Geometry- where to start, how far to go?

[DS2C]

Currently I am face deep in three math books- my issued text for algebra, Schaum's Elementary Algebra, and Kiselev's Book I (Planimetry).

I love the stuff so far and want to be as knowledgeable as possible for when I can declare my major to Physics. One thing I know for sure is that algebra and trigonometry are absolutely essential not just for calculus but for physics in general. But can the same be said for geometry (I know that trigonometry entails geometry, but not sure to what level geometry is needed)?

Without going into too much detail, I know jack squat about geometry other than what I've read so far in Kiselev's book. I want to learn this stuff, but for the sake of time, I'm wondering if it's necessary to go through Book I before I get into Book II, which is Stereometry. Or would I be able to just jump into stereometry?

I'm not trying to take any shortcuts, it's a matter of putting my time in what would be most beneficial. For my normal classes as well as my side-study maths, I'm putting in 35 hours a week of study time outside of class. I just want to make sure that it's going into the right areas.

Thanks for any help.

 

[symbolipoint]

The two possible sequences of course study you want should be either of these:

1. Intermediate Algebra
2. Geometry
3. Trigonometry

or

1. Geometry
2. Intermediate Algebra
3. Trigonometry

 

[jedishrfu]

Here's a bloggers view of Algebra vs Geometry that catches the right mood:

https://www.theodysseyonline.com/algebra-vs-geometry

In physics, geometry is everywhere. Its inherent in the equations you compose and solve. Often some algebraic solutions are discarded because they don't fit the geometry of the problem under study. Bottom line is you need to know both Algebra, Geometry and Trigonometry to appreciate Calculus and from there appreciate the beauty of Physics.

I was taught in the traditional sense:
algebra, geometry (Euclid's theorems), trigonometry, pre-calculus (sequences, series, complex numbers..., calculus...

 

[DS2C]

Ok thanks for the clarification guys.

 

[Buffu]

Currently I am face deep in three math books- my issued text for algebra, Schaum's Elementary Algebra, and Kiselev's Book I (Planimetry).

I love the stuff so far and want to be as knowledgeable as possible for when I can declare my major to Physics. One thing I know for sure is that algebra and trigonometry are absolutely essential not just for calculus but for physics in general. But can the same be said for geometry (I know that trigonometry entails geometry, but not sure to what level geometry is needed)?

Without going into too much detail, I know jack squat about geometry other than what I've read so far in Kiselev's book. I want to learn this stuff, but for the sake of time, I'm wondering if it's necessary to go through Book I before I get into Book II, which is Stereometry. Or would I be able to just jump into stereometry?

I'm not trying to take any shortcuts, it's a matter of putting my time in what would be most beneficial. For my normal classes as well as my side-study maths, I'm putting in 35 hours a week of study time outside of class. I just want to make sure that it's going into the right areas.

Thanks for any help.

There is no geometry without linear or abstract algebra.

 

[Mark44]

There is no geometry without linear or abstract algebra.

No, you are mistaken.
Geometry can be (and is) taught all by itself. I'm not sure what the U.S. high school curriculum is now, but geometry typically was taught in the 10th grade here. Neither linear algebra nor abstract algebra played the slightest part in the geometry course.

Linear algebra depends to some extent on geometry, but the geometric content in abstract algebra is either none at all or very minimal, as I recall from the year-long sequence I took in grad school.

 

[symbolipoint]

No, you are mistaken.
Geometry can be (and is) taught all by itself. I'm not sure what the U.S. high school curriculum is now, but geometry typically was taught in the 10th grade here. Neither linear algebra nor abstract algebra played the slightest part in the geometry course.

Linear algebra depends to some extent on geometry, but the geometric content in abstract algebra is either none at all or very minimal, as I recall from the year-long sequence I took in grad school.

You bet your ass!

 

[symbolipoint]

Please excuse last comment because it is understood as a way to express agreement. I believe but not sure that the cleaner sense of the word is supposed to be used.

