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

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SUMMARY

This discussion focuses on the need for a comprehensive list of arithmetic topics suitable for students progressing to pre-calculus. Participants emphasize the importance of understanding the logic behind mathematical concepts, not just execution. Recommendations include utilizing textbooks and additional resources to enhance comprehension. Specific authors such as Aufmann & Barker, Lial, and Larson & Hostetler are suggested for their effective teaching methods in foundational mathematics.

PREREQUISITES
  • Understanding of basic arithmetic concepts
  • Familiarity with pre-algebra and algebra topics
  • Knowledge of calculus fundamentals
  • Ability to analyze mathematical logic and reasoning
NEXT STEPS
  • Research comprehensive arithmetic textbooks by Aufmann & Barker and Lial & Miller
  • Explore online resources that provide structured learning paths for pre-calculus
  • Study the logical foundations of mathematics to enhance conceptual understanding
  • Investigate used books for Pre-Algebra and Algebra courses to build a solid foundation
USEFUL FOR

Math students, physics majors, tutors, and educators seeking to deepen their understanding of arithmetic and pre-calculus concepts will benefit from this discussion.

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.
 

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