Learn Calculus: Required Math Concepts & Beginner Books

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Discussion Overview

The discussion focuses on the mathematical prerequisites for studying calculus and recommendations for beginner books and resources. It encompasses both theoretical foundations and practical learning materials.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants suggest that a good knowledge of basic algebra, geometry, and trigonometry is necessary to start learning calculus.
  • One participant recommends the book "Basic Mathematics" by Lang as a comprehensive resource for foundational topics.
  • Another participant mentions a free calculus book by Keisler, highlighting its historic approach using infinitesimals, while noting that standard approaches are also covered.
  • A different viewpoint emphasizes that the minimal prerequisites for studying calculus include Intermediate Algebra and Trigonometry, but suggests that additional knowledge in Geometry and College Algebra, or a Pre-Calculus course, would be beneficial.
  • One participant shares a resource, specifically a video series from MIT on calculus, as a helpful supplementary material.

Areas of Agreement / Disagreement

Participants generally agree on the necessity of certain mathematical topics as prerequisites for calculus, but there are varying opinions on the specific topics and resources that are most effective for beginners.

Contextual Notes

Some claims about prerequisite knowledge and resource recommendations depend on individual learning styles and may not apply universally. The discussion does not resolve which specific resources are superior or most appropriate for all learners.

thecosmos123456
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Inorder to start with calculus ,which topics in mathematics are required and are there any books for beginners to learn calculus?
 
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You will need a good knowledge of basic algebra, geometry and trigonometry. You will find a collection of everything you need to know in the book "Basic Mathematics" by Lang.
There are many books on calculus. My favorite one is the free book by Keisler, which takes the historic approach using infinitesimals. This is nonstandard nowadays, but the standard approach is covered too. https://www.math.wisc.edu/~keisler/calc.html
 
thecosmos123456 said:
Inorder to start with calculus ,which topics in mathematics are required and are there any books for beginners to learn calculus?
The most minimalist minimum to be able to study Calculus, or start studying Calculus is Intermediate Algebra and Trigonometry. Learning more than just the minimum will improve your ability to handle learning Calculus, so you really should include Geometry and College Algebra, or additionally a Pre-Calculus course. A student who has the prerequisite knowledge can begin using any typical good undergraduate college textbook on first-year Calculus.
 
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