 

[Mark44]

Please excuse last comment because it is understood as a way to express agreement. I believe but not sure that the cleaner sense of the word is supposed to be used.

Seems innocuous enough to me. If there are any complaints I'll edit it to something a bit more genteel.

 

[DS2C]

Please excuse last comment because it is understood as a way to express agreement. I believe but not sure that the cleaner sense of the word is supposed to be used.

Oh I hope you're not apologizing to me! After seven years in the Navy, no one has a fouler mouth than I!

 

[Mark44]

Back to your original question, I don't know about Kiselev's books at all. They are likely a lot more complex than ordinary geometry as taught in high school.

The contents of a typical high school geometry class (as I remember them) are more-or-less the following:

• Triangle geometry, including congruent triangles (same sizes of corresponding angles and sides), and similar triangles (same shape, but different sizes)
• Several theorems on when two triangles are congruent
  • SAS -- two sides and the included angle in one triangle are congruent to the corresponding sides/angle of another triangle
  • ASA -- two angles and the included side in one triangle are congruent to the corresponding angles/side of another triangle
  • SSS - all three sides of one triangle are congruent to the corresponding sides of another triangle
• Theorems about the angles made when a line cuts two parallel lines
• Theorem of Pythagoras
• Definitions of geometric shapes, such as rectangles, triangles, parallelograms, circles, spheres, rhombi (pl. of rhombus), trapezoids

There was probably more, but it's been > 50 years since I took geometry. A lot of the time was devoted to writing relatively simple proofs of statements about angles and triangles. In the proof you were supposed to justify each step you used.

I'm reasonably sure you could self-study all this and get up to speed for subsequent classes. Analytic geometry is a combination of algebra and geometry, so a basic level of geometry knowledge is assumed. There's probably a Schaum's Outline that covers geometry. I would recommend something like that over a more focussed book like the one you mentioned.

 

[DS2C]

Thank you for the extensive post Mark. I'm really not sure what to compare Kiselev to, as we didn't have a book for Geometry in high school and my teacher came to class high on oxycontin (seriously, he got fired a couple years after I left). It's an extremely interesting and well written book, with fairly difficult proof style questions at the end of each chapter. I also have Shaum's, as you've mentioned, and skimming through it I can see it's mostly analytical geometry (finding volumes, etc). Maybe I'll put Kiselev to the side and come back to it later and focus more on Schaum's to get the quick and dirty.

 

[Dr Transport]

Oh I hope you're not apologizing to me! After seven years in the Navy, no one has a fouler mouth than I!

Ex Army-DI... never offended by language.

As for the question at hand, geometry is taught in 9th or 10th grade in US high schools, you need some algebra but no linear algebra is required.

to answer the OP, get as much geometry/trigonometry as possible, I am having to relearn a bunch of it at my age because I am helping to re-write a major computer code at my employer and it uses immense amounts of the subject.

 

[DS2C]

Ex Army-DI... never offended by language.

As for the question at hand, geometry is taught in 9th or 10th grade in US high schools, you need some algebra but no linear algebra is required.

to answer the OP, get as much geometry/trigonometry as possible, I am having to relearn a bunch of it at my age because I am helping to re-write a major computer code at my employer and it uses immense amounts of the subject.

Sounds like the consensus is to press forward with the shapey things. Thanks for your response and your service!

 

[symbolipoint]

To be clearer on the point:
One needs just a little bit of simple basic algebra to learn Geometry as it is taught in high school. One does not need Intermediate Algebra in order to learn Geometry, although having it does not hurt.
Algebra (1 and 2) are very different from Geometry, but there is some overlap between Intermediate Algebra and Geometry . Algebra focuses on properties of numbers, inequalities, equations, and graphs. Geometry focuses on points, lines, planes, shapes, and angles.

 

[DS2C]

Ok great thank you. Right now I am in what is just under college algebra, so I think its kind of a combination of alegbra 1 and 2. So I think it will suffice considering algebra 2 came after geometry when I was in high school.

