Learning Mathematical Problem Solving

[tuxscholar]

So far it seems to be the case that to learn math one inevitably needs to learn problem solving for the sake of developing mathematical intuition. I tried to solve some elementary level algebraic math problems on my own especially as discussed in the book elements of algebra by Euler, but i still find most of the time clueless to solve even problems whose concepts I've previously learned and constantly referring back and forth to find the proper solution. I realized that first of all i need to develop mathematical problem solving skills in a more comprehensive way. So for that purpose I've decided to work with these books in specific order :
For elementary coverage : Welchons Algebra, Geometry by Keiselev and Gelfands works in Basic Mathematics

Then for having a decent ground in mathematical problem solving :

• How to Solve It by George Polya
• Mathematics and Plausible Reasoning by George Polya
• The Art and Craft of Problem Solving by Paul Zeitz
• Problem Solving Through Problems by Loren Larson
• Problem-Solving Strategies by Arthur Angel
• Geometry Revisited by Coxeter & Greitzer
• Putnam and Beyond by Gelca & Andreescu
• Winning Ways by Berlekamp, Conway & Guy
• Problem Solving Through Recreational Mathematics by Bonnie Averbach et al.

Do anyone struggling with problem solving in math? How they manage to develop a decent intellectual grounding when it comes to problem solving of various kinds of mathematical topics?

 

[PeroK]

So far it seems to be the case that to learn math one inevitably needs to learn problem solving for the sake of developing mathematical intuition. I tried to solve some elementary level algebraic math problems on my own especially as discussed in the book elements of algebra by Euler, but i still find most of the time clueless to solve even problems whose concepts I've previously learned and constantly referring back and forth to find the proper solution. I realized that first of all i need to develop mathematical problem solving skills in a more comprehensive way. So for that purpose I've decided to work with these books in specific order :
For elementary coverage : Welchons Algebra, Geometry by Keiselev and Gelfands works in Basic Mathematics

Then for having a decent ground in mathematical problem solving :

• How to Solve It by George Polya
• Mathematics and Plausible Reasoning by George Polya
• The Art and Craft of Problem Solving by Paul Zeitz
• Problem Solving Through Problems by Loren Larson
• Problem-Solving Strategies by Arthur Angel
• Geometry Revisited by Coxeter & Greitzer
• Putnam and Beyond by Gelca & Andreescu
• Winning Ways by Berlekamp, Conway & Guy
• Problem Solving Through Recreational Mathematics by Bonnie Averbach et al.

Do anyone struggling with problem solving in math? How they manage to develop a decent intellectual grounding when it comes to problem solving of various kinds of mathematical topics?

Isn't the idea that you pick one book and work through that? You can't need all those books.

 

[tuxscholar]

Isn't the idea that you pick one book and work through that? You can't need all those books.

Indeed, that is quite a decent idea. After all there is no royal road to mathematics one can do nothing better than wrestling with plenty of problems painstakingly with exhaustive efforts and deliberation. Thank you.

 

[MidgetDwarf]

Read topic. Follow examples with paper and writing tool. Ask why such and such line is true.
Finish topic. Go to exercises. Do a few until you get stuck. Think of why you are stuck. Do problems(mainly techniques) used to solve other problems help? If so, solve it and proceed to next problem. If not, throw kitchen sink at problem. If you solve it, continue on to next. If not, go back to reading topic. Rinse and repeat the above algorithim.

 

[MidgetDwarf]

Although keiselev both books are excellent. I would have found them extremely difficult to study from them on my own when I was first learning mathematics. If it works for you great. If not. Find another book.

 

[gleem]

Did you have any issues with math before college?

 

[tuxscholar]

Did you have any issues with math before college?

Well I'm not studying math in college, but for the sake of perceiving the beauty of the subject and to contribute something worthwhile in the realm of mathematics. But so far when it comes to do problems i always felt a sense of intellectual friction which most of the time leads me to procrastinate learning mathematics so to tackle that I'm solely focusing on having a decent grasp in the act of probelm solving thoroughly.

 

[gleem]

So you are trying to study math on your own. I think this would be challenging for most people and would benefit greatly from having a teacher to guide and act as a model for them. The teacher provides a structure to follow and helps you avoid pitfalls. The teacher provides a cadence for your progress, forcing you to keep pace during your learning. By yourself, you may get discouraged and frustrated pershaps developing behaviors that are counterproductive.

You did not say if you have taken advantage of the multitude of videos online, from which you can see how math is done, including those on physics. Not everybody can learn math from books and benefit from them to the same degree.