two books that I can't even find reviews for on the internet, lol.

Do you guys have any other algebra texts that might be available to me? I am way too poor to purchase the text right now, so I guess I will ahve to wait.

Until then, I might as well work through some of the books that I have.

You will find, e.g., Contemporary Abstract Algebra for less than 8 USD total on the already mentioned marketplace Abebooks. Surely you can pay that much?
 
  • #26
flybyme said:
You will find, e.g., Contemporary Abstract Algebra for less than 8 USD total on the already mentioned marketplace Abebooks. Surely you can pay that much?

Surely I cannot right now. California is very expensive. I will next month when I get paid.
 
  • #27
complexPHILOSOPHY said:
Surely I cannot right now. California is very expensive. I will next month when I get paid.
Try the free books here: http://www.freescience.info/books.php?id=248
 

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