What areas of math do you need to know in order to understand calculus

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Discussion Overview

The discussion revolves around the mathematical prerequisites needed to understand calculus, particularly from the perspective of someone with a limited educational background. Participants explore various areas of mathematics that may be beneficial, including algebra, geometry, trigonometry, and logarithms, as well as recommendations for specific learning resources.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • Some participants suggest that the level of understanding required for calculus varies significantly based on the individual's goals, referencing different resources like "Calculus Made Easy" and Spivak's calculus.
  • One participant recommends "Basic Mathematics" by Lang as a comprehensive resource that covers essential topics for learning calculus, though they caution that it may be challenging for complete beginners.
  • Another participant emphasizes the importance of foundational topics such as algebra and geometry, and mentions the utility of trigonometry and logarithms/ exponentials.
  • A participant references Euclid's geometry as a helpful background for understanding calculus concepts.
  • Links to additional resources, including Gelfand's books on various mathematical topics, are provided as supplementary materials for those preparing to study calculus.

Areas of Agreement / Disagreement

Participants generally agree on the importance of foundational mathematics for understanding calculus, but there is no consensus on the specific prerequisites or the best resources to use, indicating multiple competing views on the topic.

Contextual Notes

Some participants express uncertainty about the level of understanding required for different calculus texts, and there is a recognition that prior exposure to certain mathematical concepts may influence the ease of learning calculus.

TorqueDork
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What areas of math do you need to know in order to understand calculus? Let's assume all I have is up to a 6th grade education. Can you tell me what and how I might learn these things.
 
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It all depends on what you mean with "understand". This isn't just a smartass comment though. You can easily pick up "calculus made easy" and work through it. You won't need much prerequisite knowledge. On the other hand, you have understanding at the level of Spivak's calculus, this requires a lot more effort and prerequisite knowledge.

A good book here is "Basic Mathematics" by Lang. This book contains everything you need in order to start learning calculus. It covers elementary mathematics in a concise and non-spoonfeeding manner. However, if you've never seen these kind of mathematics before, then this book might be difficult.

If the book is too difficult, then I highly recommend the books by Gelfand. Here is the first volume: https://www.amazon.com/dp/0817636773/?tag=pfamazon01-20
He has other books on trigonometry, functions and graphs, method of coordinates. It would be good to work through all of these books before starting calculus. And it would be good to work through Lang too.
 
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algebra, geometry are basic, then trig and logs/exp are useful. have you read euclid's geometry? that is helpful. check out my notes for epsilon camp on my web site:

http://www.math.uga.edu/~roy/camp2011/10.pdf
 
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micromass said:
It all depends on what you mean with "understand". This isn't just a smartass comment though. You can easily pick up "calculus made easy" and work through it. You won't need much prerequisite knowledge. On the other hand, you have understanding at the level of Spivak's calculus, this requires a lot more effort and prerequisite knowledge.

A good book here is "Basic Mathematics" by Lang. This book contains everything you need in order to start learning calculus. It covers elementary mathematics in a concise and non-spoonfeeding manner. However, if you've never seen these kind of mathematics before, then this book might be difficult.

If the book is too difficult, then I highly recommend the books by Gelfand. Here is the first volume: https://www.amazon.com/dp/0817636773/?tag=pfamazon01-20
He has other books on trigonometry, functions and graphs, method of coordinates. It would be good to work through all of these books before starting calculus. And it would be good to work through Lang too.
Thanks so much! I am going with the latter book followed by Lang's
 
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