 

[symbolipoint]

Ok great thank you. Right now I am in what is just under college algebra, so I think its kind of a combination of alegbra 1 and 2. So I think it will suffice considering algebra 2 came after geometry when I was in high school.

"Just under college algebra"; I am just curious: what is the exact name of your course you're in now? What is the standard name or title of the course?

"Just under college algebra" might be a few possible things.
Algebra 2? Intermediate Algebra? Trigonometry (the one-semester course)? I cannot think of other possibilities.

 

[DS2C]

"Just under college algebra"; I am just curious: what is the exact name of your course you're in now? What is the standard name or title of the course?

"Just under college algebra" might be a few possible things.
Algebra 2? Intermediate Algebra? Trigonometry (the one-semester course)? I cannot think of other possibilities.

Hmm not really sure on the technical name. It's always just been referred to by it's course code. But it's referred to sometimes as "college algebra prep". It involves multiplying/dividing polynomials, factorization, radical expressions, logarithms, linear equations, rational equations, quadratic formula, etc. I know in this particular class we won't go over complex or imaginary numbers, so the level just before that.
The typical layout goes : this class > college algebra > trigonometry > calculus...
However I'll be taking college algebra and trigonometry at the same time as college algebra isn't a pre requisite for trigonometry and they're both out of the same book.

 

[symbolipoint]

The description you give seems much like your course is much like Intermediate Algebra, but the name is not very common.
Pre-Algeba is a course to help students into Algebra 1, and it is often a survey course of elementary algebra and some basic mathe/arithmetic.
Pre-Calculus is something to prepare students for Calculus 1; and is like an advanced form of Algebra beyond Intermediate, and often includes an introduction and study of limits but not to the level of Calculus. Pre-Calculus may often be called "College Algebra And Trigonometry".

I am not interested in the "course code" title. What is the actual NAME of the course?
Your description tends to suggest that your course is or is nearly Intermediate Algebra. What is the book's name?

 

[Buffu]

No, you are mistaken.
Geometry can be (and is) taught all by itself. I'm not sure what the U.S. high school curriculum is now, but geometry typically was taught in the 10th grade here. Neither linear algebra nor abstract algebra played the slightest part in the geometry course.

Linear algebra depends to some extent on geometry, but the geometric content in abstract algebra is either none at all or very minimal, as I recall from the year-long sequence I took in grad school.

Affine and Projective Geometry do require linear algebra and even basic Algebraic geometry requires abstract algebra.
Theorems of analytical geometry like two conics having infinite zero set are equal requires basic linear algebra.

I don't say that geometry without LA or AA is not worth learning just that it won't take you far enough, anyhow you need to learn linear/abstract algebra someday either for physics or maths. So,why not learn linear algebra first and then geometry that is based on it ?

 

[Mark44]

Affine and Projective Geometry do require linear algebra and even basic Algebraic geometry requires abstract algebra.
Theorems of analytical geometry like two conics having infinite zero set are equal requires basic linear algebra.

The OP wasn't asking about affine or projective geometry -- just plain old plane geometry as preparation for intermediate algebra and trigonometry.

I don't say that geometry without LA or AA is not worth learning just that it won't take you far enough, anyhow you need to learn linear/abstract algebra somebody either for physics or maths. So,why not learn linear algebra first and then geometry that is based on it ?

The OP is quite a few classes away from being able to take linear algebra. When you post, take more care in responding to what the poster is actually asking.

 

[Buffu]

The OP wasn't asking about affine or projective geometry -- just plain old plane geometry as preparation for intermediate algebra and trigonometry.

The OP is quite a few classes away from being able to take linear algebra. When you post, take more care in responding to what the poster is actually asking.

So what else is intermediate algebra ?

 

[Mark44]

So what else is intermediate algebra ?

I don't understand what you're asking.

 

[symbolipoint]

So what else is intermediate algebra ?

I don't understand what you're asking.

This is the level of advancement between Introductory Algebra and of College Algebra; the high school algebra course which comes next after Algebra 1.

Do you want a listing of the topic contents?