Where Can I Find Challenging Math Puzzles for Calculus 2 and Beyond?

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Discussion Overview

The discussion revolves around finding challenging math puzzles suitable for someone at a Calculus 2 level and beyond. Participants share various resources, suggestions, and personal experiences related to math puzzles, competitions, and problem-solving strategies.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses a desire for creative math puzzles beyond standard assignments, referencing Richard Feynman's interest in such puzzles.
  • Several participants suggest looking into Math Olympiad problems and Putnam competitions as potential sources of challenging problems.
  • Some participants mention the appeal of problems that seem complex but become simpler with a change in perspective, as discussed by 3Blue1Brown.
  • There are suggestions to explore AP Calculus books and online resources like mathispower4u.com for a range of math topics and problem-solving videos.
  • One participant notes that they find some suggested problems too advanced for their current level, raising concerns about their math abilities.
  • Another participant discusses the importance of understanding fundamentals, suggesting that a lack of foundational knowledge might hinder problem-solving skills.
  • Discussions about prime numbers introduce complex problems related to the prime counting function and the Riemann hypothesis, highlighting the beauty and difficulty of such topics.

Areas of Agreement / Disagreement

Participants generally agree on the value of exploring various resources for challenging math problems, but there is no consensus on which specific sources are the best or most suitable for the original poster's needs. Some express uncertainty about their own abilities in tackling the suggested problems.

Contextual Notes

Some participants mention feeling overwhelmed by the difficulty of certain problems, indicating a potential gap between their current understanding and the challenges presented. There is also a discussion about the varying levels of difficulty in different math competitions and resources.

Who May Find This Useful

This discussion may be useful for students looking for challenging math puzzles, educators seeking resources for advanced problem-solving, and anyone interested in exploring creative approaches to mathematics beyond standard curricula.

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  • #32
Any other problem sources? I like to have as many wells of problems as possible.
 
  • #33
How many problems have you worked on so far? It seems pointless to keep searching if you aren't actively working on them.
 
  • #34
jedishrfu said:
How many problems have you worked on so far? It seems pointless to keep searching if you aren't actively working on them.
I've solved two Putnam problems, but I'd like to find problems that are ponderable and help foster original thinking. More puzzle focused problems.
 
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  • #35
  • #36
The reason I posted this thread was because recently I have felt strangely around math. Over the years I've been called exceptionally good at math by most of my teachers, but for some reason lately I've felt slow and unimaginative. I can't quite tell if this is just my brain annoying itself, or if I lost something I had before or if I ever even had something. I've also found the problems i've been assigned pretty boring. What have you guys done in your experience with this?
 
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  • #37
Interdimensional said:
The reason I posted this thread was because recently I have felt strangely around math. Over the years I've been called exceptionally good at math by most of my teachers, but for some reason lately I've felt slow and unimaginative. I can't quite tell if this is just my brain annoying itself, or if I lost something I had before or if I ever even had something. What have you guys done in your experience with this?
Can you give an example so that we can know what you mean when you say "math"?
 
  • #38
Recently with problems that require more creative and original thinking I feel like I've been less capable than I used to be. Kind of like a brain fog.
 
  • #39
Interdimensional said:
Recently with problems that require more creative and original thinking I feel like I've been less capable than I used to be. Kind of like a brain fog.
That's not an example. You could likewise tell your age, your level of education, and your goals. Are we talking about graduated math or highschool math?
 
  • #40
What do you mean by example? A specific problem? Or an area of math? EDIT: I see your edit.
 
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  • #41
Interdimensional said:
What do you mean by example? A specific problem? Or an area of math?
Different levels of education (high school, college, undergraduate, graduate) require different skills.
Different areas in mathematics (geometry, calculus, algebra) require different skills.
Different goals (hobby, school, study, research) require different skills.
 
  • #42
fresh_42 said:
Different levels of education (high school, college, undergraduate, graduate) require different skills.
Different areas in mathematics (geometry, calculus, algebra) require different skills.
Different goals (hobby, school, study, research) require different skills.
Oh I see. So your saying that different areas of math and education and goals require different skills. That's comforting to know. I partially thought I was losing my mind.
 
  • #43
Currently I'm in Calculus 2 but in a high school class. Eventually I'd like to get into physics research.
 
  • #44
Interdimensional said:
Currently I'm in Calculus 2 but in a high school class. Eventually I'd like to get into physics research.
Could you give us an idea of what topics you've covered in Calculus 2? Just make a list.

-Dan
 
  • #45
Sure.

Calculus 1 - of course

Calculus 2 - numerical integration, which we skipped in calculus 1 and went back around to, integration of natural logs and exponential functions, trigonometric integration, and starting integration and differentiation of hyperbolic functions.
 
  • #46
My math teacher used to say: "Everybody can differentiate but it takes an artist to integrate."

Means for us ordinary people: practice, practice, practice. Learn trick after trick: Weierstraß substitution, additive symmetry, multiplicative symmetry etc.

I like this book for that purpose:
https://www.amazon.com/dp/0846407612/?tag=pfamazon01-20

... but it seems that it is currently unavailable or very expensive. However, there are similar ones. Just look for a) a Russian author and b) written between 1950 and 1970. These criteria guarantee that you find a book close to real problems with numbers and techniques e.g. integration. The soviet study of mathematics was primarily targeted to create engineers.
 
  • #47
Interesting. I have always found integration to be a more enjoyable process than differentiation. I've heard similar things about Hungarian mathematics books as well. Are there any translation difficulties I should know about?
 
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  • #48
Interdimensional said:
Interesting. I have always found integration to be a more enjoyable process than differentiation. I've heard similar things about Hungarian mathematics books as well. Are there any translation difficulties I should know about?
The book I linked to is in English. It contains example after example, so it's not a textbook to study calculus.
 
  • #49
Take a look at the Project Euler problems, too. There is a variety of difficulties. Many of the problems are computing based, but you have to figure out how to set up the math for the computer to get the correct answer.
 
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  • #50
The Art of Problem Solving Volumes 1 and 2 cover basic algebra, geometry, and precalculus, but the problems are challenging enough to take you to the contest level.
When you take Linear algebra, look at Halmos' Problem Book
For interesting integration problems, watch blackpenredpen (and of course try to work out the problems before he does. For books on integration, see Inside Interesting Integrals by Nahin, Irresistible Integrals by Boris and Moll, and (Almost) Impossible Integrals by Valean

Are you in the US, @Interdimensional ? What grade are you in?

Do you want physics problem books as well?
 
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