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BadgerBadger92
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I’m teaching myself algebra right now so I’m not at that point, but I was wondering when I finish algebra what should I study next? Trig or Geometry?
... in order to ...?BadgerBadger92 said:I’m teaching myself algebra right now so I’m not at that point, but I was wondering when I finish algebra what should I study next? Trig or Geometry?
Depends on what you mean by Euclid. Euclidean geometry is fundamental to classical physics. Euclid's elements are not. They are a treatise of geometry by axioms, compass, and ruler. This was my interpretation of your distinction between trig and geometry. Trigonometry means literally "three angles", i.e. triangles. They are necessary for vector calculus, i.e. forces, and they are the origin of the trigonometric functions that are of tremendous importance. Now, that is geometry - at least the version that deals with computations. Since you made a distinction to geometry, I interpreted it as the constructional part of geometry: compass, ruler, and Euclid's elements. I don't think there is any use in the ability to construct a ##17##-gon in a circle with a compass and a ruler. And apart from the uselessness, I can tell you from my own experience that the errors you make with your pencil and compass build up to a veritable gap at the end of the construction.BadgerBadger92 said:Why should I stay clear of Euclid?
You do not "finish algebra". One course sequence you can use, which is good, is Introd. Algebra, Intermed. Algebra, Trigonometry.BadgerBadger92 said:I’m teaching myself algebra right now so I’m not at that point, but I was wondering when I finish algebra what should I study next? Trig or Geometry?
Something like that. And some institutions had an arrangement like this:jtbell said:More than 50 years ago, this was the sequence my school system followed, for students in the "accelerated" track:
8th grade: Algebra I
9th grade: Algebra II
10th grade: Geometry (Euclidian)
11th grade: Trigonometry and analytic geometry
12th grade: Calculus (basics of differentiation and integration)
Malawi_Glenn raised a good point. The OP has continuously made threads asking the same question. Has received various insightful post, but the OP for whatever reason, keeps asking the same question over and over.malawi_glenn said:Kinda depends on what you mean by geometry and trigonometry. They are related.
Isn't this like your 10th time asking this or a similar question?
I dislike Clifford and Boolean for a reason, but the rest are ok.malawi_glenn said:its like asking "I want to learn algebra", what kind of algebra?
The irony is that if he engaged with this three years ago (or is it more?) that he'd be done now.malawi_glenn said:Isn't this like your 10th time asking this or a similar question?
If, by classical geometry, all you mean is constructions with a compass and a straightedge, I'll agree, but in my high school geometry course, we learned more than just that, like the basic structure of a proof, etc. I find one of the biggest stumbling blocks for intro physics students is analyzing the geometry in a problem, like recognizing when two angles are equal or when two triangles are similar. I recall most of this material was covered in high school geometry, not in algebra or trig.fresh_42 said:I dare to claim that someone, whose goal is to learn phýsics and the mathematics needed for it in self-study does not need to learn classical geometry. This would be a total waste of time. You can afford such as a kid, but not so much afterward. Some give advice along the lines of "one fits all". To be able to construct a perpendicular line with a compass is useless. One needs Thales, Pythagoras, and the intercept theorems, if at all. And Pythagoras comes automatically with the cosine theorem in trigonometry.
As I said, intercept theorems.vela said:If, by classical geometry, all you mean is constructions with a compass and a straightedge, I'll agree, but in my high school geometry course, we learned more than just that, like the basic structure of a proof, etc. I find one of the biggest stumbling blocks for intro physics students is analyzing the geometry in a problem, like recognizing when two angles are equal or when two triangles are similar. I recall most of this material was covered in high school geometry, not in algebra or trig.
