For real world problem solving, a 32 or 64-bit processor is easier. But for learning it doesn't make any difference. In fact the limited size of 8-bit is an educational advantage as the programmer is forced to deal with overflow rather than just ignoring the possibility. You can work on interesting problems like "write the code to multiply two 16-bit values". I find these sort of problems an excellent way to start learning assembly language.
While 8-bit processors take multiple cycles per instruction, the number of cycles is usually fixed. On superscalar pipeline processors it is very difficult for the programmer to predict the performance without profiling.
Looking back at what I studied in my EE degree in the early 90s, my first introduction to assembly language and hardware was with the 6809. Then I moved on to the 68000. I am probably biased but I think starting with 8-bit then moving to a simple 32-bit architecture is a good introduction to computer hardware.
Another problem with these incentives to attract new users is how do you think existing users feel when they see discounts offered to new users? Their loyalty is rewarded by paying full price.
I may be the outlier but I have almost no interest in new user incentives. I know the discount will only last a short while before I am paying full price so I never factor the discount into the total cost of using the service.
Even free trials don't interest me as there is still the hassle of signing up and remembering to cancel before the trial ends. Why bother signing up for something that I intend to cancel a month later? If I intend to keep using the service then as I said above, the discount is meaningless in the long term.
This is a great resource. I'm slowly relearning my engineering maths from 30 years ago. It is good to have source of problems to work through.
A couple of suggestions.
1. It would be nice to be able designate one of the comments as the best answer rather than have to wade through a lot of comments to find the solution.
2. I find the name "Teach Yourself Math" a bit misleading. The names suggests that the site provides a structured introduction to math much like a textbook, not a bunch a math problems that require some existing knowledge to work on. Some of this expectation comes from associating the "Teach Yourself" name with the Teach Yourself series of books intended for self learners.
I've avoided Alexa for years. I've never had any interest in anything voice controlled. Anyway one day at the Amazon checkout, Amazon wanted to sell me an Echo Pop for I think it was $20. I figured I'll give it a try, I can afford to lose $20 and not be too grumpy about it.
I found the whole experience very underwhelming. Alexa frequently misunderstood me. At one time I tried asking it to play a particular type of music and it said I require a subscription. I tried some of the skills and they were total garbage. And then there are the privacy issues. I live alone so I was not too concerned but I would always make sure it was off before using the phone.
The only thing I would really want to use a product like Alexa for and pay for it with a subscription is if I could use it for language learning. But my bar for this is very high. I'm not interested in something that just feeds me phrases to learn. It would need to combine the capabilities of ChatGPT with the ability to adapt its output to my level, provide useful feedback, and have excellent voice recognition for bad accents and the ability to suggest improvements to my pronunciation and grammar. I don't see this happening any time soon.
They do this with hard drives as well. The first and last time I ever purchased hard drives from Amazon, the two drives arrived in an oversized box with no protection other than the antistatic bags they were in. I sent them back but I'm sure they'll just sell them to someone else.
Most of the time my Amazon books have arrived in good condition mostly due to sheer luck given the way they were packed. Sometimes a hardcover had a dented corner or a paperback had a bent spine. Not worth the hassle of returning and reordering (especially if the price went up since ordering as Amazon refuses to honor the original price). I do miss Book Depository as they would ship each book individually even when I ordered multiple items.
These days I try to avoid Amazon but keep getting sucked in when the price + shipping is cheaper or I can't be bothered creating an account on a website I have not used before.
You would normally use a library to create the PDF so you don't need deal with the complexity of the format. A library would likely provide a function for drawing circles that translates the circle into Bézier curves.
I've recently made a habit of labeling power adapters with the device it belongs to. Too often I have wanted to use an old device I have not used for a few years, then had to go through my box of old power adapters trying to match up the plug, voltage, and current to the device in hand.
I don't think being able to monitor my blood pressure at any random time as useful. As my doctor explained to me, the studies that determine what is the normal BP range obtain the measurements after the patient has been sitting in a relaxed environment for around 15 minutes. This is something I need to schedule once or twice a week to check that my hypertension is under control.
If I were to start taking measurements at random times, such as while walking or watching an action movie, the results would be misleading as they were not obtained under the same conditions as the gold standard measurements.
I would also question how accurate these new devices are. I used to use a wrist cuff BP monitor but one day I took it into the doctor's office and did a side by side comparison with my doctor's BP monitor. My wrist cuff BP monitor was reading about 20mmHg too low. I thought I had my hypertension under control but it wasn't. I've since replaced it with an arm cuff BP monitor. If I have to go to the effort of sitting and relaxing for 15 minutes to obtain a measurement, attaching an arm cuff is not much of an inconvenience.
I just tried out Yandex Translate on a few words. My only criticism is I find the audio playback too fast. Google Translate plays the audio at a slower rate which I find easier for learning the pronunciation of foreign words.
While 8-bit processors take multiple cycles per instruction, the number of cycles is usually fixed. On superscalar pipeline processors it is very difficult for the programmer to predict the performance without profiling.
Looking back at what I studied in my EE degree in the early 90s, my first introduction to assembly language and hardware was with the 6809. Then I moved on to the 68000. I am probably biased but I think starting with 8-bit then moving to a simple 32-bit architecture is a good introduction to computer hardware.