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.