In the 1960s, Kosmos made the best electronics sets available. If you went through the kits, you received a complete undergraduate course in electronics (less the calculus).
There ought to be something similar for calculus too. While a detailed and formal treatment of the subject can be delayed till the age at which it's introduced now, I feel that the intuition and feel for calculus can be formed more efficiently at an earlier age.
If nothing else, it may help them understand where to seek solutions for the common problems they encounter. I started learning Electronics at a fairly young age using undergraduate level textbooks that I found lying around. The need for and relationships between concepts in calculus, logarithms and trigonometry were a recurrent problem for me.
PS: If anybody is wondering, those books were from an earlier generation engineer. They were very interesting, to say the least. All the circuits (amplifiers, rectifiers, oscillators, multivibrators, mixers, various RF Txr and Rxr designs, etc) were using vacuum tubes! Diodes, triodes, pentodes, thyratrons, magnetrons, TWTs, etc were used liberally in them. It had a description of an early form of the Instrumental Landing System (ILS). There were also descriptions of some early generation semiconductor devices and their similarity to vacuum tubes. I don't think ICs were in much use back then, because the book had no mentions about them.
I used to spend hours at a time with those books when I was a child. Later I graduated in Electronics engineering and went on to work on the avionics for a satellite launcher. Vacuum tubes were museum pieces by the time I was born. But I was the only one in my undergraduate class who had seen or knew anything about vacuum tubes, when we had lessons on CRTs, magnetrons, etc. I can't stress how deeply those books influenced my education and career. Sweet memories!
> The need for and relationships between concepts in calculus, logarithms and trigonometry were a recurrent problem for me.
Oh my gosh, this was me growing up! I loved tinkering with electronics and programming, but I kept bumping against my lack of knowledge wrt more advanced math topics. I usually hacked around it, or more often just switched to a different project.
Now that I'm taking calculus, I feel like I always have a corresponding application for each topic we cover. It's very exciting!
> Now that I'm taking calculus, I feel like I always have a corresponding application for each topic we cover. It's very exciting!
Mathematical concepts need not necessarily have any practical or real-life applications (pure mathematics), but it's a worthy pursuit on its own. However, every maths concept we learn outside of specialized mathematics courses have some application (applied mathematics). That's how these courses are designed.
It's funny when some people lament that much of the mathematics they learned at school or uni/college have no real-life applications! I wonder what they think about why they learned it. It also shows a big problem with math education and pedagogy. Many people are sailing without a destination in mind, hoping that they'll just hit some land in the future. The academic practice of mathematics has turned into the drudgery of endless symbolic manipulation.
But at the same time, people like you who lean into creativity, hit the limits of their mathematical knowledge early. For them, the problem isn't that the mathematics they learned have no applications. It's that they don't know where to look for the mathematics they need. Here is the failure of math education. If everyone was taught about the different branches of Mathematics, how they relate to each other and where they're applied, I can guarantee that many students will learn those on their own before they're formally introduced to them. That would enable the talented and interested students to shape their own destiny.
> Mathematical concepts need not necessarily have any practical or real-life applications (pure mathematics), but it's a worthy pursuit on its own.
I guess I always had a sense that this was true, but taking a formal proofs class has really opened my eyes to how true this is. I'm actually planning on doing abstract algebra because I've enjoyed proof writing a ton!
> It's that they don't know where to look for the mathematics they need. Here is the failure of math education.
This is a really interesting space imo, because I did try teaching myself calculus through 3blue1brown, who has super cool visualizations, but also isn't rigorous enough to apply it to complicated problems. On the other end, I also tried Khan Academy, but found it too abstract and hard to follow.
Perhaps that was just since I was 14 at the time, and now I'm better at symbolic reasoning. Yet, there's something so enticing about visualization, that I wish there was a way to have the rigour of set theory with the intuitiveness of visualization (that call is a big reason I love the work that dynamicland.org and folk.computer are doing right now).
