Time to complete every problem in a Calculus textbook

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Discussion Overview

The discussion revolves around estimating the time required to complete every problem in a Calculus textbook, specifically covering Calculus I, II, and III. Participants explore various approaches to problem-solving, the necessity of completing all problems, and the effectiveness of different study methods.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the total number of problems in a typical Calculus textbook and emphasizes the vagueness of the original question.
  • Another participant provides a rough estimate of 7000 problems across 15 chapters, suggesting that solving each problem in 5 minutes would lead to a time commitment of at least 60 days of 10-hour study sessions.
  • Some participants argue that completing all problems may be unnecessary, suggesting that practice should focus on understanding concepts rather than repetitive problem-solving.
  • There is a distinction made between different types of textbooks, with one participant asserting that books like Stewart may not require solving all problems, while books like Apostol or Spivak may offer varied problems worth completing.
  • One suggestion is made to adopt a healthier study approach, recommending 3 hours of study per day instead of 10 hours, emphasizing quality over quantity in problem-solving.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and effectiveness of completing all problems in a Calculus textbook. There is no consensus on the best approach to studying or the time required to complete the problems.

Contextual Notes

Participants note the variability in problem types across different textbooks and the potential for diminishing returns in solving repetitive problems. The discussion reflects a range of assumptions about study habits and problem-solving strategies.

Blue and green
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Hello,
If I worked at intervals of 10 hours every day, how long would it take for me to complete every problem in a Calculus textbook (Calculus I, II, and III)? I've taken Trigonometry and Pre-Calculus and received A's there. I am above average in skill in math.
- Blue
 
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Blue and green said:
Hello,
If I worked at intervals of 10 hours every day, how long would it take for me to complete every problem in a Calculus textbook (Calculus I, II, and III)? I've taken Trigonometry and Pre-Calculus and received A's there. I am above average in skill in math.
- Blue
IDK. How many problems are there in a Calculus textbook? Do you promise to work 10 hours a day, every day, no matter how long it takes to get done, no backsies?

What you are asking is incredibly vague.
 
There are 15 chapters. About 7 sections each, and of each section there are at least 70 to 80 problems. I'm asking people who have done it before or are familiar with the task. I have the time, and dedicated persistence to do it. So, yes, I suppose I promise.
 
Blue and green said:
There are 15 chapters. About 7 sections each, and of each section there are at least 70 to 80 problems. I'm asking people who have done it before or are familiar with the task. I have the time, and dedicated persistence to do it. So, yes, I suppose I promise.

Why is that necessary though? Practice is good, but you really don't need to do 70+ problems for every single lesson in the book.
 
Is this a book like Stewart? In that case, doing all problems is absolutely useless and repetitive. Doing some problems is good sure, but after you demonstrated the ability to solve problems, you don't really need to do problems of the same type again.
If this is a book like Apostol or Spivak, then the problems are varied enough that all are worth it. (Although you can definitely get a good grasp on the books without doing all problems).
 
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Alright, so let's answer your actual question. Assume that you solve each problem in 5 minutes (the earlier problems will be solved much earlier, but the later problems become much more time intensive, so I guess it's a good lower bound). You are looking towards 7000 problems, so if you do 10 hours a day, then you are working for at least 60 days (and most likely double that).
 
It's really not necessary or even beneficial to do this. Exercises in calculus books are typically broken apart into groups. These groups often have several very simple examples, some intermediate examples, and some more complicated examples. I often skip over the easier ones, or perhaps just mentally run through the process of solving them. It's important to distinguish between conceptual understanding and repetition from memorization. If one has a solid conceptual understanding of a topic and has the ability to carry out more complicated tasks within that topic, there's really no need to go back and practice the basics.
 
Blue and green said:
Hello,
If I worked at intervals of 10 hours every day, how long would it take for me to complete every problem in a Calculus textbook (Calculus I, II, and III)? I've taken Trigonometry and Pre-Calculus and received A's there. I am above average in skill in math.
- Blue
Do something healthier: Study 3 hours per day, six or seven days a week, and do as many problems in each section until you either know the section to your satisfaction or have had enough to move onward to the next section. You should find that your mind is still on Calculus while you are resting, doing something else.
 

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