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Discussion Starter · #1 ·
I have never had much of an aptitude for mathematics, but quite recently I have developed a fascination towards the core concepts/principles behind it, yet most of the courses I take do not about mathematics teach these principles/concepts on a fundamental level (if at all).So if you are a math enthusiast/bad ass please explain them (principles, concepts, the nature of certain disciplines) to me so that I may accumulate an understanding.

*** Also if you are willing to integrate separate disciplines such as art, philosophy, music, linguistics, history, sociology with core mathematical disciplines such as statistics, geometry and algebra I'm willing to listen.
 

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I'm not a mathematician but took quite a bit for my requirements in Physics. Each area of mathematics can get rather complex and there is some usage of some areas of mathematics in others. Algebra, Trigonometry and Geometry are used in Calculus for example. I would recommend finding a university catalog and look under the mathematics department for undergraduate studies and see what the requirements are and do a little research on each topic. Wikipedia is probably good enough to give you some insight on each topic.

https://en.wikipedia.org/wiki/Algebra
https://en.wikipedia.org/wiki/Trigonometry
https://en.wikipedia.org/wiki/Geometry
https://en.wikipedia.org/wiki/Calculus
https://en.wikipedia.org/wiki/Linear_algebra
https://en.wikipedia.org/wiki/Mathematical_logic

... and etc.

I've only listened to a couple of these videos, but Feynman (Physics lecturer) has many in which he discusses mathematics and it's relationship with Physics. He is quite entertaining to listen to:

Link to youtube playlist:
Code:
https://www.youtube.com/watch?v=obCjODeoLVw&index=1&list=PL4JORNbPFbZbmf0AO99Oxt2EqBDiokDxr
 

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What is this fundamental level you are talking about? You do not mention what kind of principles/concepts that you would want to have explained. Also a principle is often defined as something like: 1) an accepted or professed rule of action or conduct. 2) a fundamental, primary, or general law or truth from which others are derived. In a way a principle or concept is often already on a fundamental level, depending what you mean with "fundamental level". Take 'addition' as an example of a concept/principle. We do not need a set theoretic definition of 'addition' in order to understand this rather intuitive concept. Maybe you could argue that you get a more fundamental understanding of the nature of 'addition' if you understand the set theoretic definition. However the set theoretic definition of 'addition' is simply an attempt to explain our intuition about 'addition' in a more formal manner and to create a coherent definition that does not cause major problems within the system. We do already understand 'addition' on a fundamental level as soon as we understand the meaning of the principle. The interesting aspect of mathematics is the philosophical aspect of this marvelous subject.
 
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Discussion Starter · #4 ·
What is this fundamental level you are talking about? You do not mention what kind of principles/concepts that you would want to have explained. Also a principle is often defined as something like: 1) an accepted or professed rule of action or conduct. 2) a fundamental, primary, or general law or truth from which others are derived. In a way a principle or concept is often already on a fundamental level, depending what you mean with "fundamental level". Take 'addition' as an example of a concept/principle. We do not need a set theoretic definition of 'addition' in order to understand this rather intuitive concept. Maybe you could argue that you get a more fundamental understanding of the nature of 'addition' if you understand the set theoretic definition. However the set theoretic definition of 'addition' is simply an attempt to explain our intuition about 'addition' in a more formal manner and to create a coherent definition that does not cause major problems within the system. We do already understand 'addition' on a fundamental level as soon as we understand the meaning of the principle. The interesting aspect of mathematics is the philosophical aspect of this marvelous subject.
I suppose fundamental was a poor word choice, but in this term I mean in the secondary aspect. The reason being, often when I was a kid, I often failed at the technical aspect of it because I couldn't get the principle of how it was applied.

It wasn't until I took a course in mathematics that delved into the historical context of it's origins and development (The Development of Mathematical Thought) that I started getting an appreciation for math. There are so many ways to actually conduct the process of mathematics, ( for example when I learned the Hindu lattice multiplication table, it altered the concept of multiplication for me on a fundamental level) in a way that I realized that math in general has more variation that I was taught it had. And the methodology in which it is currently applied, is just a commonly accepted variation.

But if you could please give me instances of mathematical principles that could be applied on a level that would alter my understanding of a core concept. (Ie: how a common function such as addition as you mentioned, is conducted differently through the use of a different method BASED on a core establishing principle of how addition is meant to function)

Hope this clarified it a bit.
 

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One of the biggest revelations of my life was when I was in twelfth grade and we studied abstract algebra (groups, rings, fields etc,) and some of the topics basically explained how operations are defined between systems, among other things. And that is when I understood where addition, subtraction, multiplication and division all come from. It was fascinating. But I think the best way to get to these concepts and principles you are talking about is by diving in and reaching very complex levels of a subject. The more complex it gets, the more you reach a deeper understanding of the very core of everything. It's truly wonderful.
 
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