Comprehensive List of Arithmetic Topics for Math Students: Resources and Books

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A comprehensive list of arithmetic topics from arithmetic to pre-calculus is sought, with an emphasis on well-organized resources. The discussion highlights the importance of understanding the logic behind mathematical concepts, not just execution of formulas, which is often lacking in traditional tutoring. It is suggested that starting with foundational materials, such as Pre-Algebra textbooks, can enhance understanding of arithmetic and geometry. Recommendations for authors of useful textbooks include Aufmann, Lial, and Larson, among others. Overall, a single resource may not suffice, and a combination of materials is encouraged for deeper comprehension.
starrynight108
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Does anyone know where I can get a complete list (that is preferably well organized) of topics from arithmetic - pre-calculus?

I've had difficulty finding one resource that is comprehensive for arithmetic. Maybe I am being too picky... I have about 9 full pages of topics for arithmetic so far that have been put together piecemeal, but it would be awesome to find one comprehensive book/online resource.

It's clear that textbooks are a good starting point, but to understand the logic and how to derive formulas/concepts there needs to be additional resources.

A little rant: If I could put mathematical learning into two categories - execution and logical understanding. Someone can be great at learning how to execute formulas, but not see how things connect (maybe this is a no-brainer!). Understanding the logic isn't explicitly taught (at least in my experiences). This is clear from our tutoring center. The majority of the tutors can tell how how to find the answer, aka use this formula, but can't explain the why. There's a fellow with a B.S. in math and of course he can explain everything backwards and forwards.

Am I trying to learn above my level? I am taking calc 1 in December. Being a physics major I really enjoy going to the core of understanding the 'why' in concepts, but it takes up so much time and it's tough with full-time work and school.
 
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I just noticed the math resources at the top of this page! Any feedback to the last item would be appreciated though.
 
You cannot get a list of all possible resources. At least you suggested what level you are. I would seriously use less advanced material starting at Pre-Algebra, if you want extensive help in understanding Arithmetic and basic common Geometry.

You should find USED BOOKS, hard-bound for courses intended for Pre-Algebra, Algebra 1, Algebra 2, Pre-Calculus, or College Algebra. You STILL might need more than any single book. Look for authors like:
Aufmann & Barker;
Aufmann, Barker, & Nation;
Wright & New;
Lial;
Lial & Miller;
Larson & Hostetler.
 
i am self learning physics. have you ever worked your way backwards again after finishing most undergrad courses? i have textbooks for junior/senior physics courses in classical mechanics, electrodynamics, thermal physics, quantum mechanics, and mathematical methods for self learning. i have the Halliday Resnick sophomore book. working backwards, i checked out Conceptual Physics 11th edition by Hewitt and found this book very helpful. What i liked most was how stimulating the pictures...

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