1. muchas_gracias Aug 13, 2024 parent

   My ex lost 80 pounds and went from unable to run to running ultras and she found that she had to alternate between walking and running in the beginning to keep her heart rate in the lower thresholds. On the converse side, maybe integrating some strength training or speed workouts or stair climbs will help you develop a strength reservoir to make it easier to run at a low heart rate.

   Now that you've recognized how gentle a low heartrate feels I'm sure a conversational pace is totally adequate for staying under your lactic threshold (but if you could sing you're going too slow!)

2. muchas_gracias Aug 5, 2022 parent

   The Elements of Style by Strunk and White is a short book of "rules" about style which boil down to making every word, letter, and punctuation mark "tell." I believe it to be essential to begin writing clearly and effectively.
3. muchas_gracias Jul 28, 2022 parent

   Have you considered getting a textbook and its solutions manual and then just trying to do all the problems? When you find yourself stuck you can turn to Khan Academy or whatever for the particular concept. I just find that lectures aren't as effective as working problems until you're stuck.
4. muchas_gracias Jul 28, 2022 parent

   As a former child from the US, my only recommendation is not to take the US school system too seriously. Every state has a different system which is further broken down into subsystems where the quality of education can be completely different. 20 years ago the standard quality of math education was terrible where I grew up, I spent my whole life trying to find resources that were outside of the system. And when I was a teachers assistant during university I was often surprised how little math the students knew. That being said, find a textbook on algebra with a solutions manual and do all the exercises. If you can't figure out an exercise use online tutorials or lectures to make sure you understand all the concepts. If you can figure out all the rules and tricks of algebra you'll have a more solid foundation than a huge proportion of American university students and you'll be ready to apply them to the other fields of math you want to study.

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