Science and Inquiry discussion

Hi, everyone! I decided to create my first post in this group! Feel free to answer the question! :D

Algebra.

Betsy wrote: "Algebra."

Oh hey, that's mine, too! I actually wrote a series of poems called Algebra Club in one of my books, and I had a love relationship with the etymology of the term algebra, which I also wrote about in the same book. XD

Probably geometry

Euclidean geometry is mine. I use it frequently in woodworking & construction. I'm no whiz, but just the basics makes so many projects easier.

Jim wrote: "Euclidean geometry is mine. I use it frequently in woodworking & construction. I'm no whiz, but just the basics makes so many projects easier."
That's so cool! I really love it when math can be applied in real life. Pure mathematics is still cool, but applied mathematics is incredibly relevant!
What kind of concepts in Euclidean geometry do you use?

Jill wrote: "Probably geometry"
Why do you like geometry, Jill?

Lucy, things like equal diagonals for a rectangle & complementary angles are the most used. Woodworking today is often based on measurement with a ruler & protractor, but that wasn't the case before the middle of the 19th century. For most of our history, construction was done By Hand & Eye ( reviewed here) using constructions & proportions. Since I usually use nonstandard sized wood (rough wood direct from the tree, not commercially sold) I find the old methods work better for me. They also fit in with Roy Underhill's wonderfully instructive books.

Jim wrote: "Lucy, things like equal diagonals for a rectangle & complementary angles are the most used. Woodworking today is often based on measurement with a ruler & protractor, but that wasn't the case befor..."

Awesome! Yeah, learning the properties of certain shapes can be helpful for stuff like that.

Lucy wrote: "Jill wrote: "Probably geometry"
Why do you like geometry, Jill?"

The visual quality. And I’m a sucker for dimensions. the local 3, and the theoretical

Jill wrote: "Lucy wrote: "Jill wrote: "Probably geometry"
Why do you like geometry, Jill?"

The visual quality. And I’m a sucker for dimensions. the local 3, and the theoretical"
Cool. I prefer algebra over geometry, but geometry is worth remembering. Since it is visual, as you said, there is a little creativity. I remember when my teacher was reviewing geometry basics for math, and there were problems that would say you would have to draw something based on certain criteria. The problems were very simple, but it was cool to have an excuse to draw on your homework. 😂
I especially like the proofs. You cannot just say that something looks congruent. You actually have to know for sure that the criteria for a certain congruence postulate are fulfilled. For instance, if you found two triangles who had two sides marked congruent, but their included angles were not marked congruent, you cannot just say that the triangles are congruent by the side-angle-side postulate simply because you think the angles look congruent. There has to be some kind of proof that the angles are congruent, so that you know that the sides AND the included angle are congruent.

I like the proofs too😆.
You can definitely get into a good rhythm with algebra. I probably like actually doing algebra than the doing of geometry🤣- it’s just pretty. But if it’s down to the pure act of doing, for some reason it’s long division for me. I used to forgo the calculator in high school physics…

Good topic for discussion. I like algebra. Everything is balanced in it and has an answer to every question. Sometimes, learning this science has certain difficulties for me. But I've found a way to solve it. My joys were boundless. Because when you do it, and it doesn't work out, it breaks you a little. So, to avoid that feeling, I've found this platform https://plainmath.net/post-secondary/... where I can get answers to the crucial questions. I try to do my best as I really like this subject, and I'm happy that there are resources where I can get support and help to understand everything.

As a mathematician, I have perhaps a different point of view. All of the fields of math blend together to a much greater extent than most students learn in the classroom. Algebraic geometry: a blend of algebra and geometry. Analytic number theory: a blend of calculus and number theory. Three-dimensional topology: a blend of geometry and topology. The list could go on. The most successful mathematicians have generally been the ones who were able to import ideas from one discipline to another. Read, for example, about Bill Thurston, who transformed topology by bringing in ideas from hyperbolic geometry, previously a sort of mathematical backwater.

When you are a student, I think it's inevitable that you will prefer one branch of mathematics to another, but just be aware that the dividing lines are somewhat artificial. You'll appreciate math the most when you can see it as one seamless continuum.

[Can I put in a small plug for my books? I write a series of books for the American Mathematical Society called "What's Happening in the Mathematical Sciences," http://www.ams.org/publicoutreach/mat..., which might be a good place for students to learn about the broader picture of mathematics.]

Dana wrote: " but just be aware that the dividing lines are somewhat artificial. You'll appreciate math the most when you can see it as one seamless continuum."
Ooh, that's a nice way of putting it!


I feel that I like calculus the best though.
I'm not the best at maths and algebra has confused me a lot in the past. I'm studying Engineering and learning calculus made a lot of maths and physics very intuitive for me.
It gave me a broader angle to see things through in general, that's why I like it.

My favorite is applications of Bayes Theorem: Tracking, AI, machine learning, fraud detection, medical diagnosis, weather forecasting, stock market analysis.