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I have been semi-diligently (4-5 hours/week as adult life allows) following this approach coupled with working my way through math texts. Although I zero proble

by nootka 7y ago

I have been semi-diligently (4-5 hours/week as adult life allows) following this approach coupled with working my way through math texts. Although I zero problem grasping concepts and parsing propositions and examples, I find it very difficult to solve end-of-chapter problems. No more than 4 or 5 problems a week, and hence my advancement is agonizingly slow. I started with Spivak & Apostol but reverted to Riley and Hobson's Foundations text because I was struggling too much with the A&S's problems. Given that I did very well on symbolic-logic proofs in an undergrad course, I figured it would be easy enough to get into math if I had diligence and sincere interest. After having been a 'D' student, my recognition of arithmetic and algebraic expressions and manipulations is hopelessly sub-par. Even many of the R&H problems are beyond my grasp. My approach has been informed by a sincere desire to engage with mathematics (one I unfortunately did not have through my formal education) as well as several "How do I self-teach maths" threads on HN, Reddit, and /sci/. Previously I had chalked up my poor grades to an undisciplined, unmotivated youth. Now I'm beginning to suspect I may simply not have the requisite intelligence, or am at least outside the age where I had enough time and neuroplasticity to pick math up in earnest.

1e-9 7y ago
Given that 1) you have zero problem grasping the concepts and understanding the examples, and 2) your difficulty is in solving the end-of-chapter problems; I think it is almost certain that your issue is one of making small mistakes that throw off your solutions (for example, didn't change a plus to a minus sign, left off a term, made an incorrect assumption, etc.). You just need to learn how to double-check your work and figure out where you went wrong. This is a skill that everyone doing nontrivial math has to learn. In a formal learning environment, you constantly get feedback on your mistakes through the grading process, which you obviously don't get when self-learning. My advice is to work the example problems before looking at the solution. After you have worked it yourself, you can then easily see where you went wrong. You should also get books of solved problems that let you practice this more extensively. There are problem books for pretty much every undergrad math topic as well as some grad-level ones. A lot of textbooks even have solution manuals that will show you how to solve the end-of-chapter problems in the textbook. An Amazon search with the word "solutions" and whatever math topic you want should turn up many examples. With practice, you learn how to detect errors and rectify them even when there is no solution manual.

by nootka 7y ago

1e-9 7y ago

Given that 1) you have zero problem grasping the concepts and understanding the examples, and 2) your difficulty is in solving the end-of-chapter problems; I think it is almost certain that your issue is one of making small mistakes that throw off your solutions (for example, didn't change a plus to a minus sign, left off a term, made an incorrect assumption, etc.). You just need to learn how to double-check your work and figure out where you went wrong. This is a skill that everyone doing nontrivial math has to learn. In a formal learning environment, you constantly get feedback on your mistakes through the grading process, which you obviously don't get when self-learning. My advice is to work the example problems before looking at the solution. After you have worked it yourself, you can then easily see where you went wrong. You should also get books of solved problems that let you practice this more extensively. There are problem books for pretty much every undergrad math topic as well as some grad-level ones. A lot of textbooks even have solution manuals that will show you how to solve the end-of-chapter problems in the textbook. An Amazon search with the word "solutions" and whatever math topic you want should turn up many examples. With practice, you learn how to detect errors and rectify them even when there is no solution manual.