> I'm actually planning on doing abstract algebra because I've enjoyed proof writing a ton!
That's interesting! I started with abstract algebra (on my own) because I don't know the proper sequence of learning it. I guess I will give proofs a try now.
> I did try teaching myself calculus through 3blue1brown, who has super cool visualizations, but also isn't rigorous enough to apply it to complicated problems. On the other end, I also tried Khan Academy, but found it too abstract and hard to follow.
> I wish there was a way to have the rigour of set theory with the intuitiveness of visualization
Agreed! Intuition and rigour are equally important in Mathematics. The hardest part is making these two meet at some point.
One such moment in my life was when I created a visual model of 3D vector calculus (divergence, curl, gradient, etc) and developed it far enough to explain all its rigourous treatment that I learned in my engineering class. Things just flowed from there. I suddenly gained the superpower to imagine up the explanations for phenomena like the skin effect, and then effortlessly derive their mathematical models.
They shouldn't teach calculus like they taught it to me and my peers. Basically we just one day started "differentiating" equations. We learnt a completely mechanical process. Like how to chop an onion, except it doesn't actually feed you or taste delicious.
It took me a while to realise the point. It's all about rates of change. They should start with that. No need to bother with the maths, just look at graphs and be like "that's a steeper slope than that", and, ooh, that one's sloping in the opposite direction. This is a fundamental intuition that's so useful to have. Most people don't understand that braking is acceleration. They just don't have the mental model that lets them see fuel burn and braking as opposite things. The sooner this intuition is there the better. Then teach the maths.
I wasn't around in the 60s but I had a chemistry set from Salter Science in the 80s and loved it. They had details on how to make simple glassware and so many other things. I didn't have carbon rods for the electrochemistry section but I managed to supplement the manual with another "science experiments book" and pulled out a few from spent batteries. Even synthesised a few simple salts based on my understanding of how things worked so that I could try out the "advanced" experiments from the book.
Modern chemistry sets are extremely lightweight and boring in comparison.
I figure it's fair enough, since this is a great but not free book, to drop https://www.allaboutcircuits.com/ - a truly amazing, and in my opinion extraordinarily well written and organized free learning resource.
Not a kid but what are the next steps after this book? I've been trying to find the steps of the ladder between "playing with muxes and clocks" and "designing a USB3 peripheral", but that has been a challenge in itself.
Is it me, or are hobby electronic shops much harder to find today, like the one that sells Arduino, basic RCL's, and common IC's? I am not sure if it's just a trend that everything is sold online or if the interest is shifting towards software.
60 comments
https://generalatomic.com/teil1/index.html
If nothing else, it may help them understand where to seek solutions for the common problems they encounter. I started learning Electronics at a fairly young age using undergraduate level textbooks that I found lying around. The need for and relationships between concepts in calculus, logarithms and trigonometry were a recurrent problem for me.
PS: If anybody is wondering, those books were from an earlier generation engineer. They were very interesting, to say the least. All the circuits (amplifiers, rectifiers, oscillators, multivibrators, mixers, various RF Txr and Rxr designs, etc) were using vacuum tubes! Diodes, triodes, pentodes, thyratrons, magnetrons, TWTs, etc were used liberally in them. It had a description of an early form of the Instrumental Landing System (ILS). There were also descriptions of some early generation semiconductor devices and their similarity to vacuum tubes. I don't think ICs were in much use back then, because the book had no mentions about them.
I used to spend hours at a time with those books when I was a child. Later I graduated in Electronics engineering and went on to work on the avionics for a satellite launcher. Vacuum tubes were museum pieces by the time I was born. But I was the only one in my undergraduate class who had seen or knew anything about vacuum tubes, when we had lessons on CRTs, magnetrons, etc. I can't stress how deeply those books influenced my education and career. Sweet memories!
> The need for and relationships between concepts in calculus, logarithms and trigonometry were a recurrent problem for me.
Oh my gosh, this was me growing up! I loved tinkering with electronics and programming, but I kept bumping against my lack of knowledge wrt more advanced math topics. I usually hacked around it, or more often just switched to a different project.