Do students and teachers continue to ignore that? And if yes, then maybe that's because of something like, "when are we really going to use this or need to know this?"vela said:If, by classical geometry, all you mean is constructions with a compass and a straightedge, I'll agree, but in my high school geometry course, we learned more than just that, like the basic structure of a proof, etc. I find one of the biggest stumbling blocks for intro physics students is analyzing the geometry in a problem, like recognizing when two angles are equal or when two triangles are similar. I recall most of this material was covered in high school geometry, not in algebra or trig.
Students and teachers seldom construct syallabus and curicula at this levelsymbolipoint said:Do students and teachers continue to ignore that? And if yes, then maybe that's because of something like, "when are we really going to use this or need to know this?"
My personal experience was that 'Pure Geometry' was my way into Maths. It was fun for me and I was fairly successful at it in School. It gave me confidence for the less visual parts of Maths. I don't know how I would have progressed without it.fresh_42 said:I dare to claim that someone, whose goal is to learn phsýsics and the mathematics needed for it in self-study does not need to learn classical geometry. This would be a total waste of time.
Ignore what?symbolipoint said:Do students and teachers continue to ignore that?
What @vela said. This:vela said:Ignore what?
If, by classical geometry, all you mean is constructions with a compass and a straightedge, I'll agree, but in my high school geometry course, we learned more than just that, like the basic structure of a proof, etc. I find one of the biggest stumbling blocks for intro physics students is analyzing the geometry in a problem, like recognizing when two angles are equal or when two triangles are similar. I recall most of this material was covered in high school geometry, not in algebra or trig.
sophiecentaur said:My personal experience was that 'Pure Geometry' was my way into Maths. It was fun for me and I was fairly successful at it in School. It gave me confidence for the less visual parts of Maths. I don't know how I would have progressed without it.
Theoretically. In fact, you have to calculate the remaining time, speed of learning, and goals you can achieve within these parameters. That caused my objections against classical geometry and proof writing on a late way to understand physics. We are talking about an optimization problem, not an ideal world.sophiecentaur said:You can't know too much!
This is only funny when you're young. I studied mathematics and probably do have the requirements to e.g. learn GR or QM. Truth is, it costs me meanwhile an enormous effort to learn the new language! My algebraic mindset doesn't want to learn the physicists' coordinate acrobatics anymore. This means: it makes a significant difference if I was asking for a way to understand GR or QM or a student the age of 18. I would definitely expect a different answer.sophiecentaur said:It reminds me of the Larsen cartoon with the student saying "My brain's full, can I go home?"
This topic? No. You can search the forums. I might have asked about books a few times. Please don’t be angry.malawi_glenn said:Kinda depends on what you mean by geometry and trigonometry. They are related.
Isn't this like your 10th time asking this or a similar question?
I haven’t had the time because I have a full time job.Vanadium 50 said:The irony is that if he engaged with this three years ago (or is it more?) that he'd be done now.
One year ago.Vanadium 50 said:The irony is that if he engaged with this three years ago (or is it more?) that he'd be done now.
Don't take those comments seriously. They all assume an environment that possibly doesn't match reality.BadgerBadger92 said:One year ago.
(... and as the probability is not always on the side of the truth, it happened ...)Heinrich von Kleist - Michael Kohlhaas - 1810 said:... und wie denn die Wahrscheinlichkeit nicht immer auf seiten der Wahrheit ist, so traf es sich ...
Yeah, I’ve noticed a lot of people on forums aren’t exactly the nicest people.fresh_42 said:Don't take those comments seriously. They all assume an environment that possibly doesn't match reality.(... and as the probability is not always on the side of the truth, it happened ...)
No one is being mean...BadgerBadger92 said:Yeah, I’ve noticed a lot of people on forums aren’t exactly the nicest people.
I simply forgot I asked.MidgetDwarf said:No one is being mean...
You keep posting the same question, expecting different answers.
Too hard to learn Trigonometry that way. A separate course before starting Calculus is more typical and easier.vanhees71 said:I'd study calculus first, because then you can introduce the trigonometric functions via their power series and derive all their properties, then linear algebra, and finally geometry in analytic form.