Now that I'm taking calculus, I feel like I always have a corresponding application for each topic we cover. It's very exciting!
> Now that I'm taking calculus, I feel like I always have a corresponding application for each topic we cover. It's very exciting!
Mathematical concepts need not necessarily have any practical or real-life applications (pure mathematics), but it's a worthy pursuit on its own. However, every maths concept we learn outside of specialized mathematics courses have some application (applied mathematics). That's how these courses are designed.
It's funny when some people lament that much of the mathematics they learned at school or uni/college have no real-life applications! I wonder what they think about why they learned it. It also shows a big problem with math education and pedagogy. Many people are sailing without a destination in mind, hoping that they'll just hit some land in the future. The academic practice of mathematics has turned into the drudgery of endless symbolic manipulation.
But at the same time, people like you who lean into creativity, hit the limits of their mathematical knowledge early. For them, the problem isn't that the mathematics they learned have no applications. It's that they don't know where to look for the mathematics they need. Here is the failure of math education. If everyone was taught about the different branches of Mathematics, how they relate to each other and where they're applied, I can guarantee that many students will learn those on their own before they're formally introduced to them. That would enable the talented and interested students to shape their own destiny.
> Mathematical concepts need not necessarily have any practical or real-life applications (pure mathematics), but it's a worthy pursuit on its own.
I guess I always had a sense that this was true, but taking a formal proofs class has really opened my eyes to how true this is. I'm actually planning on doing abstract algebra because I've enjoyed proof writing a ton!
> It's that they don't know where to look for the mathematics they need. Here is the failure of math education.
This is a really interesting space imo, because I did try teaching myself calculus through 3blue1brown, who has super cool visualizations, but also isn't rigorous enough to apply it to complicated problems. On the other end, I also tried Khan Academy, but found it too abstract and hard to follow.
Perhaps that was just since I was 14 at the time, and now I'm better at symbolic reasoning. Yet, there's something so enticing about visualization, that I wish there was a way to have the rigour of set theory with the intuitiveness of visualization (that call is a big reason I love the work that dynamicland.org and folk.computer are doing right now).
> I'm actually planning on doing abstract algebra because I've enjoyed proof writing a ton!
That's interesting! I started with abstract algebra (on my own) because I don't know the proper sequence of learning it. I guess I will give proofs a try now.
> I did try teaching myself calculus through 3blue1brown, who has super cool visualizations, but also isn't rigorous enough to apply it to complicated problems. On the other end, I also tried Khan Academy, but found it too abstract and hard to follow.
> I wish there was a way to have the rigour of set theory with the intuitiveness of visualization
Agreed! Intuition and rigour are equally important in Mathematics. The hardest part is making these two meet at some point.
One such moment in my life was when I created a visual model of 3D vector calculus (divergence, curl, gradient, etc) and developed it far enough to explain all its rigourous treatment that I learned in my engineering class. Things just flowed from there. I suddenly gained the superpower to imagine up the explanations for phenomena like the skin effect, and then effortlessly derive their mathematical models.
It took me a while to realise the point. It's all about rates of change. They should start with that. No need to bother with the maths, just look at graphs and be like "that's a steeper slope than that", and, ooh, that one's sloping in the opposite direction. This is a fundamental intuition that's so useful to have. Most people don't understand that braking is acceleration. They just don't have the mental model that lets them see fuel burn and braking as opposite things. The sooner this intuition is there the better. Then teach the maths.
https://www.worldofbooks.com/products/calculus-the-easy-way-...
> There ought to be something similar for calculus too.
mathacademy.com very thourough and highly effective.
Modern chemistry sets are extremely lightweight and boring in comparison.
That feeling when you hit the right spot on the crystal after stringing up a long antenna in your room…
Elenco continues to sell one of the kits that I used to have, less RadioShack branding.
Specifically https://www.allaboutcircuits.com/textbook/